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Page 1: Confectionery and chocolate engineering: principles and applications
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Confectioneryand ChocolateEngineering

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Confectioneryand ChocolateEngineeringPrinciples and Applications

Ferenc Á. MohosUniversity of Szeged and

Corvinus University of Budapest, Hungary

SECOND EDITION

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This edition first published 2017 © 2017 by John Wiley & Sons Ltd

Registered office: John Wiley & Sons, Ltd, The Atrium, Southern Gate, Chichester, West Sussex,PO19 8SQ, UK

Editorial offices: 9600 Garsington Road, Oxford, OX4 2DQ, UKThe Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, UK111 River Street, Hoboken, NJ 07030-5774, USA

For details of our global editorial offices, for customer services and for information about how to apply forpermission to reuse the copyright material in this book please see our website atwww.wiley.com/wiley-blackwell.

The right of the author to be identified as the author of this work has been asserted in accordance with theUK Copyright, Designs and Patents Act 1988.

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, ortransmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise,except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of thepublisher.

Designations used by companies to distinguish their products are often claimed as trademarks. All brandnames and product names used in this book are trade names, service marks, trademarks or registeredtrademarks of their respective owners. The publisher is not associated with any product or vendormentioned in this book.

Limit of Liability/Disclaimer of Warranty: While the publisher and author(s) have used their best efforts inpreparing this book, they make no representations or warranties with respect to the accuracy orcompleteness of the contents of this book and specifically disclaim any implied warranties ofmerchantability or fitness for a particular purpose. It is sold on the understanding that the publisher is notengaged in rendering professional services and neither the publisher nor the author shall be liable fordamages arising herefrom. If professional advice or other expert assistance is required, the services of acompetent professional should be sought.

Library of Congress Cataloging-in-Publication Data

Names: Mohos, Ferenc Á., author.Title: Confectionery and chocolate engineering: principles and applications

/ Ferenc Á. Mohos.Description: Chichester, West Sussex, United Kingdom ; Hoboken, New Jersey :

John Wiley & Sons Inc., 2017. | Includes bibliographical references andindex.

Identifiers: LCCN 2016035917 | ISBN 9781118939772 (cloth) | ISBN 9781118939765(Adobe PDF) | ISBN 9781118939758 (ePub)

Subjects: LCSH: Confectionery. | Chocolate. | Chemistry, Technical. |Food–Analysis.

Classification: LCC TX783 .M58 2017 | DDC 641.86–dc 3 LC record available athttps://lccn.loc.gov/2016035917

A catalogue record for this book is available from the British Library.

Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may notbe available in electronic books.

Cover image: SerAlexVi/Gettyimages

Set in 9.5/13pt, MeridienLTStd by SPi Global, Chennai, India.

10 9 8 7 6 5 4 3 2 1

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To the memory of my parents

Ferenc Mohos and Viktória Tevesz

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Contents

Preface, xxiii

Preface to the second edition, xxvii

Acknowledgements, xxix

Part I: Theoretical introduction

1 Principles of food engineering, 3

1.1 Introduction, 3

1.1.1 The Peculiarities of food engineering, 3

1.1.2 The hierarchical and semi-hierarchical structure of

materials, 4

1.2 The Damköhler equations, 6

1.2.1 The application of the Damköhler equations in food

engineering: conservative substantial fragments, 6

1.2.2 The Damköhler equations in chemical engineering, 7

1.3 Investigation of the Damköhler equations by means of

similarity theory, 8

1.3.1 Dimensionless numbers, 8

1.3.2 Degrees of freedom of an operational unit, 11

1.3.3 Polynomials as solutions of the Damköhler equations, 13

1.4 Analogies, 14

1.4.1 The Reynolds analogy, 14

1.4.2 The Colburn analogy, 15

1.4.3 Similarity and analogy, 16

1.5 Dimensional analysis, 16

1.6 System theoretical approaches to food engineering, 19

1.7 Food safety and quality assurance, 21

Further reading, 22

2 Characterization of substances used in the confectionery industry, 23

2.1 Qualitative characterization of substances, 23

2.1.1 Principle of characterization, 23

2.1.2 Structural formulae of confectionery products, 24

2.1.3 Classification of confectionery products according to

their characteristic phase conditions, 30

2.1.4 Phase inversion: a bridge between sugar sweets and

chocolate, 31

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viii Contents

2.2 Quantitative characterization of confectionery products, 33

2.2.1 Composition of chocolates and compounds, 33

2.2.2 Composition of sugar confectionery, 39

2.2.3 Composition of biscuits, crackers and wafers, 47

2.3 Preparation of recipes, 49

2.3.1 Recipes and net/gross material consumption, 49

2.3.2 Planning of material consumption, 53

2.4 Composition of chocolate, confectioneries, biscuits and wafers

made for special nutritional purposes, 56

2.4.1 Diabetes Type I and II, 56

2.4.2 Coeliac disease, 58

2.4.3 Lactose intolerance, 58

2.4.4 Particular technological matters of manufacturing

sweets for specific nutritional purposes, 58

Further reading, 60

3 Engineering properties of foods, 61

3.1 Introduction, 61

3.2 Density, 61

3.2.1 Solids and powdered solids, 62

3.2.2 Particle density, 62

3.2.3 Bulk density and porosity, 63

3.2.4 Loose bulk density, 63

3.2.5 Dispersions of various kinds and solutions, 64

3.3 Fundamental functions of thermodynamics, 65

3.3.1 Internal energy, 65

3.3.2 Enthalpy, 66

3.3.3 Specific heat capacity calculations, 67

3.4 Latent heat and heat of reaction, 71

3.4.1 Latent heat and free enthalpy, 71

3.4.2 Phase transitions, 73

3.5 Thermal conductivity, 76

3.5.1 First Fourier equation, 76

3.5.2 Heterogeneous materials, 76

3.5.3 Liquid foods, 77

3.5.4 Liquids containing suspended particles, 77

3.5.5 Gases, 78

3.6 Thermal diffusivity and Prandtl number, 78

3.6.1 Second Fourier equation, 78

3.6.2 Liquids and gases, 79

3.6.3 Prandtl number, 79

3.7 Mass diffusivity and Schmidt number, 81

3.7.1 Law of mass diffusion (Fick’s first law), 81

3.7.2 Mutual mass diffusion, 81

3.7.3 Mass diffusion in liquids, 82

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Contents ix

3.7.4 Temperature dependence of diffusion, 82

3.7.5 Mass diffusion in complex solid foodstuffs, 84

3.7.6 Schmidt number, 84

3.8 Dielectric properties, 85

3.8.1 Radio-frequency and microwave heating, 85

3.8.2 Power absorption: the Lambert–Beer law, 87

3.8.3 Microwave and radio-frequency generators, 88

3.8.4 Analytical applications, 90

3.9 Electrical conductivity, 91

3.9.1 Ohm’s law, 91

3.9.2 Electrical conductivity of metals and electrolytes: the

Wiedemann–Franz law and faraday’s law, 92

3.9.3 Electrical conductivity of materials used in confectionery, 93

3.9.4 Ohmic heating technology, 93

3.10 Infrared absorption properties, 95

3.11 Physical characteristics of food powders, 96

3.11.1 Classification of food powders, 96

3.11.2 Surface activity, 97

3.11.3 Effect of moisture content and anticaking agents, 98

3.11.4 Mechanical strength, dust formation and explosibility

index, 98

3.11.5 Compressibility, 100

3.11.6 Angle of repose, 101

3.11.7 Flowability, 102

3.11.8 Caking, 103

3.11.9 Effect of anticaking agents, 106

3.11.10 Segregation, 107

Further reading, 107

4 The rheology of foods and sweets, 109

4.1 Rheology: its importance in the confectionery industry, 109

4.2 Stress and strain, 109

4.2.1 Stress tensor, 109

4.2.2 Cauchy strain, Hencky strain and deformation tensor, 111

4.2.3 Dilatational and deviatoric tensors: tensor invariants, 113

4.2.4 Constitutive equations, 115

4.3 Solid behaviour, 115

4.3.1 Rigid body, 115

4.3.2 Elastic body (or Hookean body/model), 116

4.3.3 Linear elastic and non-linear elastic materials, 118

4.3.4 Texture of chocolate, 119

4.4 Fluid behaviour, 120

4.4.1 Ideal fluids and Pascal bodies, 120

4.4.2 Fluid behaviour in steady shear flow, 120

4.4.3 Extensional flow, 138

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4.4.4 Viscoelastic function and the idea of fading memory of

viscoelastic fluids, 145

4.4.5 Oscillatory testing, 155

4.4.6 Electrorheology, 158

4.4.7 Microrheology, 158

4.5 Viscosity of solutions, 159

4.6 Viscosity of emulsions, 161

4.6.1 Viscosity of dilute emulsions, 161

4.6.2 Viscosity of concentrated emulsions, 162

4.6.3 Rheological properties of flocculated emulsions, 163

4.7 Viscosity of suspensions, 164

4.8 Rheological properties of gels, 166

4.8.1 Fractal structure of gels, 166

4.8.2 Scaling behaviour of the elastic properties of colloidal

gels, 167

4.8.3 Classification of gels with respect to the nature of the

structural elements, 169

4.9 Rheological properties of sweets, 171

4.9.1 Chocolate mass, 171

4.9.2 Truffle mass, 179

4.9.3 Praline mass, 179

4.9.4 Fondant mass, 179

4.9.5 Dessert masses, 180

4.9.6 Nut brittle (Croquante) masses, 181

4.9.7 Whipped masses, 181

4.9.8 Caramel, 182

4.10 Rheological properties of wheat flour doughs, 183

4.10.1 Complex rheological models for describing food systems, 183

4.10.2 Special testing methods for the rheological study of

doughs, 188

4.10.3 Studies of the consistency of dough, 190

4.11 Relationship between food oral processing and rheology, 193

4.11.1 Swallowing, 194

Further reading, 194

5 Introduction to food colloids, 197

5.1 The colloidal state, 197

5.1.1 Colloids in the confectionery industry, 197

5.1.2 The colloidal region, 197

5.1.3 The various types of colloidal systems, 199

5.2 Formation of colloids, 199

5.2.1 Microphases, 199

5.2.2 Macromolecules, 200

5.2.3 Micelles, 200

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5.2.4 Disperse (or non-cohesive) and cohesive systems, 200

5.2.5 Energy conditions for colloid formation, 202

5.3 Properties of macromolecular colloids, 202

5.3.1 Structural types, 202

5.3.2 Interactions between dissolved macromolecules, 204

5.3.3 Structural changes in solid polymers, 204

5.4 Properties of colloids of association, 208

5.4.1 Types of colloids of association, 208

5.4.2 Parameters influencing the structure of micelles and

the value of CM, 210

5.5 Properties of interfaces, 210

5.5.1 Boundary layer and surface energy, 210

5.5.2 Formation of boundary layer: adsorption, 211

5.5.3 Dependence of interfacial energy on surface

morphology, 212

5.5.4 Phenomena when phases are in contact, 213

5.5.5 Adsorption on the free surface of a liquid, 216

5.6 Electrical properties of interfaces, 219

5.6.1 The electric double layer and electrokinetic phenomena, 219

5.6.2 Structure of the electric double layer, 220

5.7 Theory of colloidal stability: the DLVO theory, 221

5.8 Stability and changes of colloids and coarse dispersions, 224

5.8.1 Stability of emulsions, 224

5.8.2 Two-phase emulsions, 226

5.8.3 Three-phase emulsions, 226

5.8.4 Two liquid phases plus a solid phase, 226

5.8.5 Emulsifying properties of food proteins, 228

5.8.6 Emulsion droplet size data and the kinetics of

emulsification, 228

5.8.7 Bancroft’s rule for the type of emulsion, 230

5.8.8 HLB value and stabilization of emulsions, 231

5.8.9 Emulsifiers used in the confectionery industry, 232

5.9 Emulsion instability, 233

5.9.1 Mechanisms of destabilization, 233

5.9.2 Flocculation, 234

5.9.3 Sedimentation (creaming), 236

5.9.4 Coalescence, 241

5.9.5 Ostwald ripening in emulsions, 242

5.10 Phase inversion, 243

5.11 Foams, 245

5.11.1 Transient and metastable (permanent) foams, 245

5.11.2 Expansion ratio and dispersity, 246

5.11.3 Disproportionation, 248

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5.11.4 Foam stability: coefficient of stability and lifetime

histogram, 251

5.11.5 Stability of polyhedral foams, 252

5.11.6 Thinning of foam films and foam drainage, 253

5.11.7 Methods of improving foam stability, 254

5.11.8 Oil foam stability, 256

5.12 Gelation as a second-order phase transition, 256

5.12.1 Critical phenomena and phase transitions, 256

5.12.2 Relaxation modulus, 257

5.12.3 Gelation theories, 258

5.12.4 The critical gel equation, 259

5.12.5 Gelation of food hydrocolloids, 259

Further reading, 261

Part II: Physical operations

6 Comminution, 265

6.1 Changes during size reduction, 265

6.1.1 Comminution of non-cellular and cellular substances, 265

6.1.2 Grinding and crushing, 265

6.1.3 Dry and wet grinding, 266

6.2 Rittinger’s surface theory, 266

6.3 Kick’s volume theory, 267

6.4 The third or Bond theory, 268

6.5 Energy requirement for comminution, 268

6.5.1 Work index, 268

6.5.2 Differential equation for the energy requirement for

comminution, 269

6.6 Particle size distribution of ground products, 269

6.6.1 Particle size, 269

6.6.2 Screening, 270

6.6.3 Sedimentation analysis, 273

6.6.4 Electrical sensing zone method of particle size

distribution determination (Coulter method), 273

6.7 Particle size distributions, 273

6.7.1 Rosin–Rammler (RR) distribution, 273

6.7.2 Normal distribution (Gaussian distribution, N

distribution), 274

6.7.3 Log-Normal (LN) distribution (Kolmogorov

distribution), 274

6.7.4 Gates–Gaudin–Schumann (GGS) distribution, 274

6.8 Kinetics of grinding, 275

6.9 Comminution by five-roll refiners, 276

6.9.1 Effect of a five-roll refiner on particles, 276

6.9.2 Volume and mass flow in a five-roll refiner, 278

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6.10 Grinding by a melangeur, 280

6.11 Comminution by a stirred ball mill, 284

6.11.1 Kinetics of comminution in a stirred ball mill, 284

6.11.2 Power requirement of a stirred ball mill, 285

6.11.3 Residence time distribution in a stirred ball mill, 286

Further reading, 289

7 Mixing/kneading, 290

7.1 Technical solutions to the problem of mixing, 290

7.2 Power characteristics of a stirrer, 290

7.3 Mixing time characteristics of a stirrer, 292

7.4 Representative shear rate and viscosity for mixing, 292

7.5 Calculation of the Reynolds number for mixing, 292

7.6 Mixing of powders, 294

7.6.1 Degree of heterogeneity of a mixture, 294

7.6.2 Scaling up of agitated centrifugal mixers, 297

7.6.3 Mixing time for powders, 298

7.6.4 Power consumption, 299

7.7 Mixing of fluids of high viscosity, 300

7.8 Effect of impeller speed on heat and mass transfer, 301

7.8.1 Heat transfer, 301

7.8.2 Mass transfer, 301

7.9 Mixing by blade mixers, 302

7.10 Mixing rolls, 303

7.11 Mixing of two liquids, 304

Further reading, 304

8 Solutions, 306

8.1 Preparation of aqueous solutions of carbohydrates, 306

8.1.1 Mass balance, 306

8.1.2 Parameters characterizing carbohydrate solutions, 307

8.2 Solubility of sucrose in water, 308

8.2.1 Solubility number of sucrose, 309

8.3 Aqueous solutions of sucrose and glucose syrup, 309

8.3.1 Syrup ratio, 310

8.4 Aqueous sucrose solutions containing invert sugar, 311

8.5 Solubility of sucrose in the presence of starch syrup and invert

sugar, 312

8.6 Rate of dissolution, 312

8.7 Solubility of bulk sweeteners, 315

Further reading, 316

9 Evaporation, 317

9.1 Theoretical background: Raoult’s law, 317

9.2 Boiling point of sucrose/water solutions at atmospheric

pressure, 318

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9.3 Application of a modification of Raoult’s law to calculate the

boiling point of carbohydrate/water solutions at decreased

pressure, 319

9.3.1 Sucrose/water solutions, 319

9.3.2 Dextrose/water solutions, 319

9.3.3 Starch syrup/water solutions, 319

9.3.4 Invert sugar solutions, 319

9.3.5 Approximate formulae for the elevation of the boiling

point of aqueous sugar solutions, 320

9.4 Vapour pressure formulae for carbohydrate/water solutions, 323

9.4.1 Vapour pressure formulae, 323

9.4.2 Antoine’s rule, 325

9.4.3 Trouton’s rule, 326

9.4.4 Ramsay–Young rule, 328

9.4.5 Dühring’s rule, 329

9.5 Practical tests for controlling the boiling points of sucrose

solutions, 330

9.6 Modelling of an industrial working process for hard boiled

sweets, 331

9.6.1 Modelling of evaporation stage, 332

9.6.2 Modelling of drying stage, 334

9.7 Boiling points of bulk sweeteners, 335

Further reading, 335

10 Crystallization, 337

10.1 Introduction, 337

10.2 Crystallization from solution, 337

10.2.1 Nucleation, 337

10.2.2 Supersaturation, 338

10.2.3 Thermodynamic driving force for crystallization, 339

10.2.4 Metastable state of a supersaturated solution, 340

10.2.5 Nucleation kinetics, 341

10.2.6 Thermal history of the solution, 343

10.2.7 Secondary nucleation, 344

10.2.8 Crystal growth, 346

10.2.9 Theories of crystal growth, 349

10.2.10 Effect of temperature on growth rate, 350

10.2.11 Dependence of growth rate on the hydrodynamic

conditions, 351

10.2.12 Modelling of fondant manufacture based on the

diffusion theory, 352

10.3 Crystallization from melts, 355

10.3.1 Polymer crystallization, 355

10.3.2 Spherulite nucleation, spherulite growth and crystal

thickening, 357

10.3.3 Melting of polymers, 360

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10.3.4 Isothermal crystallization, 360

10.3.5 Non-isothermal crystallization, 370

10.3.6 Secondary crystallization, 371

10.4 Crystal size distributions, 371

10.4.1 Normal distribution, 371

10.4.2 Log-normal distribution, 372

10.4.3 Gamma distribution, 372

10.4.4 Histograms and population balance, 372

10.5 Batch crystallization, 374

10.6 Isothermal and non-isothermal recrystallization, 375

10.6.1 Ostwald ripening, 375

10.6.2 Recrystallization under the effect of temperature or

concentration fluctuations, 376

10.6.3 Ageing, 376

10.7 Methods for studying the supermolecular structure of

fat melts, 376

10.7.1 Cooling/solidification curve, 376

10.7.2 Solid fat content, 378

10.7.3 Dilatation: Solid fat index, 378

10.7.4 Differential scanning calorimetry, differential thermal

analysis and low-resolution NMR methods, 379

10.8 Crystallization of glycerol esters: Polymorphism, 381

10.9 Crystallization of cocoa butter, 385

10.9.1 Polymorphism of cocoa butter, 385

10.9.2 Tempering of cocoa butter and chocolate mass, 387

10.9.3 Shaping (moulding) and cooling of cocoa butter and

chocolate, 391

10.9.4 Sugar blooming and dew point temperature, 393

10.9.5 Crystallization during storage of chocolate products, 394

10.9.6 Bloom inhibition, 396

10.9.7 Tempering of cocoa powder, 398

10.10 Crystallization of fat masses, 398

10.10.1 Fat masses and their applications, 398

10.10.2 Cocoa butter equivalents and improvers, 399

10.10.3 Fats for compounds and coatings, 401

10.10.4 Cocoa butter replacers, 403

10.10.5 Cocoa butter substitutes, 406

10.10.6 Filling fats, 407

10.10.7 Fats for ice cream coatings and ice

dippings/toppings, 410

10.11 Crystallization of confectionery fats with a high trans-fat

portion, 411

10.11.1 Coating fats and coatings, 411

10.11.2 Filling fats and fillings, 411

10.11.3 Future trends in the manufacture of trans-free special

confectionery fats, 412

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10.12 Modelling of chocolate cooling processes and tempering, 414

10.12.1 Franke model for the cooling of chocolate coatings, 414

10.12.2 Modelling the temperature distribution in cooling

chocolate moulds, 416

10.12.3 Modelling of chocolate tempering process, 419

10.13 EU programme ProPraline, 421

Further reading, 422

11 Gelling, emulsifying, stabilizing and foam formation, 424

11.1 Hydrocolloids used in confectionery, 424

11.2 Agar, 424

11.2.1 Isolation of agar, 424

11.2.2 Types of agar, 425

11.2.3 Solution properties, 425

11.2.4 Gel properties, 426

11.2.5 Setting point of sol and melting point of gel, 427

11.2.6 Syneresis of an agar gel, 427

11.2.7 Technology of manufacturing agar gels, 428

11.3 Alginates, 429

11.3.1 Isolation and structure of alginates, 429

11.3.2 Mechanism of gelation, 430

11.3.3 Preparation of a gel, 430

11.3.4 Fields of application, 431

11.4 Carrageenans, 432

11.4.1 Isolation and structure of carrageenans, 432

11.4.2 Solution properties, 432

11.4.3 Depolymerization of carrageenan, 434

11.4.4 Gel formation and hysteresis, 434

11.4.5 Setting temperature and syneresis, 435

11.4.6 Specific interactions, 435

11.4.7 Utilization, 436

11.5 Furcellaran, 437

11.6 Gum arabic, 437

11.7 Gum tragacanth, 438

11.8 Guaran gum, 439

11.9 Locust bean gum, 439

11.10 Pectin, 440

11.10.1 Isolation and composition of pectin, 440

11.10.2 High-Methoxyl (HM) pectins, 440

11.10.3 Low-Methoxyl (LM) pectins, 441

11.10.4 Low-Methoxyl (LM) amidated pectins, 441

11.10.5 Gelling mechanisms, 442

11.10.6 Technology of manufacturing pectin jellies, 442

11.11 Starch, 444

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11.11.1 Occurrence and composition of starch, 444

11.11.2 Modified starches, 445

11.11.3 Utilization in the confectionery industry, 446

11.12 Xanthan gum, 447

11.13 Gelatin, 448

11.13.1 Occurrence and composition of gelatin, 448

11.13.2 Solubility, 449

11.13.3 Gel formation, 449

11.13.4 Viscosity, 450

11.13.5 Amphoteric properties, 450

11.13.6 Surface-active/protective-colloid properties and

utilization, 451

11.13.7 Methods of dissolution, 452

11.13.8 Stability of gelatin solutions, 453

11.13.9 Confectionery applications, 453

11.14 Egg proteins, 453

11.14.1 Fields of application, 453

11.14.2 Structure, 455

11.14.3 Egg-white gels, 455

11.14.4 Egg-white foams, 456

11.14.5 Egg-yolk gels, 457

11.14.6 Whole-egg gels, 458

11.15 Foam formation, 458

11.15.1 Fields of application, 458

11.15.2 Velocity of bubble rise, 459

11.15.3 Whipping, 462

11.15.4 Continuous industrial aeration, 463

11.15.5 Industrial foaming methods, 465

11.15.6 In Situ generation of foam, 465

Further reading, 466

12 Transport, 468

12.1 Types of transport, 468

12.2 Calculation of flow rate of non-newtonian fluids, 468

12.3 Transporting dessert masses in long pipes, 470

12.4 Changes in pipe direction, 471

12.5 Laminar unsteady flow, 472

12.6 Transport of flour and sugar by airflow, 472

12.6.1 Physical parameters of air, 472

12.6.2 Airflow in a tube, 472

12.6.3 Flow properties of transported powders, 473

12.6.4 Power requirement of airflow, 475

12.6.5 Measurement of a pneumatic system, 475

Further reading, 477

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13 Pressing, 478

13.1 Applications of pressing in the confectionery industry, 478

13.2 Theory of pressing, 478

13.3 Cocoa liquor pressing, 480

Further reading, 482

14 Extrusion, 483

14.1 Flow through a converging die, 483

14.1.1 Theoretical principles of the dimensioning of extruders, 483

14.1.2 Pressure loss in the shaping of pastes, 486

14.1.3 Design of converging die, 488

14.2 Feeders used for shaping confectionery pastes, 491

14.2.1 Screw feeders, 491

14.2.2 Cogwheel feeders, 492

14.2.3 Screw mixers and extruders, 493

14.3 Extrusion cooking, 495

14.4 Roller extrusion, 497

14.4.1 Roller extrusion of biscuit doughs, 497

14.4.2 Feeding by roller extrusion, 499

Further reading, 500

15 Particle agglomeration: instantization and tabletting, 501

15.1 Theoretical background, 501

15.1.1 Processes resulting from particle agglomeration, 501

15.1.2 Solidity of a granule, 503

15.1.3 Capillary attractive forces in the case of liquid bridges, 504

15.1.4 Capillary attractive forces in the case of no liquid bridges, 504

15.1.5 Solidity of a granule in the case of dry granulation, 506

15.1.6 Water sorption properties of particles, 506

15.1.7 Effect of electrostatic forces on the solidity of a granule, 508

15.1.8 Effect of crystal bridges on the solidity of a granule, 510

15.1.9 Comparison of the various attractive forces affecting

granulation, 510

15.1.10 Effect of surface roughness on the attractive forces, 511

15.2 Processes of agglomeration, 512

15.2.1 Agglomeration in the confectionery industry, 512

15.2.2 Agglomeration from liquid phase, 513

15.2.3 Agglomeration of powders: tabletting or dry granulation, 513

15.3 Granulation by fluidization, 514

15.3.1 Instantization by granulation: wetting of particles, 514

15.3.2 Processes of fluidization, 515

15.4 Tabletting, 516

15.4.1 Tablets as sweets, 516

15.4.2 Types of tabletting, 517

15.4.3 Compression, consolidation and compaction, 518

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15.4.4 Characteristics of the compaction process, 520

15.4.5 Quality properties of tablets, 524

Further reading, 524

Part III: Chemical and complex operations: stability ofsweets: artisan chocolate and confectioneries

16 Chemical operations (inversion and caramelization), ripening and

complex operations, 527

16.1 Inversion and caramelization, 527

16.1.1 Inversion, 527

16.1.2 Caramelization, 534

16.2 Acrylamide formation, 538

16.2.1 Acrylamide and carcinogenicity, 538

16.2.2 Investigations on acrylamide formation, 539

16.2.3 Strategies to reduce acrylamide levels in food, 540

16.3 Alkalization of cocoa material, 540

16.3.1 Purposes and methods of alkalization, 540

16.3.2 German process, 541

16.4 Ripening, 542

16.4.1 Ripening processes of diffusion, 542

16.4.2 Chemical and enzymatic reactions during ripening, 545

16.5 Complex operations, 545

16.5.1 Complexity of the operations used in the confectionery

industry, 545

16.5.2 Conching, 545

16.5.3 New trends in the manufacture of chocolate, 556

16.5.4 Modelling the structure of dough, 559

16.6 Drying/frying, baking and roasting, 562

16.6.1 Drying/frying, 563

16.6.2 Baking, 566

16.6.3 Roasting, 570

Further reading, 577

17 Water activity, shelf life and storage, 579

17.1 Water activity, 579

17.1.1 Definition of water activity, 579

17.1.2 Adsorption/desorption of water, 580

17.1.3 Measurement of water activity, 581

17.1.4 Factors lowering water activity, 586

17.1.5 Sorption isotherms, 588

17.1.6 Hygroscopicity of confectionery products, 589

17.1.7 Calculation of equilibrium relative humidity of

confectionery products, 592

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xx Contents

17.2 Shelf life and storage, 594

17.2.1 Definition of shelf life, 594

17.2.2 Role of light and atmospheric oxygen, 595

17.2.3 Role of temperature, 595

17.2.4 Role of water activity, 595

17.2.5 Role of enzymatic activity, 595

17.2.6 Concept of mould-free shelf life, 596

17.3 Storage scheduling, 601

Further reading, 602

18 Stability of food systems, 604

18.1 Common use of the concept of food stability, 604

18.2 Stability theories: types of stability, 604

18.2.1 Orbital stability and Lyapunov stability, 604

18.2.2 Asymptotic and marginal (or Lyapunov) stability, 605

18.2.3 Local and global stability, 606

18.3 Shelf life as a case of marginal stability, 606

18.4 Stability matrix of a food system, 607

18.4.1 Linear models, 607

18.4.2 Nonlinear models, 607

Further reading, 608

19 Artisan chocolate and confectioneries, 609

19.1 Actuality of artisanship in the confectionery practice, 609

19.2 The characteristics of the artisan products, 609

19.3 Raw materials and machinery, 610

19.4 The characteristics of the artisan confectionery technologies, 611

19.5 Managing an artisan workshop, 611

19.6 An easy and effective shaping technology for producing praline

bars, 612

Further reading, 614

Part IV: Appendices

1 Data on engineering properties of materials used and made by the

confectionery industry, 617

A1.1 Carbohydrates, 617

A1.2 Oils and fats, 626

A1.3 Raw materials, semi-finished products and finished products, 626

2 Comparison of Brix and Baumé concentrations of aqueous sucrose

solutions at 20 ∘C (68 ∘F), 643

3 Survey of fluid models: some trends in rheology, 645

A3.1 Decomposition method for calculation of flow rate of

rheological models, 645

A3.1.1 The principle of the decomposition method, 645

A3.1.2 Bingham model, 646

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A3.1.3 Casson models, 647

A3.1.4 Herschel–Bulkley–Porst–Markowitsch–Houwink

(HBPMH) (or generalized Ostwald–de Waele) model, 651

A3.1.5 Ostwald–de Waele model (The power law), 653

A3.2 Calculation of the friction coefficient (𝝃) of non-newtonian

fluids in the laminar region, 653

A3.3 Tensorial representation of constitutive equations: The fading

memory of viscoelastic fluids, 654

A3.3.1 Objective derivatives and tensorial representation of

constitutive equations, 654

A3.3.2 Boltzmann’s equation for the stress in viscoelastic

solids: The fading memory of viscoelastic fluids, 656

A3.3.3 Constitutive equations of viscoelastic fluids, 657

A3.3.4 Application of the constitutive equations to dough

rheology, 658

A3.3.5 Rheological properties at the cellular and macroscopic

scale, 659

A3.4 Computer simulations in food rheology and science, 660

A3.5 Ultrasonic and photoacoustic testing, 660

A3.5.1 Ultrasonic testing, 660

A3.5.2 Photoacoustic testing, 661

Further reading, 661

4 Fractals, 663

A4.1 Irregular forms: fractal geometry, 663

A4.2 Box-counting dimension, 664

A4.3 Particle-counting method, 665

A4.4 Fractal backbone dimension, 666

Further reading, 666

5 Introduction to structure theory, 668

A5.1 The principles of the structure theory of blickle and seitz, 668

A5.1.1 Attributes and their relations: structure, 668

A5.1.2 Structure of attributes: a qualitative description, 669

A5.1.3 Hierarchic structures, 670

A5.1.4 Structure of measure: a quantitative description, 670

A5.1.5 Conservative elements: conservative substantial

fragments, 670

A5.1.6 New way of looking, 672

A5.2 Modelling a part of fudge processing plant by structure theory, 673

Further reading, 674

6 Technological layouts, 675

Further reading, 686

References, 687

Index, 737

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Preface

The purpose of this book is to describe the features of the unit operations in con-

fectionery manufacturing. The approach adopted here might be considered as a

novelty in the confectionery literature. The choice of the subject might perhaps

seem surprising, owing to the fact that the word confectionery is usually associated

with handicraft instead of engineering. It must be acknowledged that the attrac-

tiveness of confectionery can be partly attributed to the coexistence of handicraft

and engineering in this field. Nevertheless, large-scale industry has also had a

dominant presence in this field for about a century.

The traditional confectionery literature focuses on technology. The present

work is based on a different approach, where, by building on the scientific back-

ground of chemical engineering, it is intended to offer a theoretical approach

to practical aspects of the confectionery and chocolate industry. However, one

of the main aims is to demonstrate that the structural description of materials

used in chemical engineering must be complemented by taking account of the

hierarchical structure of the cellular materials that are the typical objects of food

engineering. By characterizing the unit operations of confectionery manufacture,

without daring to overestimate the eventual future exploitation of the possibil-

ities offered by this book, I intend to inspire the development of new solutions

in both technology and machinery, including the intensification of operations,

the application of new materials and new and modern applications of traditional

raw materials.

I have studied unit operations in the confectionery industry since the 1960s.

During my university years, I began dealing with the rheological properties of

molten chocolate (the Casson equation, rheopexy, etc.). This was an attractive

and fruitful experience for me. Later on, I worked for the Research Laboratory

of the Confectionery Industry for 3 years. Altogether I spent – on and off – half

a century in this field, working on product development, production, quality

control/assurance, purchasing and trading. These tasks, related mainly to sugar

confectionery and chocolate, convinced me that a uniform attitude is essential

for understanding the wide-ranging topics of confectionery and chocolate manu-

facture. As a young chemical engineer, I also started lecturing undergraduate and

graduate students. Having gathered experience in education (compiling lectures,

etc.), I found that this conviction was further confirmed.

In the late 1960s, my attention was firmly focused on the unit operations in

this industry, and I tried to utilize and build on the results produced by the Hun-

garian school of chemical engineering (M. Korach (Maurizio Cora), P. Benedek,

A. László and T. Blickle). Benedek and László discussed the topics of chemical

engineering, placing the Damköhler equations in the centre of the theory, simi-

larly to the way in which electricity is based on the Maxwell equations. Blickle

xxiii

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xxiv Preface

and the mathematician Seitz developed structure theory and applied it to chem-

ical engineering. Structure theory exploits the tools of abstract algebra to analyse

the structures of system properties, materials, machinery, technological changes,

etc. It is a useful method for defining concepts and studying their relations. The

outcome of these studies is well reflected in several books and university lectures

published by me and serves as the theoretical background for the present book

as well.

Chapter 1 introduces the Damköhler equations as a framework for chemical

engineering. This chapter outlines the reasons why this framework is suitable for

studying the unit operations of the confectionery industry in spite of the cellular

structure of the materials. In Chapter 2, the structural characterization of raw

materials and products is discussed by means of structure theory. This chapter

also demonstrates in detail the methods for preparing confectionery recipes tak-

ing compositional requirements into account.

Chapter 3 and Appendices 1 and 2 all deal with the engineering properties

of the materials used in confectionery. Heat transfer and mass transfer are not

discussed individually but are included in other chapters.

Rheology is essential to confectionery engineering. Therefore, a relatively large

part of the book (Chapter 4) discusses the rheological properties of both New-

tonian and non-Newtonian fluids, along with elasticity, plasticity, extensional

viscosity, etc. Non-Newtonian flow, especially that of Casson fluids, is discussed

in Chapter 12 and Appendix 3.

Some relevant topics in colloid chemistry are discussed in Chapters 5 and 11.

In this context, the basics of fractal geometry cannot be ignored; thus, Appendix

4 offers an outline thereof. Comminution plays an important role in this field,

as new procedures and machines related to comminution enable new chocolate

technologies to be developed.

Chapters 7–9 discuss the operations of mixing, as well as the topics of solutions

of carbohydrates in water and the evaporation of these solutions. These chapters

provide confirmation that the Dühring rule, the Ramsay–Young rule, etc. are also

valid for these operations.

Crystallization (Chapter 10) from aqueous solutions (candies) and fat melts

(chocolate and compounds) is a typical operation in confectionery practice, and

thus I highlight its dominant characteristics. In Chapter 13, pressing is briefly

discussed. Extrusion (Chapter 14) and agglomeration (Chapter 15) are typical

operations that manifest the wide-ranging nature of the confectionery industry.

Chapter 16 deals with inversion, the Maillard reaction and such complex oper-

ations as conching and also new trends in chocolate manufacture and (tangen-

tially) baking.

Chapter 17 deals with the issues of water activity and shelf life. A separate

chapter (Chapter 18) is devoted to food stability. The real meaning of such an

approach is that from the start of production to the consumer’s table, the kinetics

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Preface xxv

of the changes in the raw materials and products must be taken into considera-

tion. Furthermore, in the light of this attitude, the concept of food stability must

be defined more exactly by using the concepts of stability theory.

For the sake of completeness, Appendix 6 contains some technological out-

lines.

I intended to avoid the mistake of he who grasps much holds little (successfully?

who knows?); therefore, I have not been so bold as to discuss such opera-

tions – however essential – as fermentation, baking and panning, about which I

have very little or no practical knowledge. Similarly, I did not want to provide a

review of the entire circle of relevant references.

Thus the substance that I grasped turned out to be great but rather difficult, and

I wish I could say that I have coped with it. Here the gentle reader is requested to

send me their remarks and comments for a new edition hopefully to be published

in the future.

My most pleasant obligation is to express my warmest thanks to all the col-

leagues who helped my work. First of all, I have to mention the names of my pro-

fessors, R. Lásztity (Technical University of Budapest) and T. Blickle (University

of Chemical Engineering, Veszprém), who were my mentors in my PhD work,

and Professor J. Varga (Technical University of Budapest), my first instructor in

chocolate science. I am grateful to Professor S. Szántó and Professor L. Maczelka

(Research Laboratory of the Confectionery Industry), who consulted me very

much as a young colleague on the topics of this field. I highly appreciate the

encouragement obtained from Mr M. Halbritter, the former president of the

Association of Hungarian Confectionery Manufacturers; Professor Gy. Karlovics

(Corvinus University of Budapest and Bunge Laboratories, Poland); Professor

A. Fekete (Corvinus University of Budapest); Professor A. Salgó (Technical Uni-

versity of Budapest); Professor G. Szabo (Rector, Szeged University of Sciences);

Professor A. Véha (Dean, Szeged University of Sciences); and Professor E. Gyimes

(Szeged University of Sciences).

I am also indebted to Professor C. Alamprese (Università degli Studi di

Milano, Italy); Ms P. Alexandre, a senior expert at CAOBISCO, Brussels,

Belgium; Professor R. Scherer (Fachhochschule Fulda, Germany); and Professor

H.-D. Tscheuschner and Professor K. Franke (Dresden University of Technol-

ogy, Germany), as well as to D. Meekison for his valuable help provided in

copyediting.

Last but not least, I wish to express my deep and cordial thanks to my family:

to my daughter Viktória for correcting my poor English and to my wife Irén,

who with infinite patience has tolerated my whimsicality and the permanent

and sometimes shocking disorder around me and (despite all this) assured me a

normal way of life.

Ferenc Á. Mohos

Budapest, Hungary

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Preface to the second edition

Since the appearance of the first edition in 2010, important developments have

emerged in the food engineering that called for a certain revision of the origi-

nal version of the work completed 5 years ago. Therefore, the objectives of the

current edition are twofold: on the one hand, it seeks to reflect main relevant

research results, and on the other hand, it also intends to incorporate the dis-

cussion of such operations as drying, baking and roasting which are important

topics in the confectionary practice. My hope is that new additions will not only

enrich the content of the first edition but also shed light on fresh trends in the

industry.

Individual chapters have been completed by the following themes: In Chapter

1 (and Appendix 5), the Blickle–Seitz system theory and SAFES methodology are

presented in connection with the principles of food engineering. An easy matrix

method of dimensional analysis is outlined. Relevant new issues in relation to

food safety and quality assurance are also discussed in this chapter. Chapter 2

now also includes recipes of chocolate of high cocoa content and confectioner-

ies for special dietetic purpose. Further in Chapter 4, new results concerning

yield stress, microrheology and food oral processing are discussed. Chapter 10

highlights an important new initiative of the European Union, the so-called the

ProPraline project. As a result of the new edition, Chapter 16 includes the topic

of acrylamide formation in confectioneries of high current relevance. Also the

operations of drying, baking and roasting are discussed here. A completely new

chapter was added (Chapter 19) in order to reflect on the topics of manufactur-

ing artisan chocolate and confectioneries. Important modifications also concern

Appendix 3 in relation to linear flow models, whereby the Bingham, the Cas-

son and the Ostwald–de Waele flow curves and the corresponding volume rates

are presented. Furthermore, the constitutive equations of rheology in tensorial

and in fractional calculus are briefly presented. Finally, topics of ultrasonic and

photoacoustic testing are also highlighted as new emerging topics.

xxvii

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Acknowledgements

The author gratefully acknowledges the permission granted to reproduce the

copyright material in this book: AarhusKarlshamn, Denmark (Figs 10.8–10.10

and 10.21); Akadémiai Kiadó, Budapest (Fig. 14.1); AVI Publishing Co. Inc.,

Westport, USA (Figs 3.1–3.3; Tables 3.1, 3.2, 3.19 and 3.20); Archer Daniels Mid-

land Co. (ADM), IL, USA (Fig. 17.5); Carle & Montanari SpA, Milan (Figs 6.3,

6.5 and 6.6; Table 6.4); Elsevier Science Ltd, The Netherlands (Figs 5.10, 9.1,

9.2, 10.5(a)–(d), 10.6, 10.24–10.30 and 11.6; Tables 3.8 and 3.9); Professor K.

Kerti, Budapest (Table 10.3); Professor R. Lásztity, Budapest (Figs 4.26 and 4.27);

Professor J. Nyvlt, Prague, Czech Republic (Figs 10.1 and 10.7); Springer Sci-

ence and Business Media, The Netherlands (Tables 17.2, 17.3 and 17.8; Section

17.1.6); Professor J.F. Steffe, Michigan, USA (Figs 4.5, 4.11, 4.13, 4.15–4.18 and

4.23; Table 4.1); P. Székely, Budapest (Figs 16.1 and 16.2; Tables 16.3 and 16.4);

Wiley-VCH Verlag GmbH & Co KGaA, Germany; and Mrs Liselotte Rumpf, Karl-

sruhe, Germany (Figs 15.1–15.4; Table 15.1).

Every effort has been made to trace copyright holders and to obtain their per-

mission for the use of copyright material. The author apologizes for any errors

or omissions in the above list and would be grateful if notified of any corrections

that should be incorporated in future reprints or editions of this book.

xxix

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PART I

Theoretical introduction

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CHAPTER 1

Principles of food engineering

1.1 Introduction

1.1.1 The Peculiarities of food engineeringFood engineering is based to a great extent on the results of chemical engineer-

ing. However, the differences in overall structure between chemicals and foods,

that is, the fact that the majority of foods are of cellular structure, result in at least

three important differences in the operations of food engineering – the same is

valid for biochemical engineering.

1 Chemical engineering applies the Gibbs theory of multicomponent chemical

systems, the principal relationships of which are based on chemical equilib-

rium, for example, the Gibbs phase rule. Although the supposition of equilib-

rium is only an approximation, it frequently works and provides good results.

In the case of cellular substances, however, the conditions of equilibrium do not

apply in general, because the cell walls function as semipermeable membranes,

which make equilibrium practically possible only in aqueous media and for

long-lasting processes. Consequently, the Gibbs phase rule cannot be a basis

for determining the degrees of freedom of food engineering systems in gen-

eral. For further details, see Section 1.3.2.

2 Another problem is that cellular substances prove to be chemically very com-

plex after their cellular structure has been destroyed. In the Gibbs theory,

the number of components in a multicomponent system is limited and well

defined, not infinite. The number of components in a food system can be practically

infinite or hard to define; in addition, this number depends on the operational condi-

tions. Certainly, we can choose a limited set of components for the purpose of

a study – and this is the usual way – but this choice will not guarantee that

exclusively those components will participate in the operation considered.

Therefore, interpretation of the degrees of freedom in food engineering

systems causes difficulties and is often impossible, because the number and

types of participants (chemical compounds, cell fragments, crystalline sub-

stances, etc.) in food operations are hard to estimate: many chemical and

physical changes may take place simultaneously, and a small change in the

conditions (temperature, pH, etc.) may generate other types of chemical or

physical changes. If we compare this situation with a complicated heteroge-

neous catalytic chemical process with many components, it is evident that

Confectionery and Chocolate Engineering: Principles and Applications, Second Edition. Ferenc Á. Mohos.© 2017 John Wiley & Sons Ltd. Published 2017 by John Wiley & Sons Ltd.

3

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4 Confectionery and chocolate engineering: principles and applications

in food engineering we struggle with complex tasks that are not easier, only

different.

Evidently, comminution plays a decisive role in connection with these

peculiarities. However, in the absence of comminution, these two pecu-

liarities – the existence of intact cell wall as barriers to equilibrium and the

very high number of operational participants – may appear together as well;

for example, in the roasting of cocoa beans, the development of flavours

takes place inside unbroken cells. In such cases, cytological aspects (depot fat,

mitochondria, etc.) become dominant because the cell itself works as a small

chemical plant, the heat and mass transfer of which cannot be influenced by

traditional (e.g. fluid-mechanical) means. This problem is characteristic of

biochemical engineering.

3 The third peculiarity, which is a consequence of the cellular structure, is that

the operational participants in food engineering may be not only chemical

compounds, chemical radicals and other molecular groups but also fragments

of comminuted cells.

In the case of chemical compounds/radicals, although the set of these par-

ticipants can be infinitely diverse, the blocks from which they are built are

well defined (atoms), the set of atoms is limited and the rules according to

the participants are built are clear and well defined.

In the case of cellular fragments, none of this can be said. They can, admit-

tedly, be classified; however, any such classification must be fitted to a given

task without any possibility of application to a broader range of technolog-

ical problems. This is a natural consequence of the fact that the fragments

generated by comminution, in their infinite diversity, do not manifest such

conspicuous qualitative characteristics as chemicals; nevertheless, they can

be distinguished because slight differences in their properties, which occur by

accident because of their microstructure, may become important.

This situation may be understood as the difference between discrete and

continuous properties of substances: while chemical systems consist of atoms

and combinations of them, to which stoichiometry can be applied, the systems

of food engineering cannot be built up from such well-defined elements. This

stoichiometry means that well-defined amounts by mass (atomic masses or

molecular masses) may be multiplied by integers in order to get the mass

fluxes in a reaction. However, in the recipes that are used for describing the

compositions of foods, the mass fluxes are treated as continuous variables,

contrary to the idea of stoichiometry.

1.1.2 The hierarchical and semi-hierarchical structureof materials

Although foods also consist of atoms in the final analysis, it is characteristic of

food engineering that it does not go to an elementary decomposition of the entire

raw material; however, a certain part of the raw material will be chemically

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Principles of food engineering 5

modified, and another part will be modified at the level of cells (by comminu-

tion). The structures of materials are hierarchical, where the levels of the hier-

archy are joined by the containing relation, which is reflexive, associative and

transitive (but not commutative): A→B means that B contains A, that is, → is

the symbol for the containing relation. The meaning of the reflexive, associative

and transitive properties is:

• Reflexive: A contains itself.

• Associative: if A→ (B→C), then (A→B)→C.

• Transitive: if A→B→C, then A→C (the property is inheritable).

The transitive property is particularly important: if A= atom, B= organelle

and C= cell (considered as levels), then the transitive relation means that if an

organelle (at level B) contains an atom (at level A) and if a cell (at level C) con-

tains this organelle (at level B), then that cell (at level C) contains the atom in

question (at level A) as well.

The hierarchical structure of materials is illustrated in Figure 1.1. For the sake

of completeness, Figure 1.1 includes the hierarchical levels of tissue, organs and

organisms, which are of interest when one is choosing ripened fruit, meat from

a carcass and so on. In a sense, the level of the organism is the boundary of the

field of food (and biochemical) engineering.

This hierarchical structure is characteristic of cellular materials only when

they are in an intact, unbroken state. Comminution may disrupt this structure;

for example, if cellular fragments are dispersed in an aqueous solution and these

fragments may themselves contain aqueous solutions as natural ingredients,

Atom

Group of atoms

Chemicalcompound

Cellular organelle

Cell

Tissue, organ,organism

Foodengineering

andbiochemicalengineering

Chemicalengineering

Figure 1.1 Hierarchical structure of materials.

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6 Confectionery and chocolate engineering: principles and applications

then these relations can be represented by

A1 → C → A2

where A1 represents the natural ingredients of a cell (an aqueous solution), C

represents the cellular material and A2 represents the aqueous solution in which

the cellular material is dispersed. Evidently, in this case, the hierarchical levels

are mixed, although they still exist to some extent. Therefore, for such cases of

bulk materials, the term semi-hierarchical structure seems more appropriate.

If we allow that the degrees of freedom cannot be regarded as the primary

point of view, a more important, in fact crucial, question is whether the set of

chemical and/or physical changes that occur in an operation can be defined at

all. The answer is difficult, and one must take into consideration the fact that an

exact determination of this set is not possible in the majority of cases. Instead, an

approximate procedure must be followed that defines the decisive changes and,

moreover, the number and types of participants. In the most favourable cases,

this procedure provides the result (i.e. product) needed.

1.2 The Damköhler equations

1.2.1 The application of the Damköhler equations in foodengineering: conservative substantial fragments

In spite of the differences discussed earlier, the Damköhler equations, which

describe the conservation of the fluxes of mass, component, heat and momen-

tum, can provide a mathematical framework from the field of chemical engi-

neering that can be applied to the tasks in food engineering (and biochemical

engineering), with a limitation referring to the flux of component.

The essence of this limitation is that the entire set of components cannot be

defined in any given cases. This limitation has to be taken into account by defin-

ing both the chemical components studied and their important reactions. The

conservation law of component fluxes does hold approximately for this partial

system. The correctness of the approximation may be improved if this partial set

approaches the entire set of components. For example, if we consider the back-

ing of biscuit dough, it is impossible to define all the chemical reactions taking

place and all the components participating in them; therefore, the conservation

equations for the components cannot be exact, because of the disturbing effect

of by-reactions. However, what counts as a by-reaction? This uncertainty is the

source of inaccuracy.

The conservation equations for mass, heat and momentum flux can be used

without any restriction for studying the physical (and mechanical) operations

since their concern is bulk materials. In Appendix 5, the concepts conservative

elements and conservative substantial fragments are discussed in detail. In food

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Principles of food engineering 7

engineering, the concept conservative substantial fragment can substitute the

concept of conservative elements (Mohos, 1982) which latter are essential in the

chemistry. The epithet conservative practically means here that the Damköhler

conservation equations hold also for these fragments. For example, diffusion of

humidity (water) in cellular substances can be regarded if the other fraction of

the substances were unchanged, that is, for the water content the Fick equation

[see the Damköhler equation (1.4)] were exactly hold. However, it has to be

mentioned that the conservation of these fragments are determined by the

technological (physical and chemical) conditions. The situation is the same as in

the case of atoms: in certain conditions also the atoms are splitting.

1.2.2 The Damköhler equations in chemical engineeringThis chapter principally follows the ideas of Benedek and László (1964).

Some further important publications (although not a comprehensive list)

that are relevant are Charm (1971), Pawlowski (1971), Schümmer (1972),

Meenakshi Sundaram and Nath (1974), Loncin and Merson (1979), Stephan and

Mitrovic (1984), Zlokarnik (1985), Mahiout and Vogelpohl (1986), Hallström

et al. (1988), Stichlmair (1991), VDI-Wärmeatlas (1991), Zogg (1993), Chopey

(1994), Stiess (1995), Perry (1998), Hall (1999), Sandler (1999), McCabe et al.

(2001), Zlokarnik (2006) and Dobre and Marcano (2007).

According to Damköhler, chemical–technological systems can be described by

equations of the following type:

convection + conduction + transfer + source = local change (1.1)

In detail,

div[Γv] − div[𝛿 grad Γ] + 𝜔𝜀 ΔΓ + G = −𝜕Γ𝜕t

(1.2)

where v is the linear velocity (in units of m/s); Γ is a symbol for mass, a compo-

nent, heat or momentum; 𝛿 is the generalized coefficient of convection (m2/s);

𝜔 is the transfer surface area per unit volume (m2/m3); 𝜀 is the generalized coef-

ficient of transfer; G is the flux of source and t is the time (s). Such equations can

be set up for fluxes of mass, components, heat and momentum.

The Damköhler equations play a role in chemical and food engineering simi-

lar to that of the Maxwell equations in electrodynamics. The application of the

Damköhler equations to food-technological systems is presented in Chapter 2.

Let us consider these equations one by one.

Flux of mass:

div[𝜌v] − [Dgrad𝜌] + 𝜔𝛽′Δ𝜌 + G = −𝜕𝜌𝜕t

(1.3)

where v is the linear velocity (m/s), 𝜌 is the density (kg/m3), 𝛽′ is the mass trans-

fer coefficient (m/s), D is the self-diffusion coefficient (m2/s) and G is the source

of mass flux (kg/m3 s).

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8 Confectionery and chocolate engineering: principles and applications

Flux of a component:

div[civ] – div[D grad ci] + ωβΔci + vir = –𝜕ci / 𝜕t

Fick’s 2nd law (1.4)

where ci is the concentration of the ith component (mol/m3), D is the diffusion

coefficient (m2/s), 𝛽 is the component transfer coefficient (m/s), 𝜈i is the degree

of reaction for the ith component and r is the velocity of reaction [(mol/(m3 s)].

Flux of heat:

div[ρcpTv] – div[λ grad T] + ωα ΔT + vir ΔH = –𝜕(ρcpT) / 𝜕t

Fourier’s 2nd law Newton’s law of cooling (1.5)

where cp is the specific heat (p is constant) [J/(kg K)], T is the temperature (K),

𝜆 is the thermal conductivity (W/m K), ΔH is the heat of reaction (J/mol) and 𝛼

is the heat transfer coefficient [J/(m2 s K)].

The flux of momentum is described by the Navier–Stokes law,

Div{𝜌v ⋅ v} − Div{𝜂 Grad v} + 𝜔𝛾 Δv + grad p = −𝜕[𝜌v]𝜕t

(1.6)

where Div is tensor divergence, Grad is tensor gradient, ⋅ is the symbol for a

dyadic product, 𝜂 is dynamic viscosity [kg/(m s)], 𝛾 = (f′𝜌v/2) is coefficient of

momentum transfer [kg/(m2 s)], f ′ is frictional (or Darcy -) coefficient [dimen-

sionless], and p is pressure [kg/(m s2)].

Equations (1.3)–(1.6) are called the Damköhler equation system.

In general, the Damköhler equations cannot be solved by analytical means.

In some simpler cases, described later, however, there are analytical solutions.

For further details, see Grassmann (1967), Charm (1971), Loncin and Merson

(1979), Hallström et al. (1988) and Banks (1994).

1.3 Investigation of the Damköhler equations bymeans of similarity theory

1.3.1 Dimensionless numbersLet us suppose that a set of Damköhler equations called Form 1 are valid for

a technological system called System 1, and a set of equations Form 2 are valid

for System 2. It is known from experience that if similar phenomena take place

in the two systems, then this similarity of phenomena can be expressed by a

relationship denoted by ∼, as in Form 1∼Form 2. Similarity theory deals with the

description of this relationship.

The simplest characteristics of this similarity are the ratios of two geometric

sizes, two concentrations and so on. These are called simplex values.

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Principles of food engineering 9

1.3.1.1 Complex valuesThe first perception of such a relationship is probably connected with the name

of Reynolds, who made the observation, in relation to the flow of fluids, that

System 1 and System 2 are similar if the ratios of momentum convection to momentum

conduction in these systems are equal to each other.

Let us consider Eqn (1.1),

convection + conduction + transfer + source = local change (1.1)

for momentum flux. Since the terms for convection, conduction and so forth on

the left-hand side evidently have the same dimensions in the equation, their

ratios are dimensionless. One of the most important dimensionless quantities is

the ratio of momentum convection to momentum conduction, which is called

the Reynolds number, denoted by Re. Re=Dv𝜌/𝜂, where D is a geometric quantity

characteristic of the system and v is a linear velocity,

v = QR2𝜋

(1.7)

where Q is volumetric flow rate (m3/s) and R is radius of tube (m).

For conduits of non-circular cross section, the definition of the equivalent diam-

eter De is

De = area of stream cross sectionwetted perimeter

(1.8)

The value of De for a tube is 4D2𝜋/4D𝜋 =D (the inner diameter of the tube), and

for a conduit of square section, it is 4a2/4a= a (the side of the square). For heat

transfer, the total length of the heat-transferring perimeter is calculated instead

of the wetted perimeter (e.g. in the case of part of a tube).

It has been shown that several different types of flow can be characterized by

their Reynolds numbers:

Re< about 2300: laminar flow

Re> 2300 to Re< 10 000: transient flow

Re> 10 000: turbulent flow

This means, for example, that if for System 1 the Reynolds number Re(1) is

1000 and for System 2 the Reynolds number Re(2) is 1000, then the flow shows

the same (laminar) properties in both systems. Moreover, all systems in which the

Reynolds numbers are the same show the same flow properties.

In order to understand the role of the Reynolds number, let us interpret the

form of Eqn (1.6) as

momentum convection + momentum conduction = local change of momentum

If Re= 1, this means for the momentum part that convection= 50% and con-

duction= 50%; if Re= 3, then convection= 75% and conduction= 25%; and if

Re= 99, then convection=99% and conduction=1%.

It is difficult to overestimate the importance of Reynolds’ idea of similarity,

because this has become the basis of modelling. One can investigate the

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10 Confectionery and chocolate engineering: principles and applications

phenomena first with a small model, which is relatively cheap and can be made

quickly, and then the size of the model can be increased on the basis of the

results. Modelling and increasing the size (scaling-up) are everyday practice in

shipbuilding, in the design of chemical and food machinery, and so on.

If, for a given system, D, 𝜌 and 𝜂 are constant, the type of flow depends on the

linear velocity (v) if only convection and conduction take place.

Using similar considerations, many other dimensionless numbers can be

derived from the Damköhler equations; some of these are presented in

Tables 1.1 and 1.2. From Table 1.1, we have the following, for example:

• In Eqn (1.4), the ratio of convection to conduction is the Peclet number for

component transfer (Pe′),

Pe′ =div[civ]

div[Dgrad ci]= vd

D

• In Eqn (1.6), the ratio of the momentum source to the momentum convection

is the Euler number (Eu),

Eu =gradp

Div{𝜌v ⋅ v}=

Δp

𝜌v2

Another way of deriving dimensionless numbers is illustrated in Table 1.2. In

the third column of this table, the ratio of transfer to conduction is represented

instead of the ratio of transfer to convection, and in this way another system of

dimensionless numbers (i.e. variables) is derived.

Note that:

• If the source is a force due to a stress, equal to Δp d2, then the Euler number is

obtained.

• If the source is a gravitational force, equal to 𝜌gd3, then the Fanning number is

obtained.

Table 1.1 Derivation of dimensionless numbers.

Flux Convection/conduction Transfer/convection Source/convection

Component (Eqn 1.4) Pe′ St′ Da(I)

Heat (Eqn 1.5) Pe St Da(III)

Momentum (Eqn 1.6) Re f′/2 Eu or Fa

Table 1.2 Another way of deriving dimensionless numbers.

Flux Convection/conduction Transfer/conduction Source/convection

Component (Eqn 1.4) Pe′ Nu′ Da(I)

Heat (Eqn 1.5) Pe Nu Da(III)

Momentum (Eqn 1.6) Re A (no name) Eu or Fa

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Principles of food engineering 11

The dimensionless numbers in Tables 1.1 and 1.2 are as follows:

Pe′ = vd/D, the Peclet number for component transfer.

Pe= vd/a, the Peclet number for heat transfer (a= temperature conduction coeffi-

cient or heat diffusion coefficient).

St′ = 𝛽/v, the Stanton number for component transfer (𝛽 = component transfer coef-

ficient).

St= 𝛼/𝜌cpv, the Stanton number for heat transfer (𝛼 =heat transfer coefficient).

𝛾 = f′𝜌v/2, the momentum transfer coefficient (f′/2= 𝛾/𝜌v).

Da(I)= 𝜈ird/civ, the first Damköhler number; this is the component flux produced

by chemical reaction divided by the convective component flux.

Da(III)= 𝜈i ΔH rd/𝜌cpvΔT, the third Damköhler number; this is the heat flux pro-

duced by chemical reaction divided by the convective heat flux.

Eu=Δp/𝜌v2, the Euler number; this is the stress force divided by the inertial force.

Fa= gd/v2, the Fanning number; this is the gravitational force divided by the iner-

tial force.

Nu′ = 𝛽𝛽d/D, the Nusselt number for component transfer (D= diffusion coefficient).

Nu= 𝛼d/𝜆, the Nusselt number for heat transfer (𝜆= thermal conductivity).

Following van Krevelen’s treatment (1956), 3×3= 9 independent dimension-

less numbers can be derived in this way from three equations (rows) and four

types of phenomena (columns, namely, convection, conduction, transfer and

sources), and three rates can be produced from these numbers. With the help

of such matrices of nine elements (see Tables 1.1 and 1.2), other dimensionless

numbers can also be obtained, which play an important role in chemical and

food engineering. For example, values of efficiency can be derived in this way:

Pr= Pe/Re= 𝜈/a, the Prandtl number

Sc= Pe′/Re= 𝜈/D, the Schmidt number

Le= Sc/Pr= a/D, the Lewis number

1.3.2 Degrees of freedom of an operational unitThe number of degrees of freedom of an operational unit is a generalization of

corresponding concept in the Gibbs phase rule. The question of how to deter-

mine the number of degrees of freedom of an operational unit was first put by

Gilliland and Reed (1942); further references are Morse (1951), Benedek (1960)

and Szolcsányi (1960).

For multiphase systems, the Gibbs classical theory, as is well known, prescribes

the equality of the chemical potentials for each component in each phase in

equilibrium. If 𝜇kf (where k= 1, 2, … , K, and f= 1, 2, … , F) denotes the chemical

potential of the kth component in the fth phase, then the following holds in

equilibrium:

• For the fth phase, when there are K components,

𝜇f1 = 𝜇

f2 = · · · = 𝜇

fK

that is, F(K− 1) equations.

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12 Confectionery and chocolate engineering: principles and applications

• For the kth component, when there are F phases,

𝜇1k = 𝜇2

k = · · · = 𝜇Fk

that is, K(F− 1) equations.

In equilibrium, the additional variables which are to be fixed are T and p.

Consequently, in equilibrium, the number of variables (𝜑) which can be freely

chosen is

𝜑 = F(K − 1) − K(F − 1) + 2 = K − F + 2 (1.9)

This is the Gibbs phase rule, which is essential for studying multiphase systems.

Even in the extreme case where the solubility of a component in a solvent is

practically zero, the phase rule can nevertheless be applied by considering the

fact that the chemical potential of this component is sufficient for equilibrium in

spite of its very small concentration.

The generalization that we need in order to obtain 𝜑 for an operational unit is

given by

𝜑 = L − M (1.10)

where 𝜑 is the number of degrees of freedom, L is the total number of variables

describing the system and M is the number of independent relations between

variables.

In the simplest case, that of a simple stationary operational unit with an iso-

lated wall, if the number of input phases is F and the number of output phases

is F′, then the total number of variables is

L = (F + F′)(K + 2)

where K is the number of components. (To describe a homogeneous phase,

(K+2) data points are needed.)

Let us now consider the constraints. There are constraints derived from the

conservation laws for every component and also for energy and momentum,

which means (K+ 2) constraints for every phase.

The number of constraints for equilibrium between two phases is (K+ 2),

which means (F′ − 1)(K+ 2) constraints for the output phases. Consequently,

the total number of constraints is

M = (K + 2) + (F′ − 1)(K + 2)

and, finally,

𝜑 = F(K + 2) (1.11)

However, in the case of cellular substances, the conditions of equilibrium

typically do not apply; moreover, the number of components can usually

not be determined. Therefore, the Gibbs phase rule cannot be used for

food-technological systems except in special cases where exclusively chemical

changes are taking place in the system studied. This uncertainty relating to the

degrees of freedom is an essential characteristic of food engineering.

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Principles of food engineering 13

1.3.3 Polynomials as solutions of the Damköhler equationsThe solution of the Damköhler equation system can be approximated by the

product:

Π1a can be obtained in the form

∏b

2

×∏c

3

× · · · ×∏d

i

× · · · (1.12)

whereΠi is dimensionless numbers created from the terms of the Damköhler

equations and a, b, c, d, … are exponents which can be positive/negative integers

or fractions.

First of all, it is to be remarked that Eqn (1.12) supposes that the solution

is provided by the so-called monom (not by binom as, e.g. Π1a can be obtained

in the form Π2b ×Π3

c × · · · ×Πid×· · ·, i.e. monom does not contain addition but

multiplication operation only) – this supposition is not fulfilled in each case!

While derivation of dimensionless numbers from the Damköhler equations

refers to a special circle of phenomena of transfer, which is crucial from our point

of view, dimensional analysis is a general method that is not limited to chemi-

cal engineering. The principle of dimensional analysis has been first expressed

likely by Buckingham, therefore, it is known as Buckingham’s Π-theorem. This

theorem is the base of Eqn (1.12) as well. According to the formulation of Loncin

and Merson (1979), ‘if n independent variables occur in a phenomenon and

if n′ fundamental units are necessary to express these variables, every relation

between these n variables can be reduced to a relation between n–n′ dimension-

less variables.’

The principal idea represented by Eqn (1.12) is that convergent polynomial

series, for example, a Taylor series, can approximate well almost any algebraic

expression and thus also a solution of the Damköhler equations. But it is not

unimportant how many terms are taken into account. There are algebraic

expressions that cannot be approximated by a monomial, because they are not

a product of terms but a sum of terms.

However, the general idea is correct, and formulae created from the dimen-

sionless numbers Πi according to Eqn (1.12) provide good approximations of

monomial or binomial form. (Trinomials are practically never used.)

How can this practical tool be used? Let us consider a simple example. A warm

fluid flows in a tube, which heats the environment; for example, this might be the

heating system of a house. If heat radiation is negligible, the Nusselt, Reynolds

and Peclet numbers for the simultaneous transfer of momentum and heat should

be taken into account (see Table 1.2). Since the appropriate dimensionless num-

bers created from the terms of the Damköhler equations are:

Nu for heat (convection/conduction)

Re for momentum (convection/conduction)

Pe for heat (convection/conduction) or Pr=Pe/Re, therefore, neglecting the grav-

itational force

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14 Confectionery and chocolate engineering: principles and applications

We obtain the following function f:

Nu = f (Re, Pr) (1.13)

which is an expression of Eqn (1.12) for the aforementioned case.

Equation (1.12) is one of the most often applied relationships in chemical and

food engineering. Its usual form is

Nu = CRea × Prb (1.14)

which has the same monomial form as Eqn (1.12).

Many handbooks give instructions for determining the values of the exponents

a and b and the constant C, depending upon the boundary conditions. Let us

consider the physical ideas on which this approach is based.

1.4 Analogies

1.4.1 The Reynolds analogyAn analogy can be set up between mechanisms as follows:

Momentum transfer↔heat transfer

Momentum transfer↔ component transfer

Component transfer↔heat transfer

This analogy can be translated into the mathematical formalism of the transfer

processes.

From physical considerations, Reynolds expected that the momentum flux (Jp)

and the heat flux (Jq) would be related to each other, that is, if

Jq = 𝛼

cp𝜌× AΔ(𝜌cpT) (1.15)

then

Jq = 𝛾

𝜌× AΔ(𝜌v) (1.16)

In other words, the moving particles transport their heat content also. Then he sup-

posed that𝛼

cp𝜌= 𝛾

𝜌(1.17)

or, in another form,f ′

2= 𝛼

cp𝜌= St (1.18)

If the flux of a component is

Ji = 𝛽FΔci (1.19)

then Reynolds’ supposition can be extended to this third kind of flux as follows:

St = St′ =f ′

2(1.20)

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Principles of food engineering 15

where St is the Stanton number for heat transfer (St= 𝛼/cp𝜌), St′ is the Stanton

number for component transfer (St′ = 𝛽/v), f′/2= 𝛾/𝜌v and 𝛾 is the momentum

transfer coefficient.

If the Reynolds analogy formulated in Eqn (1.20) is valid, then if we know

one of the three coefficients 𝛼, 𝛽 or 𝛾, the other two can be calculated from

this equation. This fact would very much facilitate practical work, since much

experimental work would be unnecessary.

But proof of the validity of the Reynolds analogy is limited to the case of strong

turbulence. In contrast to the Reynolds analogy,

a ≠ v ≠ D (1.21)

that is,

Pr ≠ Sc ≠ Le (1.22)

Equation (1.17) is valid only for turbulent flow of gases. In the case of gases,

Pr ≈ 0.7–1 (1.23)

is always valid.

1.4.2 The Colburn analogyColburn introduced a new complex dimensionless number, and this made it pos-

sible to maintain the form of the Reynolds analogy:

Jq = St Pr2∕3 (1.24)

Ji = St′ Sc2∕3 (1.25)

and

Jp =f ′

2(1.26)

Finally, formally similarly to the Reynolds analogy,

St Pr2∕3 = St′ Sc2∕3 =f ′

2(1.27)

The Colburn analogy formulated in Eqn (1.27) essentially keeps Reynolds’ prin-

cipal idea about the coupling of the momentum (mass) and thermal flows and

gives an expression that describes the processes better. Equation (1.27) is the basis

of the majority of calculations in chemical engineering.

In view of the essential role of Eqn (1.27), it is worth looking at its structure:

St = NuRePr

= 𝛼

𝜌cpv

St′ = Nu′

ReSc= 𝛽

v

f ′

2= 𝛾

𝜌v

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16 Confectionery and chocolate engineering: principles and applications

The numbers Pr and Sc are parameters of the fluid:

Pr = va

Sc = vD

Additional material parameters are needed for calculations, namely, 𝛼, 𝜌 and cp.

If v is known, f′ and 𝛽 can be calculated.

This theoretical framework (see Eqns 1.13, 1.14 and 1.27) can be modified

if, for example, a buoyancy force plays an important role – in such a case, the

Grashof number, which is the ratio of the buoyancy force to the viscous force,

appears in the calculation. A detailed discussion of such cases would, however,

be beyond the scope of this book. A similar limitation applies to cases where the

source term is related to a chemical reaction: chemical operations in general are

not the subject of this book.

A more detailed discussion of these topics can be found in the references given

in Section 1.2.

1.4.3 Similarity and analogySimilarity and analogy are quite different concepts in chemical and food engi-

neering, although they are more or less synonyms in common usage. Therefore,

it is necessary to give definitions of these concepts, which emphasize the differ-

ences in our understanding of them in the present context.

Similarity refers to the properties of machines or media. Similarity means that

the geometric and/or mechanical properties of two machines or streaming media

can be described by the same mathematical formulae (i.e. by the same dimen-

sionless numbers) that our picture of the flux (e.g. laminar or turbulent) is similar

in two media. Similarity is the basis of scaling-up.

Analogy refers to transfer mechanisms. Analogy means that the mechanisms

of momentum, heat and component transfer are related to each other by the

way that components are transferred by momentum and, moreover, components

transfer heat energy (except in the case of heat radiation). This fact explains the

important role of the Reynolds number, which refers to momentum transfer.

1.5 Dimensional analysis

This is a simple mathematical tool for creating relationship between physical vari-

ables, keeping the rule that the physical expressions shall be homogeneous from the

viewpoint of dimension: both sides of the equations must have the same dimension.

Homogeneity also means that the equation remains unchanged if the system

of the fundamental units changes (e.g. SI ↔Anglo-Saxon system). Dimensional

analysis can be very fruitful for solving complicated problems easily in various

fields of physics, biology, economics and others.

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Principles of food engineering 17

Dimensional analysis contracts physical variables into dimensionless groups,

which will be the new variables; by so doing, the number of variables will be

decreased. The lesser the number of variables, the greater the advantage: for

example, if instead of 6 variables only 3 variables are to be studied experimen-

tally, supposed that 5 points of every variable are to be measured, then instead of

56 =15 625 only 53 =125 points are to be measured in the labour experiments.

There is a developed theory of dimensional analysis which abundantly applies

the results of linear algebra and computerization (see Barenblatt, 1987; Hunt-

ley, 1952; Zlokarnik, 1991). Instead of discussing these classical methods based

on solutions of linear equation system, we represent here the Szirtes method

(Szirtes, 1998; 2006) by examples in a rather simplified and slightly modified

form, which is very easy and can be generally used.

Szirtes exhaustively details the cases as well for which the approaches of

dimensional analysis must be cautiously used. Two considerations of him are

mentioned here:

1 The Buckingham Π-theorem relates to products of dimensionless 𝜋-numbers,

that is, monoms, which do not contain the algebraic operation addition (+).

If a formula contains addition (i.e. it is binom, trinom, etc.), its transforma-

tion into a dimensionless formula by dimensional analysis either needs some

special considerations or impossible.

2 The obtained dimensionless formula needs experimental checking in every case,

since the dimensional correctness is only a necessary but not a sufficient

condition.

Example 1.1 Heat transfer by fluid in tubeThe choice of variables is done according to physical considerations:

𝛼 : heat transfer coefficient (kg s−3)

w : velocity of fluid (m s−1)

q : heat capacity (kg m−1 s−2)

𝜈 : kinematic viscosity of fluid (m2 s−1)

d: diameter of tube (m)

𝜆 : coefficient of thermal conductivity (kg m s−3)

Δt : temperature different between the fluid and the tube wall (K)

Variables

Units 𝜶 w q 𝝂 d 𝝀 𝚫t

M (kg) 1 0 1 0 0 1 0L (m) 0 1 −1 2 1 1 0T (s) −3 −1 −2 −1 0 −3 0t (K) −1 0 −1 0 0 −1 1

We obtained the so-called dimension matrix of (4×7) size. In dimension matrix,

a non-singular quadratic matrix has to be chosen (i.e. its determinant is not zero),

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18 Confectionery and chocolate engineering: principles and applications

which is shown by bold numbers here, denoted by A. The sequence of variables

has to be written in such a way that this quadratic matrix should be on the right

side. The residue of the dimension matrix on the left side is denoted by B. That

is, the dimension matrix has B A the following form:

In the next step, this dimension matrix of (4×7) size has to be completed to a

quadratic matrix as follows.

1 0 0 0 0 0 0

0 1 0 0 0 0 0

0 0 1 0 0 0 0

1 0 1 0 0 1 0

0 1 −1 −2 1 1 0

−3 −1 −2 −1 0 −3 0

−1 0 −1 0 0 −1 1

The completed quadratic matrix has the following form (I: unit matrix; 0: zero

matrix):

The next step is to calculate

I 0B A the inverse of the completed quadratic

matrix.

Variables 𝝅1 𝝅2 𝝅3

𝛼 1 0 0 0 0 0 0

w 0 1 0 0 0 0 0

q 0 0 1 0 0 0 0

𝜈 0 −1 1 −3 0 −1 0

d 1 1 0 5 1 2 0

𝜆 −1 0 −1 1 0 0 0

Δt 0 0 0 1 0 0 1

The structure of the inversed matrix is as follows:

From the inverse matrix

I 0–A–1×B A–1

, the values of the dimen-

sionless numbers can be directly obtained:

𝜋1 = 𝛼d𝜆−1 =Nusselt number

𝜋2 =wd𝜈−1 =Reynolds number

𝜋3 = q𝜈𝜆−1 =Prandtl number

That is, the classical formula is obtained: Nu= constant×Rea Prb

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Principles of food engineering 19

Evidently, the choice of variables is contingent: in this case, the temperature

difference (Δt) turned out to be a surplus! This uncertainty can be, on the one

hand, an inadequacy of dimensional analysis but sometimes also an advantage

as the aforementioned example shows, since it can be seen from the calcula-

tion – before any experiment! – that Δt can be neglected. The lesson of this

example is that only six variables have to be accounted instead of seven; in addi-

tion, the experiments need only three variables (No, Re, Pr), and the constants

can be determined by linearization.

Example 1.2 By the Szirtes method, let us calculate the flow rate (V)in a tube of D diameter if the pressure difference is Δp and the viscosityof fluid is 𝜂 (the solution is the well-known Hagen–Poiseuilleequation). This example is derived from Szirtes (1998, 2006).

The completed dimension matrix and its inverse.

V 𝚫p 𝜼 D

1 0 0 0M(kg) 0 1 1 0

L (m) 3 −2 −1 1

T (s) −1 −2 −1 0

𝝅1

V 1 0 0 0

Δp −1 −1 0 −1

𝜂 1 2 0 1

D −4 0 1 −1

Solution: 𝜋1 = (V𝜂/Δp D4), that is, V= constants×Δp D4/𝜂

Remark: In case of more or other variables (e.g. the length or/and cross section

of tube), the solution is too complicated. Also this example demonstrates that

albeit dimensional analysis is very many-sided but not omnipotent.

1.6 System theoretical approaches to food engineering

A strong tendency in food process engineering is the growing attention paid to

the relations between processes, products, emerging technologies, heat treat-

ments and food safety. Research tools like mathematical modelling, especially

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20 Confectionery and chocolate engineering: principles and applications

computer fluid dynamics, and sophisticated methods of product characterization

are the most intensively developing fields (see Bimbenet et al., 2007).

The models currently used in food process engineering simplify too much

both the food system description and the mechanisms and rate equations of

changes: The food system is supposed to be homogeneous and continuous.

In this way, thermodynamic and kinetic equations deduced for ideal gas or

liquids, in conditions close to equilibrium are applied to cellular solid foods, in

conditions far away from the equilibrium. However, it is necessary to develop

advanced concepts and methodologies in food process engineering. The new

models for food and processes development must incorporate information

about all these aspects (thermodynamic, structural, chemist and biochemist and

even mechanics). Only in this way, they would be able to calculate and predict

the real changes in the whole quality of food product in line with the process

progression.

In the spirit of such ideas the system theory of chemical engineering developed

by Blickle and Seitz (1975), Blickle (1978) was adapted to food engineering by

Mohos (1982). For the mathematical details and examples, see Appendix 5.

Fito et al. (2007) present a comprehensive model of food engineering called

systematic approach to food process engineering (SAFES) in the sense of food

process engineering for product quality. The SAFES methodology (Fito et al.,

2007) recognizes the complexity of food system and allows coordinating the

information about food structure, composition, quality, thermodynamic and so

on in adequate tools to develop real food and processes models. This brief review

is not capable of replacing the original article, which can be found in the Internet;

therefore, it is limited to itemize the main ideas of it.

• Food product engineering: modelling of food and biological systems by studying

the structure of food system as the structure–properties ensemble (e.g. levels

of complexity in matter condensation).

• The SAFES defines a simplified space of the structured phases and components, more-

over, of aggregation states in order to describe the material structure.

• It defines the descriptive matrix, a mathematical tool to describe the food system by

the help of:

– The state variables: the share-out of matter among components and struc-

tured phases

– Mass and volume balances inside the product

– The energy inside the system: the Gibbs free energy

– Equilibrium and driving forces

– Transport mechanisms and rate equations

• Food process engineering consists of modelling of food operations and pro-

cesses:

– Definition of unit operation and stage of change

– Mass balances and transformed matrices: matrix of changes

– To construct the process matrix

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Principles of food engineering 21

1.7 Food safety and quality assurance

When studying the principles of food engineering, the concepts food safety and

quality assurance (QA) must not be omitted although a detailed discussion of

them exceeds the possibilities of this work. Therefore, this presentation is limited

to a sketch and provides the appropriate essential references, which can be found

in the Internet.

In the food industry, QA systems such as the Hygiene Code (FAO/WHO, 2009;

Codex Alimentarius Committee, 1969), the Hazard Analysis Critical Control

Points (HACCP) and the International Organization for Standardization (ISO)

9000 series are applied to ensure food safety and food quality to prevent liability

claims and to build and maintain the trust of consumers.

Quality is defined by the ISO as ‘the totality of features and characteristics of

a product that bear on its ability to satisfy stated or implied needs.’ Safety differs

from many other quality attributes since it is a quality attribute that is difficult

to observe. A product can appear to be of high quality, that is, well coloured,

appetizing, flavourful and so on, and yet be unsafe because it is contaminated

with undetected pathogenic organisms, toxic chemicals or physical hazards. On

the other hand, a product that seems to lack many of the visible quality attributes

can be safe.

Safety or QA program should focus on the prevention of problems, not simply

curing them. Safety and QA should be ongoing processes incorporating activi-

ties beginning with selecting and preparing the soil and proceeding through to

consumption of the product. Both safety and QA should focus on the prevention

of problems, not simply curing them since, once safety or quality is reduced,

it is virtually impossible to go back and improve it for that item. It is possi-

ble, however, to assure that the same problem does not affect future products

(Silva et al., 2002).

HACCP aims to assure the production of safe food products by using a system-

atic approach (i.e. a plan of steps) to the identification, evaluation and control

of the steps in food manufacturing that are critical to food safety (Leaper, 1997).

HACCP focuses on technological aspects of the primary process.

CAOBISCO (2011) provides a Guide of Good Hygiene Practices that can be

regarded a competent document in this field.

The ISO 9000 series aims to achieve uniformity in products and/or services,

preventing technical barriers to free trade throughout the world. ISO consists of

a checklist to assure managerial aspects. It requires the establishment of proce-

dures for all activities and handling, which must be followed by ensuring clear

assignment of responsibilities and authority (Hoogland et al., 1998). See further

ISO (1984, 1990, 1994) documents.

For studying further references concerning food safety, QA and food quality,

see Lásztity (2008), Carpenter et al. (2000), Defence Fuel & Food Services (2013),

Food Safety Authority of Ireland (2011) and Martin (1997). References to the

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22 Confectionery and chocolate engineering: principles and applications

confectioneries: de Zaan (2009), Minifie (1989a,b, 1999; pp. 663–670) and Bhat

and Gómez-López (2014).

Further reading

Baker, W.E., Westine, P.S. and Dodge, F.T. (1991) Similarity Methods in Engineering Dynamics:

Theory and Practice of Scale Modeling, Fundamental Studies in Engineering, vol. 12, Elsevier,

Amsterdam.

Berk, Z. (2009) Food Process Engineering and Technology, Elsevier, Academic Press.

Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002) Transport Phenomena, 2nd edn, John Wiley

& Sons, Inc., New York.

Committee on the Review of the Use of Scientific Criteria and Performance Standards for Safe

Food (2003): Scientific Criteria to Ensure Safe Food, National Academy of Sciences, USA, http://

www.nap.edu/catalog/10690.html

Couper, J.R. (ed.) (2005) Chemical Process Equipment: Selection and Design, Elsevier, Boston, MA.

Earle, R.L. and Earle, M.D. (1983) Unit Operations in Food Processing: The Web Edition. http://

www.nzifst.org.nz/unitoperations

Ghoshdastidar, P.S. (2005) Heat Transfer, 2nd edn, Oxford University Press, Oxford.

Grassmann, P., Widmer, F. and Sinn, H. (1997) Einführung in die thermische Verfahrenstechnik, 3.

vollst. überarb. Aufl edn, de Gruyter, Berlin.

Gutiérrez-López, G.F., Barbosa-Cánovas, G.V., Welti-Chanes, J. and Parada-Arias, E. (2008) Food

Engineering: Integrated Approaches, Springer Science+Business Media, LLC.

Heldmann, D.R. and Lund, D.B. (2002) Handbook of Food Engineering, 2nd edn, CRC Press, Boca

Raton, London, New York.

Ibarz, A. and Barbosa-Cánovas, G.V. (2003) Unit Operations in Food Engineering, CRC Press, Boca

Raton, USA.

Lienhard, J.H. IV, and Lienhard, J.H. V, (2005) A Heat Transfer Textbook, 3rd edn, Phlogiston Press,

Cambridge, Massachusetts.

López-Gómez, A. and Barbosa-Cánovas, G.V. (2005) Food Plant Design, Taylor & Francis Group,

CRC press, Boca Raton, USA.

Rohsenow, W.M., Hartnett, J.P. and Cho, Y.I. (eds) (1998) Handbook of Heat Transfer, 3rd edn,

McGraw-Hill Handbooks. McGraw-Hill, New York.

Sedov, L.I. (1982) Similarity and Dimensional Methods in Mechanics, Mir, Moscow.

Singh, R.P. and Heldman, D.R. (2001) Introduction to Food Engineering, Academic Press,

San Diego, CA.

Szucs, E. (1980) Similitude and Modelling, Elsevier Scientific, Amsterdam.

Toledo, R.T. (1991) Fundamentals of Food Process Engineering, Van Nostrand Reinhold, New York.

Tscheuschner, H.D. (1996) Grundzüge der Lebensmitteltechnik, Behr’s, Hamburg.

Uicker, J.J., Pennock, G.R. and Shigley, J.E. (2003) Theory of Machines and Mechanisms, 3rd edn,

Oxford University Press, New York.

Valentas, K.J., Rotstein, E. and Singh, R.P. (1997) Handbook of Food Engineering Practice, CRC

Prentice Hall, Boca Raton, FL.

Vauck, W.R.A. (1974) Grundoperationen chemischer Verfahrenstechnik, Steinkopff, Dresden.

VDI-GVC (2006) VDI-Wärmeatlas, Springer, Berlin.

Watson, E.L. and Harper, J.C. (1988) Elements of Food Engineering, 2nd edn, Van Nostrand Rein-

hold, New York.

Yanniotis, S. (2008) Solving Problems in Food Engineering, Springer Science+Business Media, LLC.

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CHAPTER 2

Characterization of substances usedin the confectionery industry

2.1 Qualitative characterization of substances

2.1.1 Principle of characterizationThe characterization of the substances used in the confectionery industry is based

on two suppositions:

1 The substances are partly of colloidal and partly of cellular nature.

2 From a technological point of view, their properties are essentially determined

by the hydrophilic/hydrophobic characteristics of their ingredients.

These substances are complex colloidal systems, that is, organic substances of

mostly natural origin which consist of various simple colloidal systems with a

hierarchical or quasi-hierarchical structure. Let us consider the example of the

hierarchical structure of a food represented in Figure 2.1.

Figure 2.1(a) shows, in outline, the structure of a substance: a solution con-

taining solids and oil droplets. Figure 2.1(b) shows a structural formula using an

oriented graph consisting of vertices and arrows. The vertices of the graph are

symbols representing the components from which the substance is theoretically

constructed. The arrows relate to the containing relation and are directed from the

contained symbol to the containing symbol; for example, dissolved substances

are contained by water. Such a diagram can be regarded as a primitive formula

of the given substance which, to some extent, imitates the structural formulae

of the simplest chemical compounds.

A quasi-hierarchical attribute is more expressive, since there can be cross rela-

tions as well; see the position of emulsifier. The structure shown in Figure 2.1 is

less complex than this, however. Although this way of representing structural

relations is very simple, it can express the hydrophilic/hydrophobic behaviour

of a system. Evidently, from an external viewpoint, this system behaves like a

hydrophilic system, as does, for example, milk cream (as opposed to milk butter);

that is, it is an oil-in-water (O/W) system.

The materials studied often have a cellular structure. The cell walls hinder the

free transport of material to a great extent, and therefore the actual material flows

are determined by the particle size, since comminution more or less destroys the

cell walls. This effect can be important in the case of cocoa mass because the

Confectionery and Chocolate Engineering: Principles and Applications, Second Edition. Ferenc Á. Mohos.© 2017 John Wiley & Sons Ltd. Published 2017 by John Wiley & Sons Ltd.

23

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24 Confectionery and chocolate engineering: principles and applications

Oil droplets

Dissolvedsubstance

Water

Solution

Solids

OildropletsSolution

Solids(a) (b)

Emulsifier

Figure 2.1 Hierarchical structure of foods. Example: an aqueous solution contains solid

particles and oil droplets coupled by an emulsifier to the aqueous phase.

amount of free cocoa butter equals the total cocoa butter content only if all the

cocoa cells are cut up.

This characterization of substances is not capable of reflecting those properties

which need to be explored by microstructural studies, for example, the polymor-

phism of lactose in milk powder and the fine structure of proteins.

2.1.2 Structural formulae of confectionery productsStructural formulae of various confectionery products obtained by the applica-

tion of structure theory (see Appendix 5) are shown in Figures 2.2–2.16. The

Water Sugar

d

d

d

d

e

(Lecithin)

Cocoa butter

Driedmilk

Fat-freecocoa

Milk fat

Crystallization

Figure 2.2 Structural formula of chocolate.

d=dispersion; e= emulsion.

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Characterization of substances used in the confectionery industry 25

Figure 2.3 Structural formula of hard-boiled candy.

s= solution.

Water

SugarGlucose

syrup

ss

s

Acid, flavour,colour

Figure 2.4 Structural formula of crystallized hard-boiled

candy. s= solution.

Water

Sugar

(Inversion +

retarded

crystallization)

Cream of

tartar

s

s

s

Acid, flavour,

colour

Figure 2.5 Structural formula of toffee/fudge.

s= solution; e= emulsion; cry= crystallization.

Water

Sugar

(Cry in the

case of fudge)

Glucose

syrup

Acid, flavour,

colour

ss

s

es

Milk

Fat

(Lecithin)

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26 Confectionery and chocolate engineering: principles and applications

Water

Sugar

+ Cry

Glucose

syrup

Acid, flavour,

colour

ss

s

Figure 2.6 Structural formula of fondant. s= solution;

cry= crystallization.

Water

SugarGlucose

syrup

Acid, flavour,

colour

Gelling

agent

ss

s sw + s

Figure 2.7 Structural formula of jelly. s= solution;

sw= swelling.

Melted

sugar

Cut

nuts

dd

Figure 2.8 Structural formula of nut brittle (croquante). d= dispersion.

Sugar

Cut

almonds

dd

Figure 2.9 Structural formula of marzipan (or of persipan, with apricot stones).

d= dispersion.

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Characterization of substances used in the confectionery industry 27

Figure 2.10 Structural formula of confectionery foams.

s= solution; sw= swelling; f= foaming.

Water

SugarGlucose

syrup

Acid, flavour,

colour

Foaming

agent

Foaming

ss

f

s sw + s

Air

Figure 2.11 Structural formula of granules, tablets and

lozenges. s= solution; d=dispersion; sw= swelling.

Water

Crystallized

sugar

Glucose

syrup

Acid, flavour,

colourBinder

Lubricant

(tablets)

dd

ds sw + s

Figure 2.12 Structural formula of dragées.

Glazing layer

Colouring layer

Coating ... n

Coating 2

Coating 1

Bonding layer

Centre

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28 Confectionery and chocolate engineering: principles and applications

Water

SugarGlutenStarch

Flour

Leavening/

yeast

Fat/

margarine

s

s e

sw + sg + s

Figure 2.13 Structural formula of dough. s= solution;

e= emulsion; g= gelling; sw= swelling.

Flour

Fat/

margarine

Sugar/

glucose

syrup

Leavening

Starch Glutend

d d

Figure 2.14 Structural formula of biscuits and crackers.

d=dispersion.

Milk/

eggs

s

ee

Leavening

Fat

(+ Lecithin)

Water

SugarGluten

Starch

Flour

dsw + sg + s

Figure 2.15 Structural formula of wafers. s= solution;

d= dispersion; e= emulsion; g= gelling; sw= swelling.

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Characterization of substances used in the confectionery industry 29

Figure 2.16 Structural formula of ice cream. s= solution;

e= emulsion; sw= swelling; f= foaming; cry= crystallization

Dried

milk

Stabilizer,

thickener

Water

FatSugar

sw + ss + cry

e + crye + cry

fAir

substances named in these figures may be considered as conserved substantial

fragments (referred to from now on simply as fragments). The set of fragments is

tailored to the technological system studied.

Let us consider chocolate (Fig. 2.2). Although the usual ingredients of milk

chocolate are sugar powder, cocoa mass, cocoa butter, milk powder and lecithin,

it is expedient to use the following fragments to describe the manufacture of

milk chocolate: sugar (powder), cocoa butter, fat-free cocoa, water and lecithin.

This is because these fragments determine such essential properties of choco-

late as viscosity and taste. The recipe for a chocolate product must obey some

restrictions on the ratios of these fragments because, on the one hand, there are

definitive prescriptions laid down by authorities (see e.g. European Union, 2000)

and, on the other hand, there are certain practical rules of thumb concerning the

fragments that provide a starting point for preparing recipes:

• Content of cocoa butter, 30–38 m/m%

• Content of sugar, 30–50 m/m% (depending on the kind of chocolate, i.e. dark

or milk)

• Content of milk dry matter (milk fat+ fat-free milk solids), 15–25 m/m%

• content of milk fat, minimum 3.5 m/m%

• Content of lecithin, 0.3–0.5 m/m%

Example 2.1Let us consider a milk chocolate with the following parameters (in m/m%):

• Sugar content, ca. 40–44

• Total fat content, 31–33

• Cocoa mass content, 12–16 (cocoa butter 50% of this)

• Lecithin content, 0.4

• Whole milk powder, 20–24 (milk fat 26% of this)

The calculation of the recipe is an iterative task.

The procedure for the calculation is:

• Calculate Total 1, which contains all the ingredients without cocoa butter (e.g.

79.2 in Version 1).

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30 Confectionery and chocolate engineering: principles and applications

• Calculate the amount of cocoa butter required to make up the total to 100

(20.8 in Version 1).

• Calculate the fat content of the ingredients (Total 1) without cocoa butter

(12.72 in Version 1).

• Add the amount of cocoa butter calculated previously (in Version 1,

20.8+ 12.72= 33.52 – the value is too high).

Note that the milk fat content is higher than 3.5 m/m% in every case. More-

over, no chemical reactions are taken into consideration. Consequently, the ele-

ments of set A (see Appendix 5) are sufficient for preparing the recipe. However,

when the Maillard reaction that takes place during conching is to be studied, a

deeper analysis of the participant substances is necessary; that is, the elements of

set B must be determined, for example, the lysine content of the milk protein,

the reducing sugar content of the sugar powder and water (Table 2.1).

2.1.3 Classification of confectionery products accordingto their characteristic phase conditions

In colloids and coarse dispersions, various phases are present (see Chapter 5).

Since the gaseous phase is of minor importance in the majority of confectionery

products, the basis of classification is the hydrophilic/hydrophobic character,

which applies to both the liquid and the solid phases.

Table 2.2 (Mohos, 1982) represents a classification of confectionery products

with the help of a 3×3 Cartesian product, which represents a combination of

hydrophobic solutions (1), hydrophilic solutions (2) and (hydrophilic) solids (3).

The gaseous phase is not represented but can be taken into account as a possible

combination in particular cases. The first factor in an element of this Cartesian

product represents the dominant or continuous phase, and the second factor

represents the contained phase; for example, 1×2 means a water-in-oil (W/O)

emulsion (e.g. milk butter or margarine) and 2×1 means an O/W emulsion (e.g.

toffee, fudge or ice cream).

Table 2.1 Calculation of a milk chocolate recipe (all values in m/m%).

Raw materials Version 1 Fat, Version 1 Version 2 Fat, Version 2 Version 3 Fat, Version 3

Lecithin 0.4 0.4 0.4 0.4 0.4 0.4

Sugar 42 0 43 0 43 0

Whole milk

powder

22 5.72 23 5.98 23 5.98

Cocoa mass 14 7 14 7 15 7.5

Water content 0.8 0 0.8 0 0.8 0

Total 1 79.2 12.72 81.2 12.98 82.2 13.38

Cocoa butter 20.8 20.8 18.8 18.8 17.8 17.8

Total 2 100 33.52 100 31.78 100 31.18

Comments Too high Fair Good

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Characterization of substances used in the confectionery industry 31

Table 2.2 Cartesian product of phases.a

1×1 1×2 1×3

Fat melts (W/O) Chocolate, compounds

Emulsions

2×1 2× 2 2× 3

(O/W) Hard-/soft-boiled candies Jellies, foams, wafers

Toffee, fudge, ice cream

3×1 3× 2 3× 3

Cocoa/chocolate powders,

pudding powders

Dragées, tablets, lozenges Biscuits, crackers

a1=hydrophobic phase; 2=hydrophilic phase; 3= solids (hydrophilic).

It should be emphasized that this classification is a simplification in the follow-

ing senses:

• There is not one single classification that is appropriate in all cases, and other

classifications which take the phase conditions into account in more detail may

give a more differentiated picture of the important properties.

• Table 2.2 contains only some large groups of finished confectionery products

that are characteristic of each element (i× j) of the product; however, all mate-

rials used or made in the confectionery industry can be classified into one or

other of these elements.

• The classification of products containing flour (biscuits, wafers, crackers, etc.)

is very haphazard because of the complexity of their structure.

• The elements (3× 1), (3×2) and (3× 3) can hardly be regarded as different;

the only difference is that the hydrophobicity decreases from cocoa/chocolate

powders to biscuits and crackers containing flour. However, cases showing the

opposite trend in the hydrophobicity are very frequent (e.g. cocoa powder with

8% cocoa butter content compared with cakes with 30% fat content).

• Chocolate and compounds are actually W/O emulsions [see element (1× 2)],

but the water content is in practice less than 1 m/m%.

• There are likely to be other appropriate classifications that are not based on

combinations of hydrophilic/hydrophobic/solid/liquid phases.

Despite these objections and contradictions, this classification correctly

expresses the hydrophobic/hydrophilic properties of the materials used and/or

made in the confectionery industry because these properties play an essential

role in the technologies used and in the shelf life of the substances (i.e. raw

materials, semi-finished products and finished products).

2.1.4 Phase inversion: a bridge between sugar sweetsand chocolate

To study the phase conditions of chocolate, Mohos, 1982 produced the so-called

crystal chocolate in the Budapest Chocolate Factory (former Stühmer). The method

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32 Confectionery and chocolate engineering: principles and applications

Table 2.3 Manufacture of crystal chocolate: experimental results.

Experiment 1 Experiment 2 Experiment 3 Experiment 4

Time(min)

Water(%)

Time(min)

Water(%)

Time(min)

Water(%)

Time(min)

Water(%)

0 17.4 0 17.4 0 17.4 0 17.4

30 3.85 30 3.73 25 7.31 20 10.7

45 1.57 45 1.46 60 1.54 50 9.74

90 0.52 90 0.33 120 0.35 70 9.2

165 0.43 165 0.22 180 0.34 100 5.2

120 6.21

140 4.67

160 3.53

190 2.68

235 1.75

265 1.38

295 0.88

325 0.72

Air temperature

(∘C)

43 43 34 72 (input)

Air RH (%)a 35 35 38 20 (input)

Air velocity (m/s) 2 2 2 22.3–25.1

aRH= relative humidity.

starts from an O/W emulsion which is typical to the sugar confectioneries (e.g.

fudge), and then this O/W emulsion reverts – on the effect of evaporation and

kneading – to a W/O emulsion, the texture of which corresponds to that of choco-

late. The brief technology is as follows:

Recipe for Experiments 1–3 (laboratory scale) (in g): sugar, 58.5; water, 19.5;

cocoa mass, 18.0; cocoa butter, 16 (sum= 112.0)

Recipe for Experiment 4 (plant scale) (in kg): sugar, 50.0; water, 16.7; cocoa

mass, 15.5; cocoa butter, 13.7 (sum= 95.9)

The results are presented in Table 2.3.

Three steps may be distinguished in the experiments:

Step 1: At a water content of about 10%, the cocoa butter phase separates. (The

consistency of the mass is similar to that of sugar sweets.)

Step 2: At about 100 min (water content≈5.2%), a phase inversion (O/W→W/O)

starts, and this lasts up to a water content of about 1.38% (235 min). In the

final period, the crystallization of sugar and the comminution of sugar crystals

by the rubbing effects of conching start.

Step 3: The consistency of crystal chocolate is developed.

A plot of water percentage versus time can be approximated by the function

wt = (w0 − w∞) exp(−kit) + w∞ (2.1)

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Characterization of substances used in the confectionery industry 33

where t= time of conching/drying (min), w0 = initial water content (%),

w∞ =water content after long drying (≈0.3%), ki = velocity constant of

drying (min−1) and i = the number of the experiment. For the aforemen-

tioned experiments, k1 = 9.83×10−3, k2 = 8.4×10−3, k3 =7.78×10−3 and k4 =2.17×10−3.

At the end of production, the size of the sugar crystals is similar to that in a

fondant mass (ca. 5–30 μm); however, after a short time, the larger crystals are

in the majority because of Ostwald ripening, similar to the changes that occur in

fondant.

A noteworthy phenomenon: The two methods of (1) comminution by mill and (2)

solution+ crystallization provide similar results. However, while comminution

is not followed by Ostwald ripening, the operations of solution+ crystallization

are. Just the same phenomenon can be observed when a ripened fondant is

re-kneaded and then shaped. While the structure of the centres of ripened fon-

dant hardly changes in storage, the centres of unripened fondant are easily dried;

that is, their structure is more changeable and less stable. All of this emphasizes

the importance of Ostwald ripening (see Sections 5.9.5, 10.6.1 and 16.4).

2.2 Quantitative characterization of confectioneryproducts

2.2.1 Composition of chocolates and compoundsQuantitative relations can be given which characterize the composition of

chocolates and compounds [see the (1 × 3) element of the Cartesian product in

Table 2.2]; the latter contain special fats instead of cocoa butter as the dispersing

phase. Dark chocolate and milk chocolate are typical examples of these product

groups.

2.2.1.1 Composition of dark chocolateIf the proportions of the ingredients (in %) are S, sugar; B, cocoa butter; M, cocoa

mass; and L, lecithin, then

S + M + B + L = 100 (2.2)

The cocoa content (C) is

C = M + B (2.3)

Taking into account the consistency requirements, the total fat content (F) must

be between 30% and 40%, that is,

F = L + cMM + B = 30 − 40 (2.4)

where cM is the cocoa butter content (mass concentration) of the cocoa mass (ca.

0.50–0.56). The usual value of S for dark chocolate is 30–50%, and the usual

value of L is 0.3–0.5%.

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34 Confectionery and chocolate engineering: principles and applications

Table 2.4 Recipes for dark chocolate.

Raw materials Version 1 Fat, Version 1 Version 2 Fat, Version 2 Version 3 Fat, Version 3

Sugar 36 0 30 0 39.6 0

Cocoa mass (50%) 60 30 70 35 46 23

Cocoa butter 3.7 3.7 0 0 14 14

Lecithin 0.3 0.3 0 0 0.4 0.4

Total 100 34 100 35 100 37.4Cocoa content 63.7 70 60

On the basis of these relations, many chocolate recipes can be prepared, as

shown in Table 2.4. Because of price considerations, the total fat content is chosen

to be nearer to 30% than to 40% (usually, F= 30–33).

A more detailed picture of the fragments is not needed in general for preparing

a recipe for chocolate; for example, the water content does not usually play any

role, since only the cocoa mass has a relatively high water content (1–2 m/m%),

which is decreased during conching. The water content of sugar, cocoa butter

(particularly if it is deodorized) and lecithin can be neglected. Also, the water

content of cocoa mass can be made low if it is refined by a special film evaporator

(e.g. the Petzomat, from Petzholdt), which can be regarded as a pre-conching

machine.

2.2.1.2 Composition of milk chocolateThe following equation (in %) is valid for a milk chocolate:

S + M + B + L + W + b = 100 (2.5)

where S, M, B and L have meanings similar to those mentioned earlier, W is the

percentage of whole milk powder and b is the percentage of (dry) milk fat (about

1 m/m% of the water content). The use of dry milk fat is optional.

Equation (2.3) is valid for the cocoa content. The usual value of S for milk

chocolate is 40–45%, and the usual value of L is 0.3–0.5%.

Taking into account the consistency requirements, the total fat content must

be between 30% and 40%; that is,

F = L + cMM + B + WcW + b = 30 − 40 (2.6)

where cW is the milk fat content (mass concentration) of whole milk powder (ca.

0.26–0.27).

An additional requirement related to the consistency is the ratio R= cocoa

butter/non-cocoa butter fats (mass/mass) because non-cocoa butter fats soften

the consistency and, in extreme cases, make it too soft for correct shaping of the

chocolate.

One principal requirement for milk chocolate, which is laid down by author-

ity (European Union, 2000), is that the milk fat content should be at least

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Characterization of substances used in the confectionery industry 35

3.5 m/m%. (In tropical countries, a value of 2.5 m/m% is accepted because of

the hot climate.) The usual values of milk fat content are in the range 3.5–6%,

and the usual values of total fat content are in the range 30–40%; consequently,

the value of R+1 can theoretically vary as follows:

403.5

≈ 11.4 ≥ R + 1 ≥306

= 5

that is,

10.4 ≥ R ≥ 4

However, a ratio R= 4 is not available, since the consistency would be very soft.

Instead, the practical minimum value is given by R+ 1=30/3.5=8.57, that is

about R= 7.6.

On the other hand, an intense milky taste is an important quality requirement

too, and therefore increasing the dry milk content is an understandable ambition

of producers. Another way to produce milk chocolate with an intensely milky

taste is to use special milk preparations, for example, condensed sugared milk

(milk crumb) or chococrumb (see Chapter 16), where the Maillard reaction

is used.

An essential quality requirement is a suitably high value of the fat-free cocoa

content, which gives the product its cocoa taste. The practical value is at least

3–4 m/m% for compounds and at least 5–6 m/m% for milk chocolate. However,

for compounds, cocoa powder of low cocoa butter content (10–12 m/m%) has

to be used because the fats used in compounds are not compatible with cocoa

butter or are only partly compatible. For a milk chocolate, this minimum value

of fat-free cocoa content means that the percentage of cocoa mass must be at

least 10–12 m/m% (assuming that the cocoa butter content of cocoa mass is

about 50 m/m%).

Example 2.2Let us calculate the recipe of a milk chocolate, supposing that the initial values

of the ingredients are as follows:

Ingredients Total fat

Sugar (S) 40.0 0.0

Lecithin (L) 0.4 0.4

Whole milk powder (W) 20.0 5.2

Cocoa mass (M) 12.0 6.0

Total 72.4 11.6

If the balance of these ingredients is made up by cocoa butter (100− 72.4

= 27.6), then the total fat content will be 27.6+11.6= 39.2% – too high!

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36 Confectionery and chocolate engineering: principles and applications

If M= 14 and S=43, then we do the following calculation.

Ingredients Total fat

Sugar 43.0 0.0

Lecithin 0.4 0.4

Whole milk powder 20.0 5.2

Cocoa mass 14.0 7.0

Total 77.4 12.6

If the balance of these ingredients is made up by cocoa butter (100−77.4=22.6), then the total fat content will be 22.6+ 12.6= 35.2% – this is acceptable.

Taking the price of cocoa butter into account, this is an important alteration.

In the aforementioned recipe, R+ 1= 35.2/(5.2+ 0.4)= 6.28, that is, R= 5.28.

The usual way of reducing the proportion of non-cocoa butter fat is to use whole

and skimmed milk powder together as follows. The amount of whole milk pow-

der is calculated according to the minimum requirement of 3.5% milk fat, that

is, 3.5%/0.26≈ 13.5%. This amount is then made up to 20%; that is, the amount

of skimmed milk powder is 6.5%.

The calculation is modified as follows.

Ingredients Total fat

Sugar 43.0 0.0

Lecithin 0.4 0.4

Whole milk powder 13.5 3.5

Skimmed milk powder 6.5 0.0

Cocoa mass 14.0 7.0

Total 77.4 10.9Cocoa butter 100− 77.4=22.6 22.6

Total 100 33.5

In this recipe, R+1= 33.5/(3.5+0.4)≈ 8.6, that is, R≈ 7.6.

Note that in this example, a blend of two kinds of milk powder has been used;

the average milk fat content of this blend is 3.5/20= 17.5% (instead of 26%).

2.2.1.3 Preparation of gianduja recipesThe relevant European Union directive (European Union, 2000) defines Gian-

duja chocolate as a blend of dark or milk chocolate and hazelnut paste (and

pieces); both dark and milk Gianduja chocolate are defined in detail. The min-

imum and maximum amounts of hazelnut are 20% and 40%, respectively, for

dark Gianduja and 15% and 40% for milk Gianduja.

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Characterization of substances used in the confectionery industry 37

The recipes for both types of Gianduja chocolate are actually very simple.

Example 2.3Seventy-five percent dark chocolate is mixed with 25% hazelnut paste, or 70%

milk chocolate is mixed with 30% hazelnut paste.

Since shelled hazelnuts have an oil content of about 40–60% and hazelnut oil

has a very low cold point (−18 ∘C), the hazelnut paste softens the consistency of

the product to a great extent. If milk chocolate of the composition calculated ear-

lier is used in a proportion of 70% and the assumed oil content of the hazelnuts

is 50%, then the distribution of the various oils/fats will be:

70% milk chocolate: 0.7× (22.6+ 7)% cocoa butter+0.7× 3.9% (lecithin+milk

fat)

30% hazelnut paste: 0.5×30% hazelnut oil

In summary, this Gianduja product contains 20.72% cocoa butter+ 2.73%

(lecithin+milk fat)+ 15% hazelnut oil (total fat content 38.45%), and therefore

R + 1 = 38.4538.45 − 20.72

= 38.4517.73

≈ 2.17, i.e. R ≈ 1.17

In order to avoid a consistency that is too soft, the hazelnuts are used partly as

paste and partly as tiny pieces. The hazelnut oil remains in the cells in the latter,

and therefore this portion of hazelnut oil does not soften the consistency of the

chocolate.

For example, the aforementioned composition can be modified so that 70%

milk chocolate is mixed with 15% hazelnut paste and 15% chopped hazelnuts.

The milk Gianduja mass will have the following composition and fat/oil distri-

bution:

70 kg milk chocolate: 20.72 kg cocoa butter+ 2.73 kg (lecithin+milk fat)

15 kg hazelnut paste: 7.5 kg hazelnut oil

The distribution of the various fats in this milk Gianduja mass will be (in %):

20.72/0.85= 24.38% cocoa butter

2.73/0.85= 3.21% lecithin+milk fat

7.5/0.85=8.82% hazelnut oil

Total: 36.41% oils/fats

For this solution, R+ 1= 36.41/(36.41− 24.38)= 36.41/12.03≈3.03, that is,

R≈ 2.03. Evidently, the softness of the consistency has been moderated.

For the sake of completeness, let us calculate a recipe for a compound that is

similar to milk chocolate. The corresponding formula (in %) is

S + P + V + L + m = 100 (2.7)

where S refers to sugar, P to cocoa powder, V to special vegetable fat, L to lecithin

and m to whole or skimmed milk powder.

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38 Confectionery and chocolate engineering: principles and applications

Taking the consistency requirements into account, the total fat content (F)

must be between 30% and 40%, that is,

F = L + cmm + V + PcP = 30 − 40 (2.8)

where cm is the milk fat content of whole or skimmed milk powder (m/m) and

cP is the cocoa butter content of cocoa powder (m/m).

The further requirements concerning compounds are similar to those for

chocolate.

Example 2.4Let us take an example in which a blend of milk powder of 15% milk fat content

and cocoa powder of 10% cocoa butter content is used. Comment: From the point

of view of cocoa taste, 6% cocoa powder (10% cocoa butter content) is equiv-

alent to 2×6%×0.9= 10.8% cocoa mass (50% cocoa butter content) since the

fat-free cocoa content of both is 6%×0.9= 5.4%. (This would be acceptable for

milk chocolate as well.) If the cocoa powder content is less than 3%, the taste of

the product is not characteristic of cocoa.

Ingredients Total fat

Sugar 43.0 0.0

Lecithin 0.4 0.4

Milk powder blend 20.0 3.0

Cocoa powder 6.0 0.6

Total 69.4 4.0Special vegetable fat 100− 69.4= 30.6 30.6

Total 100 34.6

2.2.1.4 Composition of dark chocolates of high cocoa contentUsing the designations S= sugar, B= cocoa butter, M= cocoa mass, L= lecithin,

C= total cocoa content and F= total fat content and, moreover, taking into con-

sideration that exclusively dark chocolate are made with high cocoa content, the

following two relationships are valid:

S = 100 − B − M − L ≈ 99.6 − C (2.4a)

where L=0.4 (mostly used value) and C=B+M.

F ≥ B + 0.5 × M + L (2.4b)

The taste of chocolate of high cocoa content, namely, the (sweet: bitter) balance

is strongly influenced by the {sugar (S): cocoa mass (M)} ratio.

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Characterization of substances used in the confectionery industry 39

The cocoa butter (B) does not directly influence the development of taste.

However, the strong bitterness of cocoa mass can be reduced also by increasing

the ratio of the cocoa butter; consequently, an indirect effect can be attributed to

the cocoa butter content as well.

But cocoa butter is the far most expensive ingredient; therefore, its portion is

typically low or zero.

Regarding these points of view, some compositions [kg≈%] can be found in

the following:

Version 1 Version 2 Version 3 Version 4 Version 5

S 36 27.6 27.6 27.6 20

M 60 72 70 80 80

B 3.6 0 2 0 0

L 0.4 0.4 0.4 0.4 0

C 63.9 72 72 80 80

F 34 36.4 37.2 40.4 40

2.2.2 Composition of sugar confectioneryThe composition of the various types of sugar confectionery is principally deter-

mined by the water content and the syrup ratio (SR) in the product (see Chapters

8 and 9 for further details). The SR is the ratio of the starch syrup dry content to

the sugar content, expressed in the form 100 : X or 100/X, where for each 100 kg

of sugar, there is X kg of starch syrup dry content.

Example 2.5If SR=100 : 50, this means that in the prepared solution there are dissolved

100 kg of sugar and 50 kg of starch syrup dry content. Assuming the usual dry

content of starch syrup of 80 m/m%, 100 kg of sugar and 50 kg/0.8= 62.5 kg of

(wet) starch syrup should be blended.

In addition to the water content, the reducing sugar content plays an important

role in determining the properties of sugar confectionery.

The reducing content of a sugar/starch syrup solution, derived from the dextrose

content of the syrup, can be calculated using the formula

R = (1 − W ) × DESR + 1

(2.9)

where R is the reducing sugar content of the solution (%), W is the concentration

of water in the solution, DE is the dextrose equivalent of the starch syrup (%)

and SR is the syrup ratio.

The other important source of the reducing content of carbohydrate solutions

is inversion, which produces the reducing sugar glucose (also known as dextrose)

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40 Confectionery and chocolate engineering: principles and applications

by hydrolysis of sucrose (also known as saccharose) under the action of catalysts

(acids or the enzyme invertase):

sucrose + H2O = glucose + fructose

(Water is chemically built into the dry content during inversion: 342 g sucrose+18 g water= 180 g glucose+180 g fructose, i.e. a 5% increase in dry content.)

The reducing sugar content of carbohydrate solutions and sugar confectionery

can easily be determined. Titrimetric or iodometric methods are the methods

mostly used for the determination of reducing sugar content and do not require

sophisticated, expensive laboratory equipment. However, what is measured by

these iodometric methods?

According to Erdey (1958), iodometric methods (the Fehling/Bertrand and

Fehling/Schoorl–Regenbogen methods) may be used for the quantitative deter-

mination of glucose, fructose, invert sugar, sucrose (after inversion), maltose,

galactose, mannose, arabinose, xylose and mannose by use of a table containing

the corresponding data for reduced Cooper measuring solution (0.1 N) versus the

kind of sugar measured (in mg). (The determination is not strictly stoichiomet-

ric.) Aldoses may be oxidized easily; the oxidation of ketoses (e.g. fructose) takes

place only in more strongly oxidizing media, but the alkaline medium that is typ-

ically used in these methods of sugar determination is favourable for oxidation

of all the various sugars; for further details, see Bruckner (1961).

Colorimetric methods are also widely used for determining reducing sugar

content (e.g. in investigations of human blood; see Section 16.1.1).

Why does the reducing sugar content of carbohydrate solutions play such an

important role in confectionery practice? The reducing sugar content, together

with the water content, determines the following:

• The crystallization of sucrose

• Water adsorption on the surface of the product, that is, the hygroscopic prop-

erties of the surface

• The consistency of the product

The ability of sucrose to crystallize is an important property from two contradictory

points of view:

• Certain products are of crystalline structure (e.g. crystalline drops, fondant and

fudge).

• There are types of sugar confectionery (e.g. drops, toffees, jellies and marsh-

mallows) which must not be of crystalline structure. During their produc-

tion, the crystallization of sucrose must be hindered by glucose syrup, invert

sugar, etc.

The hygroscopic properties of the surface of sugar confectionery may have

unintended consequences. Packaging materials can defend sugar confectionery

against water adsorption, which would make the surface sticky. The water

permeability of packaging materials can be adjusted to the given task. However,

if the product is left unpacked for some time, stickiness becomes a serious

problem. Experience shows that when the reducing sugar content of a sugar

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Characterization of substances used in the confectionery industry 41

mass is more than 16 m/m%, the mass becomes stickier and stickier. The SR

for a reducing sugar content of 16% (and a water concentration W of 0.02 and

DE= 40%) can be obtained from Eqn (2.9):

16 = (1 − W ) × DE∕(SR + 1) = 0.98 × 40∕(SR + 1)

From this equation, SR=1.45, hat is, 100 kg of sugar and 100/1.45≈ 69 kg of glu-

cose syrup dry content (ca. 69/0.8≈ 86.25 kg wet glucose syrup) should be mixed

to produce a solution of 16% reducing sugar content. This ratio is economic,

since the dry content of glucose syrup is always a little cheaper than sugar.

However, Eqn (2.9) does not take into account the inversion of sucrose, which

is caused by the acid content (sulphuric and hydrochloric acid) of glucose syrup

derived from the acidic conversion of starch. Although the acid content of glu-

cose syrup remaining after the conversion of starch is neutralized and the pH of

glucose syrups is about 4.5–5.5, hydrolysis caused by the residual acid must not

be ignored.

An additional reason for increasing the reducing sugar content is the presence

of other acidic agents in candies, above all the various flavouring acids (citric,

malic, lactic and tartaric acids).

The inversion abilities of various acids are rather different and cannot be

exactly characterized by a single parameter, because inversion is catalysed by

hydrogen ions: that is, the process of inversion is strongly dependent on the

conditions in the acidic medium (the kind of acid, the concentration, etc.) (for

more details, see Section 16.1 and Chapter 17).

Sokolovsky (1958) discussed in detail the hygroscopicity of sugar masses and

their ingredients under various conditions of production and storage. In con-

fectionery practice, the typical hygroscopic substances are fructose, invert sugar,

sorbitol and glycerol. The orders of hygroscopicity and of solubility are the same:

glucose < sucrose < invert sugar < fructose

On the basis of the aforementioned considerations, the conclusion is that the

reducing sugar content itself cannot characterize the hygroscopicity of sugar

masses. Instead, the kinds of sugar (monosaccharides and disaccharides) that

the reducing sugar content is composed of are decisive: the value of 16% is a

rough threshold only, and reducing sugar contents of 16% derived exclusively

from glucose and derived partly from glucose and partly from fructose have

entirely different effects.

An increase in the reducing sugar content makes the consistency of candies

softer, although an exact description of the circumstances that influence the con-

sistency has to be limited to individual cases.

Taking into account the effects of water content and reducing sugar content,

Figure 2.17 shows the approximate intervals which can be regarded as optimal

for various sugar confectioneries; see Mohos (1975). Naturally, these intervals are

experimentally determined and are not derived from any scientific law. More-

over, their boundaries are not strictly fixed, and this statement relates to the

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42 Confectionery and chocolate engineering: principles and applications

V

0 5 10

IIIII

I

15 20

Water content (%)

I:

II:

III:

IV/a:

IV/b:

V:

Drops

Fondant

ToffeeFudge

Jellies

Crystalline

drops

IV/a

15

10

5Re

du

cin

g s

ug

ar

(%)

IV/b

Amorphous

Crystalline

Figure 2.17 Reducing sugar versus water content in sugar confectionery.

dividing line between the amorphous and crystalline regions too. Nevertheless,

Figure 2.17 should be informative for the preparation of recipes for sugar con-

fectionery.

A typical instance of the crucial role of reducing sugar content is provided by

the technology for crystalline drops (or grained drops), the characteristic region for

which is denoted by II in Figure 2.17. Two kinds of technology are possible: inver-

sion of sucrose by cream of tartar (also known as cremor tartari or potassium

hydrogen tartrate) and the use of sucrose+ glucose syrup. Before flavouring,

colouring and pulling, a sugar mass made by either of these technologies has

to have the following composition:

4% water,

3% glycerol,

6% reducing sugar

The recipe for the cream of tartar technology is:

92–93 kg sugar

3 kg glycerol

ca. 0.2 kg cream of tartar

25–30 kg water for dissolution

Yield: ca. 100 kg sugar mass

In the case of the recipe for the glucose syrup technology, we assume that

the parameters of the glucose syrup are DE= 40% and dry content= 80%, that

is, 100 kg of glucose syrup contains 40 kg× 0.8=32 kg of reducing sugar. There-

fore, 6 kg of reducing sugar is contained in 6 kg/0.23= 18.75 kg of (wet) glucose

syrup, the dry content of which is 18.74 kg×0.8= 15 kg. Compared with the

cream of tartar technology, the amount of sugar is decreased by 15 kg, and the

amount is water is decreased by 3–4 kg (= 18.75− 15). The recipe is:

77–78 kg sugar

18.75 kg (wet) glucose syrup

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Characterization of substances used in the confectionery industry 43

3 kg glycerol

23–27 kg water for dissolution

Yield: c. 100 kg sugar mass

In both technologies, first atmospheric and then vacuum evaporation are nec-

essary, and there must be strictly no mixing or moving of the solution. Moreover,

an essential requirement is that the dissolution of the sugar must be perfect, that

is, no sugar crystals must remain undissolved, otherwise crystallization of sucrose

will start during the evaporation. To avoid such a mistake, sufficient water must

be used for dissolution.

But these two technologies are very different. The cream of tartar technology

is based on the inversion effect of cream of tartar, a process which is strongly

time dependent; consequently, the durations of the two evaporation steps have

definite limits imposed on them. A slow evaporation results in more reducing

sugar than necessary, and the crystallization in the end product will occur late

or be impossible. The other sensitive point of this technology is that sugar always

contains Ca2+ and Mg2+ ions, which form salts with cream of tartar, and the Ca

salt is insoluble.

Example 2.6A simple calculation shows that this consumption of cream of tartar by calcium

and magnesium ions may be considerable.

The molecular mass of cream of tartar (KHC4H4O6) is 188; that is, 188 g ofcream of tartar reacts with 40 g of calcium or 24.3 g of magnesium. The average

calcium content of sugar per kilogram is c. 0.15 g, and the corresponding value

for magnesium is c. 0.025 g. This means that 90 kg sugar contains c. 13.5 g Ca and

2.25 g Mg, which react with

13.5 g × (188∕40) + 2.25 g × (188∕24.3) = 80.87 g cream of tartar

If ca. 200 g of cream of tartar is used in the batch, the decrease in the amount of

it because of the effect of Ca2+ and Mg2+ is ca. 40%. (Naturally, these data are

indicative only.) This consumption is the reason why we give only an approx-

imate amount of cream of tartar (ca. 0.2 kg) in the recipe. This means that the

amount of cream of tartar has to be adjusted to the sugar used.

However, the quality of the product made by the cream of tartar technology

is much better: the sucrose crystals are of small (5–9 μm) and very homoge-

neous size, whereas the product made by the glucose syrup technology has a

consistency somewhat similar to that of starch sugar made from potatoes. (If

potato starch is converted by acid in aqueous solution, the evaporated reaction

mixture, containing ca. 80 m/m% dextrose, can be sold as a cheap product.

In former years, this process was done in the kitchen at home as well.) But

the glucose syrup technology is practically insensitive to the duration of the

evaporation steps.

An improved variation of the glucose syrup technology which eliminates the

consistency properties of the end product that remind consumers of starch sugar

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44 Confectionery and chocolate engineering: principles and applications

Density

Increase in

water content

1.0

0.5

010

Duration of pulling (min)

Density o

f sugar

mass (

kg/l)

Incre

ase o

f w

ate

r conte

nt (%

)

500.9

1.0

1.5

Figure 2.18 Pulling of sugar mass. Source: Data from Sokolovsky (1951).

uses liquid sugar instead of glucose syrup as follows: 18.75 kg of wet glucose

syrup (dry content= 80%, DE= 40%) contains about 15 kg of dry content and

6 kg of reducing sugar, and 9 kg sugar+ 6 kg liquid sugar dry content is equivalent

to 15 kg syrup dry content. Taking into account the usual parameters of liquid

sugars (dry content= 75% and fructose : glucose= 55 : 45), this means a blend

of 9 kg sugar+6 kg/0.75=8 kg liquid sugar.

The acid residues in both glucose syrup and liquid sugar cause unwanted inver-

sion, and therefore the acid content has to be rather low.

(In both technologies, glycerol is added because its hygroscopic effect acceler-

ates the crystallization of the product.)

Both technologies are very sensitive to the reducing sugar and water content

parameters from the point of view of both pulling and crystallization of sucrose in

the product – these latter operations are very closely connected with each other.

Sokolovsky (1951) studied the effect of pulling on the density and water con-

tent of sugar masses made for the production of grained drops; Figure 2.18 has

been compiled from this study.

It can be seen that in the pulling operation, the density of the sugar mass first

decreases, and later – after about 7 min – the density starts to increase again,

which shows that its tubular structure is becoming more and more broken. In

the pulling operation, the water content increases linearly up to about the sev-

enth minute, then a drying process starts, and after about 10 min of pulling, the

initial water content is restored. Both of these phenomena show that there is an

optimum pulling time (ca. 6–7 min); after this, pulling will be disadvantageous.

In fact, Sokolovsky measured a value of about 2.6 m/m% for the water content

of the sugar mass, whereas this parameter had a minimum of 4 m/m% in the

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Characterization of substances used in the confectionery industry 45

present author’s studies in the Research Laboratory of the Hungarian Confec-

tionery Industry in 1969 (unpublished).

However, the present author also found that if the reducing sugar content is

lower than 6 m/m%, crystallization of the sugar mass is liable to start dramatically

during the pulling operation. This may have the result that the entire amount of

sucrose is crystallized in only a few minutes, and the latent heat of crystallization

is liberated. Meanwhile, the sugar mass transforms into large crystalline pieces

and falls from the pulling arms. Because of the huge amount of liberated latent

heat, the bulk sugar mass gets very hot, almost glowing. (This may happen in

both technologies.)

Example 2.7In order to estimate the warming effect of this crystallization, let us do a cal-

culation. First, as an approximation, the effect of the size of the batch (mass,

surface area, etc.) can be neglected. The specific heat capacity of sucrose is about

1.42 kJ/kg, and its latent heat of solution (positive) or of crystallization (nega-

tive) is about 18.7 kJ/kg (see Chapter 3). For a unit weight of sugar mass, the

following equation is valid when the temperature t is close to 40 ∘C:

(t − 40) × 1.42 − 18.7 = 0 → t = 53.16 ∘C

(The liberation of latent heat – negative enthalpy – means that the system loses

heat, i.e. it is warmed; this is a thermodynamic convention.)

The temperature t increases to a value of 53.16 ∘C because of the latent heat of

crystallization. This calculation supposes a homogeneous distribution of heat dur-

ing crystallization; however, thermal inhomogeneities cause strong overheating,

which can easily be observed as mentioned earlier.

On the other hand, as the reducing sugar content approaches 10 m/m%, the

crystallization of sucrose in the product becomes slower and slower, and at about

a value of 12%, crystallization becomes impossible. Since it is rather difficult

to obtain exactly 6 m/m% of reducing sugar, a range of 6–8 m/m% is recom-

mended. Before packaging, storage of the end product for 1 or 2 days in a hot

(ca. 40 ∘C), wet (ca. 80% RH) room is desirable because crystallization is to a

certain extent stimulated by humidity and heat.

The phenomenon discussed earlier raises the question of stability; for more

details, see Chapter 18.

It is important to discuss the technology for grained drops because this product

represents an extreme case in sugar confectionery. Of all of the grained products

(e.g. fondant), grained drops have the lowest water content and reducing sugar

content.

Some other examples of the effect of reducing sugar content are:

• If the reducing sugar content of a jelly is 12–14 m/m%, graining is very prob-

able (this is unambiguously a fault).

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46 Confectionery and chocolate engineering: principles and applications

• If filled hard-boiled sugar confectionery is being produced and the sugar mass

used is dry enough (reducing sugar content ca. 12–13 m/m%), the filling, if it is

an aqueous solution (e.g. a fruit filling), can induce crystallization of the sugar

mass cover. The final product will be soft and crisp. This may be the aim in

some cases, but otherwise it qualifies as a fault.

It should be emphasized that the reducing sugar content and the water content

cannot on their own characterize completely the production conditions and the

properties of the products; nevertheless, the relations presented in Figure 2.17

should provide a useful orientation for preparing recipes and for making judge-

ments about how a product will behave if its composition is known.

Let us consider some recipes in order to show how Figure 2.17 can be applied

for preparing recipes. In these recipes, the glucose syrup has the parameters

dry content = 80%; DE = 40%

2.2.2.1 DropsThe parameters of the end product are water content, 2 m/m% and reducing

sugar content, 15%. One hundred kilograms of wet glucose syrup has 32 kg of

reducing sugar and 80 kg of dry content. Therefore, 15% of reducing sugar is

contained in 100 kg× (15/32)=46.9 kg of glucose syrup, which contains 37.5 kg

dry content (+11.4 kg water). The recipe is:

46.9 kg glucose syrup

60.5 kg sugar (=98− 37.5)

ca. 30 kg water (for dissolution, which will be evaporated)

Yield: 100 kg sugar mass (2 m/m% water content)

2.2.2.2 Agar jellyThe parameters of an agar jelly are water content, 23 m/m%; reducing sugar

content, 12 m/m%; and agar-agar content, 1.25 kg. The amount of glucose syrup

is 12 kg/0.32= 37.5 kg, which has a dry content (obtained by multiplying by 0.8)

of 30 kg. The dry content of the jelly (100 kg− 23 kg= 77 kg) consists of 30 kg dry

glucose syrup+1.25 kg agar-agar+ 45.75 kg sugar. The recipe is 1.25 kg agar-agar

mixed with 10 kg sugar is added to 35.75 kg sugar +20 kg water for dissolution.

The solution is cooked to ca. 106 ∘C. At this temperature, 37.5 kg of glucose

syrup is added to the solution, which is then boiled again. Finally, the agar solu-

tion may be flavoured, coloured, dosed with starch powder, etc.

2.2.2.3 FudgeThe parameters are:

Water content (W), 10 m/m%

Reducing sugar content (R), 10 m/m%

Milk dry content (M), 10 m/m%

The fondant content is to be 20 m/m%, which has the following parameters:

Water content, 9 m/m%

Reducing sugar content, 7 m/m%

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Characterization of substances used in the confectionery industry 47

The task is to prepare a mass I, which does not contain fondant, and to prepare

a mass II of fondant; these are then to be mixed in the proportion 4 : 1.

Recipe for mass I: Because the parameters of the fudge relate to the end product,

the parameters of mass I are calculated as follows:

W × 0.8 + 9% × 0.2 = 10%, i.e. W = 10.25%

R × 0.8 + 7 × 0.2 = 10%, i.e. R = 10.75%

M × 0.8 = 10%, i.e. M = 12.5%

Because the dry content of the condensed milk used is 70%, the amount of con-

densed milk for mass I must be

12.5 kg∕0.7 = 17.9 kg

The amount of glucose syrup for mass I must be 10.75 kg/0.32=33.6 kg,

which has a dry content of 33.6 kg×0.8= 26.9 kg. The dry content of mass I

(100 kg− 10.25 kg= 89.75 kg) consists of:

12.5 kg condensed milk dry content

26.9 kg glucose syrup dry content

50.35 kg sugar

17.9 kg condensed milk+33.6 kg glucose syrup+ 50.35 kg sugar are dissolved in

ca. 30 kg water, and this solution is boiled to ca. 122 ∘C.

Recipe for mass II: If the reducing sugar content is 7%, then the amount of

glucose syrup must be

7 kg∕0.32 = 21.9 kg

The dry content of this is

21.9 kg × 0.8 = 17.5 kg

Because the total dry content of the fondant mass II is 91%, the amount of

sugar is

(91 − 17.5)kg = 73.5 kg

Therefore, 73.5 kg sugar and 21.9 kg glucose syrup are dissolved in ca. 25 kg

water and boiled to ca. 124 ∘C.

Finally, 80 kg of mass I and 20 kg of mass II are mixed.

Comment: The exact values of the water contents mentioned earlier can be

established only by measuring the boiling points of the solutions.

These examples of agar jelly and fudge may also be informative for calculat-

ing recipes for sugar confectioneries (e.g. marshmallow) that contain ingredients

other than sugar and glucose syrup.

2.2.3 Composition of biscuits, crackers and wafersIt is almost impossible to compile a comprehensive survey of the composition

of the various biscuits, crackers, etc. that exist. Table 2.5 presents some typical

composition values of various confectionery products containing flour. Table 2.6

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48 Confectionery and chocolate engineering: principles and applications

Table 2.5 Composition of various confectionery products containing flour.

Product type Sugar (%) Fat (%) Flour (%) Water (%) Comments

Honey cake 30–38 × 0 9.5–15 ×× 50–57 × Sugar/honey

×× Wheat/rice

Weisse Lebkuchen 25 10 × 40 25 ×× × Oil-containing seeds

×× Water/egg

Elise–Makronen 33–35 22–30 × 7–13 30 ×× × Almond

×× Egg white/fruit

Nusslebkuchen 48–50 18 × 16 17 ×× × Oil kernels

×× Egg white/fruit

Makronen 45–48 13 × 24 15 × Egg white

Short biscuits/Weichkeks

For cutting 20 17 56 7 × × Egg

For shaping 16 10 60 14 × × Milk

For dosing 17 22 53 8 × × Egg

Mürbteig (1 : 2 : 3) 13–15 27 40–45 19

Spekulatius 30 15 × 40 15 ×× × Almond

×× Egg

Hard/sweet biscuits 10–12 10 70 8–10

Patience 40 × 0 37 23 × Partly caramelized

Zwieback 7 6 70 17

Ladyfingers 33 0 33 34 × × Egg

Wafers 1 8 28 63

presents the relationship between the hydrophilic character and the presence of

a gluten skeleton for various products containing flour.

We emphasize that the products listed in Tables 2.5 and 2.6 correspond roughly

to German practice [see Ölsamen und daraus hergestellte Massen und Süsswaren

(1995)] and the data are merely for information. Nevertheless, these tables illus-

trate the fact that, out of the factors related to colloidal characteristics, the most

important factors influencing the properties of these products are:

• The strength of their hydrophilic character

• The presence or absence of a developed gluten skeleton

Some additional comments are:

• All these products are of hydrophilic character, that is, none of these products,

although they contain greater or lesser amounts of fat, are hydrophobic. This

hydrophilic character means an O/W colloidal nature.

• The development of a gluten skeleton requires a rather high proportion of

water (or honey or milk, etc.) in the composition.

Meyer (1949) proposes the following recipe for honey cake: 100 kg of sugar

is dissolved in 40 kg of water, the solution is boiled to 106–107 ∘C (85 ∘R), and

finally 185 kg of wheat flour is added in portions while the mixture is continu-

ously mixed. A similar but not the same ratio of ingredients is shown in Table 2.5

for Weisse Lebkuchen which presents that only approximate ingredient ratios

can be given for the recipes.

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Characterization of substances used in the confectionery industry 49

Table 2.6 Hydrophilic character and presence of

gluten skeleton for products containing flour.a

Producttype

Hydrophiliccharacter

Glutencontent

Honey cake S Yes

Weisse Lebkuchen M No

Elise–Makronen–Lebkuchen M No

Nusslebkuchen M No

Makronen W No

Short biscuits/Weichkeks

For cutting W No

For shaping W No

For dosing W No

Mürbteig (1 : 2 : 3) W No

Spekulatius W No

Hard/sweet biscuits S No

Patience S No

Zwieback S Yes

Ladyfingers S Yes

Wafers S Yes

aS= strong, M=medium, W=weak.

Some other relevant references are Kengis (1951); Les codes d’usages en con-

fiserie (1965); Gutterson (1969); Schwartz (1974); Verordening (1979); Meiners

et al. (1984); Williams (1964); Richtlinie für Zuckerwaren (1992); Földes and

Ravasz (1998); Manley (1998a,b,c); Minifie (1999); Biscuits et gateaux, Réper-

toire des dénominations et recueil des usages (2001); Édesipari termékek (2003);

Real Decreto 1978/1978, 1982/1982, 1982/1982, 1984/1984 and 1991/1991;

and Catterall (2011).

2.3 Preparation of recipes

2.3.1 Recipes and net/gross material consumptionFrom a practical point of view, the concepts of recipe, net material consumption

(NMC) and gross material consumption (GMC) can be distinguished as follows:

Recipe: This is a description of the procedure by which a product or semi-product

is to be made. It itemizes the amounts of raw materials to be used and the

technological parameters, and it may also refer to the method of shaping.

NMC: This is defined as composition of product by weight percentage. The NMC is an

important part of the product specification which does not contain any tech-

nological parameters. It is the basis for calculating the percentage composition.

GMC: The GMC is the total amount (in kg) of raw materials used for manu-

facturing a unit (e.g. 100 kg or 1 ton) of end product. It does not contain any

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50 Confectionery and chocolate engineering: principles and applications

technological parameters. The GMC is the basis for calculation of the raw mate-

rial demand of a product, material provision, stockpiling, pricing, etc.

At this point, it is reasonable to explain two other concepts related to the NMC,

which are important in trading:

Product specification: This contains product parameters, including the percentage

composition, which every item of the product must comply with. These

parameters may be either continuous (e.g. the value of a mass) or discrete

(e.g. a number of pieces).

Certificate: This refers to a certain lot, and therefore the number of the lot is the

basis for identification. Certificates are issued by the quality assurance depart-

ment of the producer. The parameters in the certificate, which are always

concrete (i.e. discrete) values that have been measured or determined, must

comply with the product specification.

What is the relationship between these concepts? A recipe is the salient point

for preparing a product composition (i.e. the NMC) and the GMC.

Example 2.8Let us consider an example of the preparation of the NMC and GMC for a milk

chocolate in a way which takes into account the steps of the technology, that is,

starting from batch recipes.

In Example 2.2, the recipe was prepared as follows.

Ingredients Total fat

Sugar 43.0 0.0

Lecithin 0.4 0.4

Whole milk powder 13.5 3.5

Skimmed milk powder 6.5 0.0

Cocoa mass 14.0 7.0

Total 77.4 10.9Cocoa butter 100− 77.4=22.6 22.6

Total 100 33.5

It can be seen that the recipe contains the amounts of raw materials in kilo-

grams. If these amounts of raw materials are mixed in a closed tank, then the

numbers of kilograms can be replaced by percentages because there is no loss

and no growth, that is, statements such as the sugar content is 43 m/m% or the fat

content of the mass is 33.5 m/m% are true. However, this recipe must be related to a

complete technological process, during which loss or growth cannot be avoided.

A brief description of the technology is as follows:

• A mass of ca. 27 m/m% fat content is made for refining.

• Dry conching (ca. 29 m/m% fat content) is carried out in a conche machine.

• Cocoa butter is then added (wet conching, with ca. 31 m/m% of cocoa butter).

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Characterization of substances used in the confectionery industry 51

• Finally, a 33.5 m/m% fat content is achieved by adding cocoa butter and

lecithin.

Although continuous kneaders are exclusively used in modern plant, we shall

do the calculation for a batch (ca. 250 kg) technology because it is more instruc-

tive.

The starting point is the aforementioned recipe, which can be regarded as

a plan of the product. Evidently, the addition of cocoa butter is necessary, since

without it the fat content would be (10.9− 0.4)/(77.4− 0.4)= 13.64% (0.4 kg of

lecithin is added at the end of conching).

The first fraction of cocoa butter added is x kg, where

10.5 + x77.0 + x

= 0.27 → x = 14.1kg

(It is assumed that the blended mass can be refined.)

The second fraction of cocoa butter added is y kg, where

10.5 + 14.1 + y

77 + 14.1 + y= 0.29 → y = 2.6kg

This mass is then dry conched.

The third fraction of cocoa butter added, in order to begin the wet conching, is

z kg, where10.5 + 14.1 + 2.6 + z77 + 14.1 + 2.6 + z

= 0.31 → z = 2.7kg

The last fraction of cocoa butter added is w kg (0.4 kg of lecithin is also added

to the mass in this step), where

10.5 + 14.1 + 2.6 + 2.7 + 0.4 + w77 + 14.1 + 2.6 + 2.7 + 0.4 + w

= 0.335 → w = 3.2kg

[For control, x+ y+ z+w= (14.1+ 2.6+ 2.7+3.2) kg= 22.6 kg; see the recipe in

the previous text.]

What is the water content of this chocolate mass? The following calculation

takes the water content of the raw materials into account.

Ingredients Water content (%) Water (kg)

Sugar 43.0 0.0 0.0

Lecithin 0.4 0.0 0.0

Whole milk powder 13.5 4.0 0.54

Skimmed milk powder 6.5 4.0 0.26

Cocoa mass 14 1.5 0.21

Cocoa butter 22.6 0.0 0.0

Total 100 1.01

Evidently, the water content of the end product that would be measured by

a laboratory measurement would be different, for example, 0.85 m/m%. What

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52 Confectionery and chocolate engineering: principles and applications

should be done in this case? It may be assumed that a certain amount of water

will be evaporated, that is, the yield is (100− 1.01) kg/0.9915= 99.84 kg [where

(100− 0.85)%= 0.9915], and the amount of water evaporated is 0.16 kg.

Therefore, all amounts of raw materials should be increased by a factor of

100/99.84=1.0016, that is, instead 43.0 kg of sugar, 43.0 kg× 1.0016=43.07 kg,

is calculated and similarly for other ingredients.

The sources of possible loss include evaporation (e.g. in the case of sugar con-

fectionery), smearing and shape defects (e.g. broken centres). On the one hand,

all of these losses are dependent on the level of the technology used, and on the

other hand, they are a question of economic efficiency: if the losses are too high,

a more advanced technology should be used because it is too expensive to use

the existing technology.

A simple rule is that for every production line and for every product made

by that line, a certain amount of loss may be accepted. For high-tech, continu-

ous machinery producing chocolate mass, the evaporation of water is the single

source of loss; however, for a batch technology, about 100.1–100.2 kg of input

results in 100 kg of end product.

Let us assume a value of 100.2 kg, so the material consumption will be as

follows (i.e. with a multiplying factor of 1.002):

Ingredients

Sugar 43.09

Lecithin 0.40

Whole milk powder 13.53

Skimmed milk powder 6.51

Cocoa mass 14.03

Cocoa butter 22.64

Total 100.20Loss 0.20Yield 100 end product

(0.85 m/m% water content)

This is the typical form of the GMC of a milk chocolate.

Since we are assuming a batch technology, the blending of raw materials fol-

lows the size of the batch (250 kg), that is, all of the amounts of raw materials and

the additional amounts of cocoa butter are to be multiplied by 2.5 (43.09 kg× 2.5,

etc.).

The exact values of the sugar content, fat content, etc. are checked by analytical

methods, and these are included in the product specification. They are the basis

of the product composition (i.e. the NMC).

It can be seen clearly that losses play an important role in the operation of a

plant: they cause costs that are mostly unnecessary and environmental pollution

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Characterization of substances used in the confectionery industry 53

as well. If 0.2 kg of chocolate is lost per 100 kg of end product, for 10 t of choco-

late, there is 20 kg of waste!

2.3.2 Planning of material consumptionThe use of the GMC is illustrated here with an example.

Example 2.9Suppose that we need to produce five products, namely, three kinds of chocolate

(A, B and C) and an unfilled (D) and a filled (E) hard-boiled sugar confectionery,

using 10 kinds of raw materials.

A general scheme for planning the material consumption of the production

processes can be given with the help of matrices, as follows:

The material matrix M10× 5 contains the GMC (per unit of product); in this

example, the ten rows relate to the raw materials, and the five columns relate

to the different products.

The production matrix P5× 1 (a column matrix) contains the amounts to be made;

in this example, the five rows relate to the amounts of the five products.

The G-matrix G10× 1 shows the possible consumption for every material accord-

ing to the GMC; in this example, the ten rows relate to the raw materials, and

the one column shows summarized amounts of the raw materials which can be

used for the different products. In the form of a matrix product,

G10×1 = M10×5 × P5×1 (2.10)

where × indicates matrix multiplication.

In the general case, the form of Eqn (2.10) is

Gn×1 = Mn×m × Pm×1 (2.11)

where the n rows of Mn×m relate to n kinds of raw material and the m columns

relate to m products, that is, this matrix contains the GMCs of m products, and

each GMC relates to n raw materials. In Pm× 1, the m rows relate to the m products

and show the amounts to be produced, and in Gn× 1, the n rows relate to the

demands for the n raw materials if m products are made.

The corresponding GMCs for 100 kg of end product are represented by the

material matrix M (Table 2.7).

Comment: It is not recommended to manufacture chocolate without cocoa mass

(see C)!

The production matrix (P) (Table 2.8) shows the amounts to be produced. The

demands for raw materials are represented by the G-matrix (Table 2.9).

Evaluation of efficiency::The opening inventory matrix O10× 1 (a column matrix) contains 10 rows concerning

the raw materials.

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54 Confectionery and chocolate engineering: principles and applications

Table 2.7 Material matrix for 100 kg of end product.

Raw materialsA

(chocolate)B

(chocolate)C

(chocolate)D

(drops)E

(drops)

Sugar 40 43 45.8 61.32 55.1

Cocoa mass 56 51.2 0 0 0

Cocoa butter 3.8 5.6 28 0 0

Cocoa powder 0 0 26 0 0

Lecithin 0.4 0.4 0.4 0 0

Vanillin crystals 0.01 0.01 0.01 0 0

Glucose syrup 0 0 0 45.24 64.2

Water 0 0 0 21.46 17.2

Citric acid hydrate 0 0 0 0.895 0.795

Fruit 0 0 0 0 4

Table 2.8 Production matrix

showing the amounts (in

tonnes and in units of 100 kg)

to be produced for each

product.

Product Amount (t) 100 kg

A 50 500

B 60 600

C 40 400

D 90 900

E 80 800

The drawing matrix F10× 1 (a column matrix) contains 10 rows concerning the raw

materials.

The closing inventory matrix Z10× 1 (a column matrix) contains 10 rows concerning

the raw materials.

The consumption matrix C10× 1 (a column matrix) contains the actual amounts of

raw materials consumed.

The G-matrix shows the obligations (soll values in German), and the column

matrix C shows the actual values consumed (ist values in German). In the form

of a matrix equation,

C10×1 = O10×1 + F10×1 − Z10×1 (2.12)

The differences are calculated using the difference matrix:

The difference matrix D10× 1 (a column matrix) shows the differences between

the prescribed amounts (G) and the actual amounts consumed for each of the

raw materials (in this example there are 10 rows, since ten raw materials are

used).

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Characterization of substances used in the confectionery industry 55

Table 2.9 G-matrix, showing

the total raw material demand

of the production process, for

each raw material.

Raw materials G=M×P

Sugar 163 388

Cocoa mass 58 720

Cocoa butter 16 460

Cocoa powder 10 400

Lecithin 600

Vanillin crystals 15

Glucose syrup 92 076

Water 33 074

Citric acid hydrate 1 441.5

Fruit 3 200

Table 2.10 Calculation of efficiency.

Raw materialsOpeninginventory Drawing

Closinginventory Consumption

Efficiency(%)

G O F Z C=O−Z+ F (C−G)/G

Sugar 163 388 4210 162 000 1751 164 459 0.6554949

Cocoa mass 58 720 153 58 000 −747 58 900 0.3065395

Cocoa butter 16 460 539 16 000 288 16 251 −1.2697448

Cocoa powder 10 400 105 11 000 553 10 552 1.4615385

Lecithin 600 128 550 29 649 8.1666667

Vanillin crystals 15 11 20 17 14 −6.6666667

Glucose syrup 92 076 24 321 75 000 7462 91 859 −0.2356749

Water 33 074 21 004 20 000 6973 34 031 2.8935115

Citric acid hydrate 1 441.5 103 1 500 119.5 1 483.5 2.9136316

Fruit 3 200 235 4 109 1150 3 194 −0.1875

In the form of a matrix equation,

D10×1 = C10×1 − G10×1 (2.13)

or, in percentages,

Efficiency(+∕−) = (C10×1 − G10×1) × 100% ∕G10×1 (2.14)

A positive value of the efficiency indicates a surplus of consumption relative to

the amount expected. Details of a calculation are shown in Table 2.10 for the

present example.

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56 Confectionery and chocolate engineering: principles and applications

Table 2.11 Values of the matrix VT and the product V1×n * Dn× 1.

Price (€/kg) DifferenceVT D=C−G V * D Materials

0.5 1071 535.5 Sugar

2 180 360 Cocoa mass

4 −209 −836 Cocoa butter

1 152 152 Cocoa powder

1 49 49 Lecithin

10 −1 −10 Vanillin crystals

0.5 −217 −108.5 Glucose syrup

0.001 957 0.957 Water

1.5 42 63 Citric acid hydrate

4 −6 −24 Fruit

Total 181.957=Σvidi

This calculation may be followed by a calculation of a value which, in the

general case, has the form

V1×n ∗ Dn×1 =∑

vidi, i = 1,2, … ,n (2.15)

where V1× n is a row matrix with n rows and one column and contains the

unit prices of n materials and * indicates a scalar product. The difference matrix

Dn× 1 = Cn× 1 −Gn× 1 shows the difference in consumption for each of the n raw

materials.

Since V1× n is a row matrix and Dn× 1 is a column matrix, their product is a

scalar (a number) – in this case, for example, it may be expressed in Euros or US

dollars. [The product of a row matrix with a column matrix (in this order!) is a

scalar.] The values of the matrix VT and the product V1× n * Dn×1 for the present

example are presented in Table 2.11. These mean a cost surplus of about 182.

(The prices in the matrix V are intended to serve as examples only.)

2.4 Composition of chocolate, confectioneries, biscuitsand wafers made for special nutritional purposes

In order to meet special nutritional requirements, certain ingredients of the tradi-

tional product composition, mostly some carbohydrate or cereals derivative (e.g.

flour), have to be replaced by appropriate substances. However, the replacement

usually raises particular issues concerning technology and food regulation.

2.4.1 Diabetes Type I and IISucrose is replaced by sugar replacers in products used for diabetes. The most fre-

quent sugar replacers are the following:

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Characterization of substances used in the confectionery industry 57

Sugar alcohols (polyols): Erythritol, hydrogenated starch hydrolysate, isomalt,

maltitol, mannitol, sorbitol, xylitol.

These are called bulk sweeteners since they can entirely replace the volume of

sucrose.

To replace the sweetness of sucrose is another essential matter, referring to

which the relative sweetness of the sugar replacers provide information; see

Table 2.12.

Artificial (intensive) sweeteners: Acesulfame potassium (Sunett, Sweet One), aspar-

tame (Equal, NutraSweet), neotame, saccharin (SugarTwin, Sweet’N Low),

sucralose (Splenda)

Novel sweeteners: Stevia extracts (date sugar Pure Via, Truvia), tagatose (Natur-

lose), trehalose

Natural sweeteners: Agave nectar, date sugar, fruit juice concentrate, honey, maple

syrup, molasses

Table 2.12 shows some informative data concerning sucrose, glucose and

polyols.

From the point of view of diabetes, the properties of erythritol and mannitol

are very beneficial.

In Chapter 3 Table 3.12 shows the latent heat and relative cooling effect of

sucrose, fructose and some polyols used in confectionery practice. The cool-

ing effect is an important property which can be beneficial in products of mint

flavour. However, its acceptance by consumers is not widely unanimous. The fact

is of technological importance that sugar replacers (polyols) do not participate in

the Maillard reaction.

A comprehensive survey on the sugar replacers is provided by the references of

Mitchell (2006), American Diabetes Association (2010), International Diabetes

Federation (2006) and Monro (2002).

Table 2.12 Glycaemic index, insulinaemic index, relative sweet and energy

values of sucrose, glucose and various polyols.

SubstanceGlycaemicindex (GI)

Insulinaemicindex (II)

Relativesweetness

Energy(cal/g)

Erythritol 0 2 70 0.2

Xylitol 13 11 100 2.5

Sorbitol 9 11 60 2.5

Mannitol 0 0 60 1.5

Maltitol 35 27 75 3

Isomalt 9 6 55 2.1

Lactitol 6 4 35 2

Polyglycitol 39 23 33 2.8

Sucrose 65 43 100 4

Glucose 100 100 74 4

The values of glycaemic index (GI) and insulinaemic index (II) are given by Livesey (2003).

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58 Confectionery and chocolate engineering: principles and applications

2.4.2 Coeliac diseaseIn the case of coeliac disease or gluten-sensitive enteropatia (gluten intolerance), the

gluten proteins of cereal trigger an autoimmune disease. These triggers are gluten

in wheat, secalin in rye and hordein in barley. Mostly avelin in rye does not

induce coeliac symptoms.

Gluten is a water-insoluble, complex mixture of cereal proteins (prolamins and

glutenins) and other constituents, the prolamins of wheat, barley, rye and oats

being gliadins, hordeins, secalins and avenins, respectively. Exposure of coeliacs

to the prolamins contained in, for example, wheat, barley and rye may result

in damage to the mucosa of the small intestine, producing a variety of symp-

toms, typically malnutrition, diarrhoea and anaemia. See Food Safety Authority

of Ireland (2008).

Cereals proven to be toxic to coeliacs are wheat, rye and barley. Cereal possibly

toxic to coeliacs is oats. Cereals non-toxic to coeliacs are rice, millet (pearl, proso,

foxtail), sorghum and maize.

For further information, see the reference CODEX STAN 11-1979 and its draft

(2007), US FDA: Gluten-Free Labeling, Food Safety Authority of Ireland (2008),

Li, J. (2009), Belton and Taylor J. (2002), Case (2006), Fenster (2007), Hagman

(2000), Washburn and Butt (2003) and Wenniger (2005).

2.4.3 Lactose intoleranceLactose intolerance, also called lactase deficiency and hypolactasia, is the inability to

digest lactose, a sugar found in milk and to a lesser extent, in dairy products. For

detailed information see NDDIC (2011).

Chocolate and confectionery industry uses a lot of semi-finished milk products

such as whole/skimmed milk powder, condensed milk with/without sugar, whey

powder, cream and milk fat. Milk fat does not contain lactose practically but oth-

ers are rich in lactose, primarily the skimmed milk powder and whey powder. All

these milk derivatives are already produced by the dairy industry in lactose-free

variations by enzymatic hydrolysis of lactose to glucose and galactose.

2.4.4 Particular technological matters of manufacturingsweets for specific nutritional purposes

2.4.4.1 Sugar-free chocolateThe task is to replace the sucrose content in the recipe by any polyol. In addition,

if the sweetening effect of polyol is less than that of sucrose, the deficiency has

to be compensated with any intensive sweetener (e.g. aspartame).

However, there is high probability that the chocolate paste produced this

way will strongly differ in consistency from the one traditionally produced. In

extreme case, the crystal water of polyol (sorbitol; cc. 9 m/m%) becomes free

at about 45 ∘C during the conching, and the consistency of the chocolate mass

gets as the mud. (A similar phenomenon takes place if the sucrose is replaced

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Characterization of substances used in the confectionery industry 59

by dextrose monohydrate if dextrose chocolate is produced.) Even in normal

conditions the consistency of the sugar-free chocolate depends on the polyol in

application. Consequently, this may disadvantageously influence the amount of

cocoa butter needed.

2.4.4.2 Sugar confectioneriesPolyols differ considerably regarding water solubility from the point of view

of compressibility, hygroscopicity, melting point, boiling point of aqueous solu-

tion, etc.

Some examples are as follow:

The boiling point of an aqueous sucrose solution of 2 m/m% is about 140 ∘C;

the one of same isomalt solution is about 157 ∘C. However, a hard-boiled sweet of

isomalt (2 m/m% water content) can be produced without any syrup, exclusively

from water and isomalt. Moreover, such a product is not hygroscopic at all: it can

be stored unpacked for 2 years(!) without any problem.

For the production of chewing or bubbling gums, various polyols seem avail-

able and are frequently used. However, during the production of comprimates,

they behave differently and need appropriate food additives. On the other hand,

sorbitol can be easily compressed.

In general, polyols are available for producing jellies, dragées and lozenges,

but the specific properties of these raw materials have to be taken into account

in developing the technology. During the production of confectioneries (e.g.

fondant, fudge), the necessary amount of syrup can be substituted by aqueous

solution of a mixture of polyols of different water solubilities.

2.4.4.3 Biscuits and wafers produced for special nutritional purposesIn recipe preparation, the significant task is to substitute the wheat flour with the

types of flour of cereals being non-toxic to coeliacs. However, such a substitution

raises a lot of technological issues which are rooted in the given technological and

machinery conditions. Therefore, a general solution cannot be recommended.

In this product group, the novel and natural sweeteners (see previous text)

are applied with a growing frequency. However, these applications raise compli-

cated labelling issues, thus a consultation with nutritional experts before product

development is highly recommended.

For further references, see Zumbé et al. (2001), Chetana (2004) and

Taylor (2006).

Currently, the so-called fortified products are in vogue. They can be regarded

as nutritional supplements which may contain vitamins, crude fibre, metal ions,

flavonoids, etc. in an increased amount. The production of such products with

traditional technologies is possible in general since the amount of these supple-

ments remain in a magnitude of some percents. However, the nutritional claims

concerning these products are strict and need therefore special expertise.

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60 Confectionery and chocolate engineering: principles and applications

Further reading

Jellies, G. (2009) The Encyclopaedia of Cereal Diseases, HGCA – BASF.

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CHAPTER 3

Engineering properties of foods

3.1 Introduction

It is important to study the changes in physical properties of foodstuffs during

unit operations because some properties (often called engineering properties)

influence heat and mass transport; such properties include, for instance, the

density, specific heat capacity and thermal conductivity/diffusivity; see Hallström

et al. (1988) or Bálint (2001).

Knowledge of the physical properties of foods is required to perform the var-

ious engineering calculations that are involved in the design of food-producing

machinery and storage and refrigeration equipment and for estimating process

times for the refrigeration, freezing, heating and drying of foods. The thermal

properties of foods are strongly dependent upon chemical composition and tem-

perature, and there are a multitude of food and raw material items available. It is

difficult to generate a database of experimentally determined physical properties

for all possible conditions and compositions of foods. The most viable option is to

predict the physical properties of foods using mathematical models that account

for the effects of chemical composition and temperature.

These properties of foods have been discussed in detail by, among others, Rha

(1975), Loncin and Merson (1979, pp. 24–30), Szczesniak (1983), Hallström et al.

(1988, Chapter 2) and Fricke and Becker (2001). Appendix 1 gives data on the

materials used in and made by the confectionery industry, classified according to

the kinds of materials.

3.2 Density

The definition of the density 𝜌 is

𝜌 =mass (kg)

volume (m3)(3.1)

In the simplest case, the structure of the substance is homogeneous and continu-

ous, in which case this definition does not need any further expansion. However,

the structures of foods can be of very different kinds, such as solids, powdered

Confectionery and Chocolate Engineering: Principles and Applications, Second Edition. Ferenc Á. Mohos.© 2017 John Wiley & Sons Ltd. Published 2017 by John Wiley & Sons Ltd.

61

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62 Confectionery and chocolate engineering: principles and applications

Table 3.1 Densities of some ingredients.

Material Density (kg/dm3)

Glucose 1.56

Sucrose 1.59

Starch 1.5

Cellulose 1.27–1.61

Protein (globular) 1.4

Fat 0.9–0.95

Salt 2.16

Citric acid 1.54

Water 1

Source: Peleg (1983). Reproduced with permission from Springer.

solids, solutions and dispersions of solids, fluids or gases, and therefore the com-

position is not homogeneous. Since the density of a food is dependent on its

composition, several different definitions of density are applicable.

In spite of all this, most foods and particles have a similar solid density of about

900–1500 kg/m3, depending on the moisture and fat content. Let us consider the

various kinds of density.

3.2.1 Solids and powdered solidsThe solid density is the density of the solid material from which the particles of

a material are made, disregarding any internal pores. (This definition is valid

for all substances and foods, whether they are porous or not, of course.) This

similarity in density is due mainly to the similar densities of the main ingredi-

ents (Table 3.1). Notable exceptions are salt-based and fat-rich powders, whose

density may vary considerably according to composition.

3.2.2 Particle densityAnother density is the particle density, which is defined as follows:

Particle density =actual mass of particles

actual volume of particles(3.2)

This parameter takes account of the existence of internal pores and therefore can

be considered as a measure of the true density of the particles. (This parameter is

more relevant to situations where the relationship between particle weight and

interparticle forces is of concern.) However, this parameter does not provide any

information regarding the shapes of the internal pores and their positions in the

particle structure. The latter can have distinctly different forms, whose character

depends on the type of process and the conditions under which the particles were

formed.

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Engineering properties of foods 63

3.2.3 Bulk density and porosityThe bulk (or apparent) density is the mass of particles that occupies a unit volume

of a bed. It is usually determined by weighing a container of known volume and

dividing the net weight of the powder by the container’s volume.

The porosity is the fraction of the volume not occupied by particles or solid

material and therefore can be expressed as either

Total porosity = 1 −bulk density

solid density(3.3)

or

Interparticle porosity = 1 −bulk density

particle density(3.4)

Because powders are compressible, their bulk density is usually given with an

additional specifier, that is, as the loose bulk density (as poured), the tapped bulk

density (after vibration) or the compact density (after compression).

Another way to express the bulk density is in the form of a fraction of the solid

density of the particles, which is sometimes referred to as the theoretical density.

This expression, as well as the use of porosity instead of density, enables and

facilitates a unified treatment and meaningful comparison of powders that may

have considerably different solid or particle densities.

3.2.4 Loose bulk densityApproximate values of the loose bulk density of a variety of food powders are

listed in Table 3.2, which shows that with very few exceptions, food powders

have apparent densities in the range 0.3–0.8 g/cm3. As previously mentioned,

the solid density of most food powders is about l.4, and therefore these values

are an indication that food powders have high porosity (i.e. 40–80%), which can

be internal, external or both. There are many published theoretical and experi-

mental studies of porosity as a function of the particle size, distribution and shape.

Mostly they pertain to free-flowing powders or models (e.g. steel shot and metal

powders), where porosity can be treated as primarily due to geometrical and

statistical factors only; see Gray (1968) and McGeary (1967–1970).

Even though the porosity can vary considerably in such cases, depending on

such factors as the concentration of fines, it is still evident that the exceed-

ingly low density of food powders cannot be explained by geometrical consider-

ations only.

Most food powders are known to be cohesive (Carr, 1976), which means that

their attractive interparticle forces are significant relative to the weight of the

particles. Since the bulk density of food powders depends on the combined effects

of interrelated factors, namely, the intensity of the attractive interparticle forces,

the particle size and the number of contact points (Rumpf, 1961), a change in

any one of the characteristics of a powder may result in a significant change in

the bulk density, with a magnitude that cannot always be anticipated; for details,

see Peleg et al. (1982).

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64 Confectionery and chocolate engineering: principles and applications

Table 3.2 Approximate bulk density and moisture content of various food

powders.

PowderBulk density(kg/dm3)

Moisturecontent (%)

Baby formula 0.40 2.5

Cocoa 0.48a 3–5b

Coffee (ground and roasted) 0.33c 7c

Coffee (instant) 0.33c 2.5c

Coffee creamer 0.47 3

Cornmeal 0.66a 12b

Cornstarch 0.56a 12b

Egg (whole) 0.34a 2–4b

Gelatin (ground) 0.68 12

Microcrystalline cellulose 0.68 6

Milk 0.61a 2–4

Oatmeal 0.43a 8b

Onion (powdered) 0.51 1–4

Salt (granulated) 0.96a 0.2b

Salt (powdered) 0.95 0.2b

Soy protein (precipitated) 0.28 2–3

Sugar (granulated) 0.80 0.52

Sugar (powdered) 0.48 0.52

Wheat flour 0.48 12b

Wheat (whole) 0.801 12b

Whey 0.56 4.5b

Yeast (active dry baker’s) 0.52 8

Yeast (active dry wine) 0.82 8

aData from Carr (1976).bData from Watt and Merrill (1975).cData from Schwarzenberg (1982).

Source: Reproduced from Peleg (1983, Table 10.1), with kind permission from

Springer Science+Business Media.

3.2.5 Dispersions of various kinds and solutionsMost solid foodstuffs contain gas, which is in general a mixture of air and water

vapour. The gas is contained in capillaries, which can be open or completely

closed. If the diameter of some of the pores is less than 10−7 m, the material is

said to be capillary porous.

Tables 3.7 and 3.8 in this chapter show data and power series for approximate

calculation of the densities of the principal components of foods, as a function of

temperature. The basis of the calculations is the fact that density is an additive

property:

𝜌 =∑

xi𝜌i (3.5)

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Engineering properties of foods 65

where 𝜌 is the density of a substance that is a mixture of n components, labelled

by i= 1, 2, … , n; 𝜌i is the density of the ith component (in kg/m3); and xi is the

mass fraction of the ith component (in kg/kg).

3.3 Fundamental functions of thermodynamics

3.3.1 Internal energyIn this section, capital letters denote molar quantities, except for T (temperature).

The internal energy U is the total microscopic energy of a system. It is related to

the molecular structure and the degree of molecular activity in the system. In

this respect, it can be considered as the sum of the potential and kinetic energy

of the system, but at the molecular scale such as the energy used for chemical

bonds between atoms or molecules. It is defined by

U = TS − pV + 𝜇N (3.6)

where S is molar entropy, p pressure, V molar volume, 𝜇 chemical potential and

N molar number. From this relationship, the so-called fundamental functions of

thermodynamics can be derived; the functions most often used are summarized

in Table 3.3.

The enthalpy (ΔH) is of great practical importance since it equals the change of

internal energy of the system plus the work provided to its surroundings. It can

therefore be used to calculate the heat absorbed or released during a reversible

isobaric (constant pressure) reaction.

The usual name of the function F is the Helmholtz free energy, and the Gibbs

energy (or free enthalpy, G) is the maximum quantity of energy that can be

released as non-expansion (process initiating) work from a closed system dur-

ing an isothermal and isobaric reaction. To reach this maximum it has to be a

reversible (quasi-static) process.

In food practice, the importance of non-molar quantities cannot be overesti-

mated, because the molar amounts of foods are usually unknown. Therefore, in

the following discussion, we often ignore the convention of using capital letters to

denote molar quantities only. We emphasize that thermodynamic relationships

Table 3.3 Some fundamental functions of thermodynamics.

Fundamental function Molar relationship

Enthalpy H=U+pV= TS+𝜇N

Free energy F=U− TS=−pV+𝜇N

Free enthalpy G=U− TS+ pV=𝜇N

Energy U= F+ TS

Enthalpy H=G+ TS

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66 Confectionery and chocolate engineering: principles and applications

that are valid in general are valid also for molar quantities, but the converse of

this statement cannot be assumed to be true.

The molar specific heat capacity at constant volume (CV ≡ (𝜕U/𝜕T)V) and at constant

pressure (Cp) can be derived (if p= constant) from the following equation:

H = U + pV → dH = dU(T;V ) + p dV (3.7)(

dHdT

)

p

≡ Cp =(𝜕U𝜕T

)

V+(𝜕U𝜕V

)

T

(𝜕V𝜕T

)

p+ p

(𝜕V𝜕T

)

p

= CV +[(𝜕U𝜕V

)

T+ p

] (𝜕V𝜕T

)

p(3.8)

For an ideal gas, pV=RT, that is, (𝜕U/𝜕V)T = 0 and (𝜕V/𝜕T)p =R/p, where

R=8.31434 J/mol K, the molar gas constant. Consequently, for an ideal gas,

Cp = CV + R (3.9)

For real gases, the appropriate alternative gas law (van der Waals equation, van

Laar equation, Beattie-Bridgeman equation, Redlich-Kwong equation etc.) is the

basis of calculations. The relationship

cp > cV (3.10)

is a general rule for all substances, where cp and cV are the specific heat capacities

per unit mass at constant pressure and volume, respectively. For gases, cp and cV

are of the same magnitude.

The difference between the two types of specific heat capacity for homoge-

neous solids and liquids can be calculated on the basis of the second law of

thermodynamics:

Cp − CV = T(𝜕p∕𝜕T)V (𝜕V∕𝜕T)p = TV ∘𝛼2∕𝜒 (3.11)

where V∘ is the volume for a given standard condition, 𝛼 = (1/V∘)(𝜕V/𝜕T)p is the

coefficient of thermal expansion (>0) and 𝜒 =−(1/V∘)(𝜕V/𝜕p)T is the coefficient

of compressibility (>0). This difference between the two types of specific heat

capacity corresponds to the work of volume, and for solids and liquids this is only

a small percentage of Cp (or cp), in contrast to the case of gases, for which the

work of volume can be important.

The relationships between the two types of specific heat capacity are important

because a practical determination of cV cannot be carried out: heating at constant

volume is not possible. In practice, the specific heat capacity at constant pressure

is always used.

3.3.2 EnthalpyThe enthalpy can be calculated as an integral of the specific heat capacity over a

given interval of temperature:

h =∫

T2

T1

cp dT (3.12)

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Engineering properties of foods 67

Normally, cp is almost constant within the temperature region of interest (in

which T is usually measured in ∘C and usually−20 ∘C< T< 100 ∘C), and therefore

the aforementioned equation (3.12) may be approximated as

h = cp(T2 − T1) (3.13)

This supposition of constant specific heat capacity is reflected in Tables 3.7

and 3.8 and Eqn (3.19), which give average values of the density, specific

heat capacity and thermal conductivity for various food components (water,

carbohydrate, protein, fat, air, ice and inorganic minerals). If the composition of

a foodstuff is known, an approximate calculation of these material parameters

can be done.

3.3.3 Specific heat capacity calculationsThe specific heat capacities of foodstuffs depend very much on the composition.

The specific heat capacity of water is 4.18 kJ/kg K, while that of the solid con-

stituents is much lower, 1–2 kJ/kg K (Table 3.4). Heldman (1975) suggested the

following formula, together with numerical values, to estimate the specific heat

capacities of foodstuffs based on composition:

cp =∑

xicpi (3.14)

where xi is the mass concentration of the ith constituent, that is, the proportion

by mass. Equation (3.14) expresses the fact that specific heat capacity is an addi-

tive property, but calculations based on the data in Table 3.4 do not differentiate

between the various kinds of carbohydrates, fats and so on. Thus the fact, for

example, that aqueous solutions of 80 m/m% sucrose and 80 m/m% corn syrup

are different cannot be taken into account.

However, if a change of phase or some other type of transformation takes place,

the enthalpy of the system changes because of latent heat. In this case a so-called

apparent specific heat capacity is measured; see Section 3.4.2.

Table 3.4 Thermal properties of food constituents.

ComponentMass concentration

(kg/kg)Density(kg/m3)

Specific heatcapacity (kJ/kg K)

Thermal conductivity(W/m K)

Water cw 1000 4.182 0.60

Carbohydrate cc 1550 1.42 0.58

Protein cpr 1380 1.55 0.20

Fat cf 930 1.67 0.18

Air ca 1.24 1.00 0.025

Ice ci 917 2.11

Inorganic minerals cm 2400 0.84

Source: Reproduced with kind permission from Springer Science+Business Media.

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68 Confectionery and chocolate engineering: principles and applications

Table 3.5 Calculation of specific heat capacity of milk chocolate and dark chocolate.a

Milk chocolate {8.301} Dark chocolate {8.302}

cp

Ingredients(g/kg) cp (J/g K)

Ingredients(g/kg) cp (J/g K)

Calculation using the data in Table 3.4

Water 4.182 8 33.456 10 41.82

Ash 0.84 19 15.96 12 10.08

Protein 1.55 86 133.3 62 96.1

Fat 1.67 348 581.16 310 517.7

Carbohydrate 1.42 539 765.38 606 860.52

Total for composition 1529.256 J/kg K 1526.22 J/kg K

Calculation using Eqns (3.17) and (3.18)

Milk chocolate {8.301} Dark chocolate {8.302}

cp =1.67+2.5xw (Eqn 3.17) 1.69 kJ/kg K 1.695 kJ/kg K

cp =1.40+3.2xw (Eqn 3.18) 1.423 kJ/kg K 1.432 kJ/kg K

aSource of compositions: Livsmedelstabeller – energi och vissa näringsämnen (1978). The numbers in braces

{ } are the product numbers used in that publication.

Table 3.6 Calculation of specific heat capacity of orange marmalade and almond paste.a

Orange marmalade {8.100} Almond paste {8.350}

cp Ingredients (g/kg) cp (J/g K) Ingredients (g/kg) cp (J/g K)

Calculation using the data in Table 3.4

Water 4.182 408 1706.256 90 376.38

Ash 0.84 2 1.68 13 10.92

Protein 1.55 0 0 98 151.9

Fat 1.67 0 0 229 382.43

Carbohydrate 1.42 590 837.8 570 809.4

Total for composition 2545.736 J/kg K 1731.03 J/kg K

Calculation using Eqns (3.17) and (3.18)

Orange marmalade {8.100} Almond paste {8.350}

cp =1.67+2.5xw (Eqn 3.17) 2.69 kJ/kg K 1.895 kJ/kg K

cp =1.40+3.2xw (Eqn 3.18) 2.706 kJ/kg K 1.688 kJ/kg K

aSource of compositions: Livsmedelstabeller – energi och vissa näringsämnen (1978). The numbers in braces

{ } are the product numbers used in that publication.

Some calculations performed using Table 3.4 are summarized in Tables 3.5–3.7.

An approximate expression for foodstuffs containing mainly water is

cp = 4.18xw (3.15)

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Engineering properties of foods 69

Table 3.7 Calculation of specific heat capacity of cocoa nibs and sweets.a

Cocoa nibs Sweets

cp

Ingredients(g/kg)

cp

(J/g K)Ingredients

(g/kg)

cp

(J/g K)

Calculation using the data in Table 3.4

Water 4.182 27.5 115.005 100 418.2

Ash 0.84 34 28.56 0 0

Protein 1.55 23.5 36.425 0 0

Fat 1.67 525 876.75 0 0

Carbohydrate 1.42 390 553.8 900 1278

Total for composition 1610.54 J/kg K 1696.2 J/kg K

Calculation using Eqns (3.17) and (3.18)

Cocoa nibs Sweets

cp =1.67+2.5xw (Eqn 3.17) 1.739 kJ/kg K 1.92 kJ/kg K

cp =1.40+3.2xw (Eqn 3.18) 1.488 kJ/kg K 1.72 kJ/kg K

Source: Minifie (1989a,b). Reproduced with permission from Springer.

or

cp = 4.18xw + 2xd (3.16)

where xd is the dry matter content of the material (xd = 1− xw). For fish and meat,

with xw < 0.25, and for fruit and vegetables, with xw > 0.50, the following formula

was suggested by Andersen and Risum (1982):

cp = 1.67 + 2.5xw (3.17)

For sorghum and other cereals with a low water content, the following equation

may be used:

cp = 1.40 + 3.2xw (3.18)

Let us calculate some specific heat capacity values using Table 3.4 and Eqns

(3.17) and (3.18). The specific heat capacity, similarly to the density, thermal con-

ductivity and thermal diffusivity, is usually expressed as a series in T (in K or ∘C);

see Tables 3.8 and 3.9. The values for the specific heat capacity of milk choco-

late (No. 8.301; see Table 3.5) shown in Table 3.10 were calculated according to

Tables 3.8 and 3.9.

If, instead, we calculate the specific heat capacity for milk chocolate of the

same composition by the methods described earlier, where the temperature is

not taken into account, the results are as follows:

Using the data in Table 3.4, 1529 J/kg K

Using Eqn (3.17), 1690 J/kg K

Using Eqn (3.18), 1423 J/kg K

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70 Confectionery and chocolate engineering: principles and applications

Table 3.8 Thermal property equations for food components (−40 ∘C≤ t≤ 150 ∘C).

Thermal property and food component Thermal property model

Thermal conductivity [W/(m K)]

Protein k=1.7881× 10−1 +1.1958× l0−3t−2.7178× 10−6t2

Fat k=1.8071× 10−1 +2.7604× 10−3t−1.7749× l0−7t2

Carbohydrate k=2.0141× 10−1 +1.3874× 10−3t−4.3312× 10−6t2

Fibre k=1.8331× 10−1 +1.2497× 10−3t−3.1683× 10−6t2

Ash k=3.2962× 10−1 +1.4011× 10−3t−2.9069× 10−6t20

Thermal diffusivity (m2/s)

Protein a=6.8714× 10−8 +4.7578× 10−10t−1.4646× 10−12t2

Fat a=9.8777× 10−8 −1.2569× 10−10t−3.8286× 10−14t2

Carbohydrate a=8.0842× 10−8 +5.3052× 10−10t−2.3218× 10−12t2

Fibre a=7.3976× 10−8 +5.1902× 10−10t−2.2202× 10−12t2

Ash a=1.2461× 10−7 +3.7321× 10−10t−1.2244× 10−12t2

Density (kg/m3)

Protein 𝜌=1.3299× 103 −5.1840× 10−1t

Fat 𝜌=9.2559× 102 −4.1757× 10−1t

Carbohydrate 𝜌=1.5991× 103 −3.1046× 10−1t

Fibre 𝜌=1.3115× 103 −3.6589× 10−1t

Ash 𝜌=2.4238× 103 −2.8063× 10−1t

Specific heat capacity [J/(kg K)]

Protein cp =2.0082× 103 +1.2089t−1.3129× 10−3t2

Fat cp =1.9842× 103 +1.4733t−4.8008× 10−3t2

Carbohydrate cp =1.5488× 103 +1.9625t−5.9399× 10−3t2

Fibre cp =1.8459× 103 +1.8306t−4.6509× 10−3t2

Ash cp =1.0926× 103 +1.8896t−3.6817× 10−3t2

Source: KISTI.

Table 3.9 Thermal property equations for water and ice (−40 ∘C≤ t≤150 ∘C).

Thermal property and food component Thermal property model

Water

Thermal conductivity [W/(m K)] kw =5.7109× 10−1 +1.7625× 10−3t−6.7036× 10−6t2

Thermal diffusivity (m2/s) aw =1.3168× 10−7 +6.2477× 10−10t−2.4022× 10−12t2

Density (kg/m3) 𝜌w = 9.9718×102 +3.1439× 10−3t−3.7574×10−3t2

Specific heat capacity [J/(kg K)]a cp =4.0817×103 −5.3062t+9.9516× 10−1t2

Specific heat capacity [J/(kg K)]b cp =4.1762×103 −9.0864×10−2t+5.4731× 10−3t2

Ice

Thermal conductivity [W/(m K)] kice =2.2196−6.2489× 10−3t+1.0154×10−4t2

Thermal diffusivity (m2/s) aice = 1.1756× 10−6 −6.0833×10−9t+9.5037× 10−11t2

Density (kg/m3) 𝜌ice =9.1689× 102 −1.3071× 10−1t

Specific heat capacity [J/(kg K)] cp ice = 2.0623×103 +6.0769t

aFor the temperature range −40 to 0 ∘C.bFor the temperature range 0–150 ∘C.

Source: KISTI.

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Engineering properties of foods 71

Table 3.10 Specific heat capacity of milk chocolate no. 8.301

calculated according to the thermal property model of Choi

and Okos (1986).

Temperature (∘C) C(t) (J/kg K)

0 1752.179

10 1768.779

20 1784.388

35 1805.942

Source: KISTI.

Table 3.11 Specific heat capacity (J/kg K) of several materials used

or produced by the confectionery industry.

Product w (s) c (Chen, 1985)

Milk chocolate 0.992 1295.352

Bitter chocolate 0.958 1434.451

Orange marmalade 0.592 2698.106

Almond paste 0.91 1623.757

Cocoa nibs 0.973 1373.607

Sweets 0.9 1662.188

For unfrozen foods, the following simple approximation for the specific heat

capacity was given by Chen (1985):

c (J∕kgK) = 4190 − 2300w(s) − 628w(s)2 (3.19)

where w(s) is the mass fraction of the solids in the food. Using this equation,

the specific heat capacities (in J/kg K) shown in Table 3.10 were obtained for the

various foods listed in Tables 3.5–3.7 (see Table 3.11).

3.4 Latent heat and heat of reaction

3.4.1 Latent heat and free enthalpyA definition of the heat of transformation can be given by studying the general

stoichiometric relationship of a transformation:

∑rAMA →

∑rBMB (3.20)

or

LAB =(𝜕H𝜕𝜉

)

p,T

=(∑

rBHB−∑

rAHA

)(3.21)

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72 Confectionery and chocolate engineering: principles and applications

where LAB is the thermal effect of the transformation under isobaric and isother-

mal conditions when a substance A transforms to a substance B, 𝜉(0→1) is the

degree of change, rA and rB are the stoichiometric values in the stoichiometric

equation for the relationship and HA and HB are the molar enthalpies of A and

B, respectively. Equation (3.21) can be regarded as the definition of the heat of a

phase transition.

If the system studied consists of n components of chemical activity 𝜇, such that

N𝜇 =∑

Ni𝜇i, i = 1,2, … ,n (3.22)

where N is the number of molecules and 𝜇i is the chemical activity (in J/kg) of

the ith type of molecule, of number Ni (and where N=ΣNi), then the free enthalpy

function g (in J/kg) introduced by Gibbs is

g = h − Ts = N𝜇 (3.23)

where s is the entropy (J/kg K) and T is the temperature (K).

Under isothermal and isobaric conditions (i.e. T= constant and p= constant),

Δg = Δ𝜇 (3.24)

where Δ𝜇 is the change in the chemical activity of the system.

The name free enthalpy (see Eqn 3.23) can be understood since G=H− Ts. H

is the total enthalpy and Ts is the enthalpy bound to the system. The difference

between these two terms is therefore the free (available) enthalpy of the system

under isolated conditions, which can be released as a result of chemical reactions.

The bound energy relies in the arrangement of molecules and can be released

when the structure of the material is compromised as during a phase change in

chocolate when fat crystals melt.

It can be derived from the potential functions of thermodynamics that(𝜕s𝜕𝜂i

)

T ,𝜂

= 𝜆i∕T (3.25)

where 𝜂i is the concentration of the substance the latent heat (𝜆i) of which is

involved in a phase transition, 𝜂 is the concentration of all other substances in

the system and T is the temperature of the phase transition.

The term latent heat, although old-fashioned, is reasonable since during a phase

transition the temperature remains constant (an isothermal condition), that is, heat

absorption is not accompanied by an increase in temperature, because during the

phase transition a structural transformation (e.g. ice→water at 0 ∘C) takes place.

According to the convention used in thermodynamics, a process is endother-

mic (LAB is positive) if the system absorbs heat; in the opposite case it is exother-

mic, that is, the system loses (produces) heat; see Lund (1983).

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Engineering properties of foods 73

3.4.2 Phase transitionsIn the traditional classification scheme of Ehrenfest (see Fényes, 1971), phase

transitions are divided into two broad categories.

First-order phase transitions are those that involve a latent heat. During such

a transition, a system either absorbs or releases a fixed (and typically large)

amount of energy. Because energy cannot be instantaneously transferred

between the system and its environment, first-order transitions are associated

with mixed-phase regimes, in which some parts of the system have completed

the transition and others have not. This phenomenon is familiar to anyone

who has boiled a pan of water: the water does not instantly turn into gas, but

forms a turbulent mixture of water and water vapour bubbles. Mixed-phase

systems are difficult to study, because their dynamics are violent and hard to

control. According to IUPAC (1997), a first-order phase transition is a transition

in which the molar Gibbs energies (G, the free enthalpy) or molar Helmholtz

energies (F, the free energy) of the two phases (or the chemical potentials of all

components in the two phases) are equal at the transition temperature, but their

first derivatives with respect to temperature and pressure are discontinuous at

the transition point, that is,

(𝜕G𝜕T

)

p=(𝜕𝜆i

𝜕T

)

p

=𝜆i

0→ ∞

where T is constant, that is, 𝜕T=0.

At this temperature, dissimilar phases coexist and can be transformed into one

another by a change in a field variable such as the pressure, temperature, mag-

netic field or electric field.

The second class of phase transitions is that of continuous phase transitions,

also called second-order phase transitions. These have no associated latent heat.

Examples are the ferromagnetic transition and the superfluid transition – but

these are not interesting from the point of view of our study. Gelation can be

regarded a second-order phase transition; see Chapter 5.12.

Several transitions are known to be infinite-order phase transitions. For fur-

ther details, see Fényes (1971). The topic of phase transitions is a current research

area in physics and mathematics.

An up-to-date classification of the order of a phase transition is given by Fisher

(1974, 1998):

A phase transition occurs if in the thermodynamic limit the free energy den-

sity f (or other thermodynamic potentials) is non-analytic as a function of its

parameters (T, temperature; H, enthalpy).

A phase transition is of n′th order if the thermodynamic potential has (n−1)

continuous derivatives, but the n′th derivative is discontinuous or divergent.

For more details, see Stauffer et al. (1982) and Privman et al. (1990).

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74 Confectionery and chocolate engineering: principles and applications

The definition of the heat of transformation in Eqn (3.21) can also be written

in the form ∑rAHA+ΔH =

∑rBHB (3.26)

where ΔH is the change of enthalpy in a chemical reaction or the latent heat if

Eqn (3.26) relates only to a phase transition.

In practice, the process takes place over a temperature range from t1 to t2, and

one or more components of the substance may partially melt or evaporate, that

is, phase transitions may occur to some extent without any chemical reaction.

For such a process, the enthalpy balance is∑

aicai =∑

bjcbj (3.27)

where ai and bj are the amounts of the output and input substances, respectively,

and cai and cbj are the specific heat capacities of the output and input substances,

respectively.

In such cases the specific heat capacity of the output substances cbi apparently

incorporates latent heats too. Therefore, such specific heat capacities should be

called apparent specific heat capacities. A deeper thermal analysis of the process

needs a determination of the latent heat separately.

Let us consider the types of phase transitions that are important from

the viewpoint of confectionery manufacture. These are, in general, evapo-

ration/condensation, melting/solidification and modification of the crystal

structure of fats and oils (e.g. cocoa butter) and of lactose.

In confectionery practice, the solubility of carbohydrates (e.g. sucrose) in water

and the solid-phase content of the fats used also play an important role.

3.4.2.1 Solution–evaporation–crystallizationThe heat of vaporization of water is 2256 kJ/kg at l00 ∘C and 101.3 kPa. Other

volatile substances in food are normally of minor importance when one is cal-

culating the heat of vaporization. For liquid foods, the boiling point is somewhat

higher than 100 ∘C, depending on the concentration of solids. For well-defined

solutions, the elevation of the boiling point is proportional to the molar concen-

tration of the solute. This topic is discussed in detail for the solutions used in

confectionery manufacture in Chapters 8 and 9.

Table 3.12 shows the (positive) latent heat of solution of some carbohydrates

and polyalcohols (bulk sweeteners) that are important in confectionery prac-

tice. Their cooling effect is a consequence of the positivity of the latent heat of

solution. For further details relating to bulk sweeteners, see Albert et al. (1980).

In the mouth, these carbohydrates exert a cooling effect according to the follow-

ing equation, which treats the mouth as an adiabatic (closed) system:

Δh + cpΔT = 0 (3.28)

where Δh is the latent heat (in J/kg) of the carbohydrate to be dissolved in

the mouth, cp is the specific heat capacity of saliva and ΔT is the change in

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Engineering properties of foods 75

Table 3.12 Latent heat and relative cooling effect of sucrose, fructose and

some polyols used in confectionery practice.

Substance Latent heat [kJ/kg] Relative cooling effect

Sucrose 18.7 1

Fructose 48.6 =48.6/18.7=2.6

Sorbitol 82.3 4.4

Xylitol 125.3 6.7

Maltitol 46.8 2.5

Isomalt 39.3 2.1

Lactitol 26.2 1.4

Remark: The example of fructose presents how the relative cooling effect is calcu-

lated related to the cooling effect of sucrose.

temperature due to the effect of the dissolution of the carbohydrate. Because

Δh> 0, ΔT<0 (cp > 0). The cooling effect is strongest in the case of xylitol; the

smallest effect, which can be imperceptible, is exerted by sucrose. Although the

supposition of an adiabatic system is only a rough approximation, it characterizes

the conditions correctly.

Another important consequence of the positive latent heat of these substances

is that the process of dissolution can be made to take place more effectively by

warming.

The latent heat of crystallization is equal to the latent heat of solution, but the

sign is negative. This means that the crystallization of these carbohydrates is an

exothermic process and crystallization can be induced by cooling; this is done,

for example, in the manufacture of fondant mass.

The exothermic nature of the crystallization of sucrose can be observed well

during the operation of pulling when satin bonbons of grained structure are pro-

duced: the arms of the pulling machine must be cooled to prevent sticking of the

invert sugar content of the sugar mass. Moreover, if the reducing sugar content

of the sugar mass is too low (below ca. 4%), a very rapid crystallization starts,

and as a consequence the sugar mass transforms into large crystals while very

rapidly growing warm. For further details, see Chapter 10.

3.4.2.2 Chemical reactionsIf a chemical reaction takes place, then ΔH relates to the change of enthalpy called

the heat of reaction. In confectionery practice, the pyrolysis of carbohydrates plays

an important role, for example, in the melting of sugar. Raemy and Schweizer

(1982, 1986) have carried out extensive calorimetric investigations of the ther-

mal degradation of a range of sugars and polysaccharides. Under the experimen-

tal conditions employed in their studies, the decomposition reactions yielded

exothermic transitions; temperature and enthalpy values are given in Table 3.13.

For example, in the case of sugar, pyrolysis starts at 190 ∘C and culminates at

215 ∘C. The pyrolysis of sucrose is discussed in detail in Chapter 16.

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76 Confectionery and chocolate engineering: principles and applications

Table 3.13 Temperatures and enthalpies (ΔH) of exothermic reactions of carbohydrates during

pyrolysis.

Carbohydrate Onset temperature (∘C) Peak temperature (∘C) Enthalpy (kJ/kg)

Monosaccharides 170–200 195–230 620–780

Disaccharides 190–220 215–245 600–800

Polysaccharides 160–200 200–245 630–720

Intense exothermic effects were observed by Raemy (1981), Raemy and Lam-

belet (1982) and Raemy and Loliger (1982) with foods of high carbohydrate

content (>60%), such as coffee and chicory products and a range of cereals and

oilseeds; the roasting and carbonization of these materials were linked to the

pyrolytic exothermic events.

Concerning the heat of reaction, we should mention that the energy content of

foods from the point of view of nutrition is equal to their heat of combustion. This

nutritional topic, however, is beyond the scope of this book.

3.5 Thermal conductivity

3.5.1 First Fourier equationIn a steady-state situation, the rates of heat transfer in every section of a rod con-

ducting heat are equal. Considering an element of the rod of differential length

dx, the rate of heat transfer through this element is given by the first Fourier

equation:dQdt

= −𝜆AdTdy

(3.29)

where y is the distance in the direction of heat transfer (m), Q is the amount of

heat transferred (J) (dQ/dt is in units of W), t is the time (s), A is the area at right

angles to the direction of heat transfer (m2), 𝜆 is the thermal conductivity of the

material (W/m K) and T is the temperature (K).

The steady-state situation is equivalent to

dQdt

= constant anddTdt

= 0 (3.30)

3.5.2 Heterogeneous materialsIn food and confectionery practice, the materials processed are mainly heteroge-

neous, although there are a few exceptions, for example, crystalline sucrose, salt

and anhydrous citric acid.

The simplest case is of a food consisting of two components. If the thermal

conductivities in a two-component material are 𝜆1 and 𝜆2, the total apparent or

effective conductivity depends on the heat flow direction. If the flow of heat is

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Engineering properties of foods 77

parallel to the layers of material, the thermal conductivity is given by

𝜆∥ = 𝜆1(1 − x) + 𝜆2x (3.31)

where x is the volume fraction of material 2. On the other hand, if the heat flow

is perpendicular to the layers of material, the thermal conductivity is given by

1𝜆⟂

= 1 − x𝜆1

+ x𝜆2

(3.32)

or

𝜆⟂ =𝜆1𝜆2

x𝜆1 + (1 − x)𝜆2

(3.33)

Evidently, Eqns (3.31) and (3.32) follow Kirchhoff’s laws.

If the materials are not oriented in layers as assumed earlier but instead are

completely random, the conductivity will have a value between 𝜆|| and 𝜆⟂. For

further details, see Hallström et al. (1988) and Fricke and Becker (2001).

3.5.3 Liquid foodsThe thermal conductivities of liquids are generally modelled by equations as

follows:

𝜆 = 𝜆0 + BT (3.34)

or

𝜆 = 𝜆0 + BT + CT2 (3.35)

Further expressions describing the thermal conductivity as a function of temper-

ature and also of concentration and constituents can be found, for example, in

the reviews by Cuevas and Cheryan (1978) and Fricke and Becker (2001).

According to Loncin and Merson (1979), the thermal-conductivity value for

starch (0.15 W/m K) is a good average value for carbohydrates and proteins in

the compact state; this conductivity is clearly lower when these products occur

in a porous or fibrous form containing air.

3.5.4 Liquids containing suspended particlesMaxwell gave an equation for calculating the thermal conductivity of a compos-

ite medium consisting of a liquid containing suspended particles:

𝜆S = 𝜆L

[2𝜆L + 𝜆P − 2xV(𝜆L − 𝜆P)]2𝜆L + 𝜆P + xV(𝜆L − 𝜆P)

(3.36)

where 𝜆S is the thermal conductivity of the whole suspension, 𝜆L is the thermal

conductivity of the liquid suspending medium, 𝜆P is the thermal conductivity

of the dispersed particles and xV is the volume fraction of the suspended parti-

cles. The distance between the particles must be large compared with the particle

radius, that is, xV must be small. For xV greater than 0.1, modifications have to be

made to Eqn (3.36). Eucken (1940) and, later, Levy (1981) introduced a modified

version of the Maxwell equation, cited by Fricke and Becker (2001).

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78 Confectionery and chocolate engineering: principles and applications

3.5.5 GasesThe area of the thermal properties of gases is one where theoretical and empirical

methods of calculation are in relatively good agreement.

The following relationship can be derived theoretically for pure gases:

𝜆M𝜂

=(9

4

)R + CV (3.37)

where 𝜆 is the thermal conductivity [in cal/(cm K s)], 𝜂 is the dynamic viscosity

of the gas (in poise=0.1 Pa s), M is the molar mass of the gas (in g/mol), CV is the

molar specific heat capacity at constant volume (in cal/mol K) and R is the molar

gas constant=1.98 cal/mol K. Many modifications of this relationship are in use.

The dependence of the thermal conductivity on temperature can be expressed

by the simple empirical formula

𝜆1

𝜆2

=(

T2

T1

)1786

(3.38)

where the indices 1 and 2 relate to the two different temperatures T1 and T2.

More complicated formulae are in use for the dependence on pressure:

For gas mixtures, a calculation of the weighted average

𝜆 =∑

xi𝜆i (3.39)

or the weighted average of the reciprocals of the thermal conductivities

1𝜆=∑ xi

𝜆i

(3.40)

gives a relatively good result. A detailed discussion of the topic has been given

by Szolcsányi (1975).

3.6 Thermal diffusivity and Prandtl number

3.6.1 Second Fourier equationThe thermal diffusivity is defined by the second Fourier equation, which refers

to unsteady-state conditions, that is, dT/dt≠ 0:

dTdt

= 𝜆

cp𝜌

𝜕2T𝜕y2

(3.41)

𝜆

cp𝜌= a, the thermal diffusivity (m2∕s) (3.42)

where 𝜆 is the thermal conductivity of the material (W/m K), cp is the specific heat

capacity of the material [J/(kg K)] and 𝜌 is the density of the material (kg/m3).

The name thermal diffusivity suggests a similarity to the mass diffusivity D,

which is defined by the second Fick equation, which in turn is formally similar

to the second Fourier equation. However, this is more than a formal similarity:

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Engineering properties of foods 79

the mechanisms of heat and mass diffusion are not only similar but also cou-

pled – the various analogies used in chemical engineering are founded on this

idea, probably first proposed by Reynolds (see Chapter 1).

3.6.2 Liquids and gasesThe thermal diffusivity a is dependent on the thermal conductivity 𝜆, the specific

heat capacity cp and the density 𝜌 of the material in which thermal diffusion

takes place. This fact illustrates why it can be difficult to give a simple method

for exactly calculating the thermal diffusivity of a material, since all the latter

three properties themselves are difficult to calculate.

No general method exists for calculating the thermal conductivity of liquids.

Numerous measurement methods have been published; for details see Loncin

and Merson (1979) and Section 3.5.

Generally, the thermal conductivity of a weakly polar liquid diminishes slightly

when the temperature is raised; however, that of a strongly polar liquid increases.

This increase is most significant in the case of water at temperatures between 0

and 150 ∘C.

For solid or liquid products containing at least 40% water and for tempera-

tures between 0 and 100 ∘C, Riedel (1969) showed that the thermal diffusivity

is a weighted average of that of water at the same temperature and that of the

dry protein, lipid or carbohydrate material, for which he obtained a mean exper-

imental value of 0.0885× 10−6 m2/s. Thus,

a = 0.0885 × 10−6(awater − 0.0885 × 10−6)xwater (3.43)

where a is the thermal diffusivity of the product, awater is the thermal diffusivity

of liquid water at the given temperature and xwater is the mass fraction of water.

When the temperature of a product rich in water is less than 0 ∘C, the prop-

erties depend essentially on the proportion of frozen water, the thermal conduc-

tivity of ice being distinctly above that of water and of dry material.

3.6.3 Prandtl numberThe Prandtl number Pr is important in heat and mass transfer. Recall the follow-

ing numbers from Chapter 1:

Reynolds number: Re=2Rv𝜌/𝜂

Prandtl number: Pr= Pe/Re= 𝜈/a

Schmidt number: Sc= Pe′/Re= 𝜈/D

Lewis number: Le= Sc/Pr= a/D

where R is the characteristic radius of a tube, 𝜈 = 𝜂/𝜌 is the kinematic viscosity

(m2/s), D is the diffusion coefficient (m2/s) and a is the thermal diffusivity (m2/s).

The Prandtl and Schmidt numbers are material parameters of a fluid. Although

Pr= 𝜈/a, that is, it can be calculated as a ratio of two empirically measured quan-

tities, there are other relationships for calculating it too.

For gases, the following rules are recognized:

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80 Confectionery and chocolate engineering: principles and applications

Monatomic gases: Pr= 0.67±5%

Non-polar gases: Pr=0.79± 15%

Polar gases with linear molecules: Pr=0.73± 15%

Strongly polar gases: Pr=0.86± 8%

Water vapour and ammonia: Pr≈1

The dependence of Pr on the pressure can be calculated by taking account of

the specific heat capacity cp as a function of p and T and also the coefficient of

compressibility Z (Szolcsányi, 1972, 1975, Chapter 2).

For liquids, according to Denbigh (1946), the Prandtl number can be calculated

from the latent heat of evaporation (ΔH)ev or from the change of entropy (ΔS)ev

of evaporation and the normal boiling point Tn at a given temperature (T) (in K):

log Pr = 0.2

[ (ΔH)ev

RT

]− 1.8 (3.44)

or

log Pr =0.10[(ΔS)ev(Tn)]

T − 1.8(3.45)

where R= 1.98 cal/mol K, (ΔH)ev is in cal and (ΔS)ev is in cal/K.

Note that the relationships described in Eqns (3.44) and (3.45) are valid for liq-

uids consisting of chemically homogeneous substances. Therefore – disregarding

a few exceptions – they cannot be applied to confectionery practice, in which the

majority of solutions are aqueous solutions of carbohydrates, and when they are

evaporated, pure water will be evaporated and not the dry content. Nevertheless,

the enthalpy and entropy of evaporation of water and the Prandtl numbers of

such solutions are practically independent of each other.

The Riedel equation (Eqn 3.43) facilitates estimation of the Prandtl numbers

of foods with a water content of at least 40 m/m% because the calculation is

simplified to a measurement of the dynamic viscosity.

From Eqn (3.43), the thermal diffusivities a of foods lie in the following range:

0.0885 × 10−6 m2∕s < a < 0.143 × 10−6 m2∕s (3.46)

where 0.143× 10−6 m2/s is the thermal diffusivity of water at 20 ∘C. Since the

densities 𝜌 of foods lie in the range

500kg∕m3 < 𝜌 < 1500kg∕m3 (3.47)

(and the density can be calculated relatively well), the calculation of the Prandtl

number Pr= 𝜂/(a𝜌) is influenced mostly by the accuracy of the viscosity value.

If we calculate with the mean values a= 0.11×10−6 m2/s and 𝜌=1000 kg/m3,

then the Prandtl number may be estimated in the following way:

Pr = 𝜂

a𝜌= 𝜂(Pas)

0.11 × 10−3[(m2∕s)(kg∕m3)](3.48)

where Pa s= (m2/s)(kg/m3).

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Engineering properties of foods 81

Example 3.1Let us calculate the Prandtl number of a chocolate mass at 50 ∘C using the param-

eters given by Rapoport and Tarchova (1939) (valid for the interval 30–70 ∘C):

𝜌 = (1320 − 0.5t) (kg∕m3)

a × 108 = 2.7778(4 + 0.017t) (m2∕s)

if 𝜂 =3 Pa s (an average value). At 50 ∘C, 𝜌=1295 kg/m3 and a= 1.347× 10−7

m2/s; that is,

Pr = 3

1295 × 1.347 × 10−7= 1.72 × 104

In Table A1.24 in Appendix 1, a=0.1244× 106 m2/s at 35 ∘C for chocolate accord-

ing to Antokolskaya (1964).

3.7 Mass diffusivity and Schmidt number

3.7.1 Law of mass diffusion (Fick’s first law)The various transport phenomena may be divided into pressure diffusion, ther-

mal diffusion, forced diffusion and ordinary diffusion. Ordinary diffusion is the

net transport of liquid or solid without any movement of the fluid. Ordinary dif-

fusion is caused by a concentration gradient and is proportional to this gradient

according to Fick’s first law (or the first Fick equation):

m′A = −DA𝜌A

dcA

dx(3.49)

where m′A [kg∕(m2s)] is the mass flux of substance A per unit area (m2) through

a section perpendicular to the direction of flow (the prime means a time deriva-

tive), DA (m2/s) is the diffusion coefficient of A, 𝜌A (kg/m3) is the density of A,

cA is the concentration of A (kg/kg or mol/mol) and x (m) is the coordinate in

the direction of flow.

3.7.2 Mutual mass diffusionIn the case of a binary system, mutual diffusion takes place: substance A diffuses

into substance B, while B diffuses into A. For constant 𝜌A, the net flux of A may

be written as

m′A = −DA𝜌A

dcA

dx+ cA(m′

A + m′B) (3.50)

In several cases the diffusion rate of one component is zero, that is, m′B = 0.

This is, for instance, the case in convection drying, as vapour leaves the material

surface and diffuses through a boundary layer of stagnant air. With m′B = 0, Eqn

(3.50) gives

m′A = −DA𝜌A(1 − cA)−1 dcA

dx(3.51)

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82 Confectionery and chocolate engineering: principles and applications

In this example A is a gas phase (vapour), and the equation may be rewritten as

m′A = −

Mww DA

RTP

P − pw

dpw

dx(3.52)

where Mww is the molar weight of water, R is the molar gas constant, T is the

absolute temperature (K), P is the vapour pressure of pure water at T and pw is

the partial vapour pressure of water in the gas phase at T.

3.7.3 Mass diffusion in liquidsThe diffusion coefficients of liquids are, in most practical systems, heavily depen-

dent on the concentration of solids in solution. According to Besskow (1953), the

diffusion coefficients of fluids are mostly of magnitude 10−3–10−4 cm2/min, that

is, 10−9–10−10 m2/s.

According to Bruin (1979), the scale of the self-diffusivity of water is 10−9

(m2/s), and that of the diffusivity of water in some materials (cellophane,

gelatin, starch, maltodextrin, coffee extract and amylopectin) is in the range

5×10−9–10−14 (m2/s) and depends on the water concentration: lower diffusion

coefficients occur for lower concentrations.

3.7.4 Temperature dependence of diffusionThe temperature dependence may be described by means of an Arrhenius-like

equation:

D = D0 exp(−B

T

)(3.53)

where D0 and B are constants. According to Einstein,

D = kT∕f (3.54)

where D is the empirical diffusion constant (m2/s); k is the Boltzmann con-

stant, (equal to 1.38062× 10−23 J/K=R/N, where N is the Avogadro number

N ≅ 6.02217×1023/mol, and R= 8.31434 J/(mol×K) is the universal molar gas

constant).

In the laminar flow region, the following equation due to Stokes is valid for

colloids:

f = 6𝜋r𝜂 (3.55)

where r is the radius of a particle of spherical shape (m) and 𝜂 is the dynamic

viscosity of the fluid [in units of Pa s=kg/(m s)]. The empirical diffusion constant

can therefore be determined from the Stokes–Einstein equation:

D = kT6𝜋r𝜂

(3.56)

if r and 𝜂 are known.

Because the activation energy in the Arrhenius equation is the same for both

diffusion and viscosity, the temperature dependence of the phenomena can be

regarded as the same. Consequently, the product D𝜂 is approximately constant,

since the linear dependence in the Stokes–Einstein equation can be neglected

in comparison with the exponential dependence in the Arrhenius equation

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Engineering properties of foods 83

(Erdey-Grúz and Schay, 1962). In other words, if the viscosity increases, then the

diffusion coefficient decreases, and vice versa.

The following models were suggested by van der Lijn (1976) for sugar

solutions:

Maltose ∶ log D = −7.870 − 9.40(x + 0.194)(548 − T)∕T (3.57)

Sucrose ∶ log D = −8.209 − 17.8(x + 0.121)(447 − T)∕T (3.58)

Glucose ∶ log D = −8.405 − 15.9(x + 0.417)(397 − T)∕T (3.59)

where x is the mole fraction of solids (mol/mol); T is in K and D is in m2/s. (In

these equations, the logarithmic form is merely a simplification for computation;

log D has no physical meaning.)

Stokes’s law relates to the drag on particles of spherical shape, and therefore it

cannot be expected to be valid for molecules of dissolved substances, the shapes

of which are generally not spherical. Nevertheless the Stokes–Einstein equation

gives acceptable values for the diffusion coefficients of dissolved molecules. The

reason for this is likely to be that rotation of the molecules is induced so much

at the usual temperatures that the conditions of spherical symmetry are met

(Erdey-Grúz and Schay, 1962).

Example 3.2Let us calculate the diffusion coefficient of sucrose in a 20 m/m% solution at

303 K from Eqn (3.58); moreover, calculate the radius of sucrose molecule sup-

posing that it is of spherical shape; and finally, let us calculate the value of D in

such a solution using the Stokes–Einstein equation (3.56).

If the sucrose concentration is 20% m/m, then x mol fraction is x= (200 g/

342 g)/(800 g/18 g)=0.0132, where 342 g and 18 g are the molar weight of

sucrose and water, respectively.

From Eqn (3.58), if T= 303 K, then log D=− 9.344, that is, D=4.53×10−10 m2/s.

The volume of 100 g of preceding sucrose solution is (100/1.06655) ml=93.76 ml, and the volume of 80 g of water is (80/1.002) ml=79.84 ml. Suppose

the additivity of volumes; 20 g sucrose has a volume of (93.76− 79.84) cm3 =13.92 cm3, that is, the volume of 342 g (1 molar weight) sucrose is ≈238 cm3.

Since 1 mol sucrose contains 6× 1023 molecules, suppose that the sucrose

molecule is of spherical shape, the r radius of this sphere from the equation

238 cm3∕(6 × 1023) = 38 × 10−23 cm3 = 4r3𝜋∕3

→ r = 4.56 × 10−8 cm = 4.56 × 10−10 m

From the Stokes–Einstein equation (3.56),

D = kT∕(6𝜋r𝜂) = 1.38062 × 10−23∕(6 × 3.14 × 4.56 × 10−10 × 1.5 × 10−3)

≈ 3.25 × 10−10 m2∕s

taking into account the fact that the dynamic viscosity of this sugar solution(20 m/m%) is 1.5× 10−3 Pa s (Junk and Pancoast, 1973).

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84 Confectionery and chocolate engineering: principles and applications

According to Rohrsetzer (1986), the diffusion coefficient D of sucrose can be

estimated as 2.5× 10−10 m2/s.

3.7.5 Mass diffusion in complex solid foodstuffsRegarding the mass transfer properties of solid foodstuffs, two types of material

are often distinguished:

• Laminates, consisting of layers with different properties sandwiched together

• Particulates, in which discrete particles of one phase are dispersed in a contin-

uum of another (Holliday, 1963)

For a slab consisting of a laminate in which the layers are perpendicular to

the direction of flow, the mass diffusivity may be calculated (Bruin and Luyben,

1980) according to1D

=∑(

1Di𝜎i

), i = 1,2, … ,n (3.60)

where 𝜎i represents the solubility coefficient of the ith laminate.

Several examples of systems made up of one continuous polymer phase and

one dispersed phase have been described in the literature; see Holliday (1963).

Mathematically, the diffusion of particles in these materials may, essentially,

be treated like the phenomena of electrical and thermal conduction. Here,

a two-phase system is considered where a number of particles (spheres) of

material A are embedded in a continuous medium of material B. The diffusion

coefficients of the two materials, DA and DB, are assumed to be constant. The

effective mass diffusion coefficient of this medium is calculated according to

D − DB

D + 2DB

=𝛾(DA − DB)DA − 2DB

(3.61)

It is assumed that any interaction between the spheres is negligible (following

Maxwell) and 𝛾 is an empirical parameter.

3.7.6 Schmidt numberIf the diffusivity D and kinematic viscosity 𝜈 are known, the Schmidt number Sc

can be calculated from

Sc = vD

(3.62)

where 𝜈 = 𝜂/𝜌 is the kinematic viscosity. The Schmidt number plays a role in mass

transfer similar to that of the Prandtl number in heat transfer; the role of D in

mass transfer is the same as that of a (the thermal diffusivity) in heat transfer:

Prandtl number∶ Pr = Pe∕Re = v∕a

Schmidt number∶ Sc = Pe′∕Re = v∕D

These two numbers are closely connected to each other in accordance with the

Colburn analogy (see Eqn 1.24 in Chapter 1):

St Pr2∕3 = St′ Sc2∕3 =f ′

2

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Engineering properties of foods 85

Example 3.3Let us calculate the Schmidt number for an aqueous sucrose solution for which

D=2.5×10−10 m2/s (Rohrsetzer, 1986), 𝜂 = 10−3 kg/m s and 𝜌=1050 kg/m3. The

Schmidt number is

Sc = 𝜂

𝜌D= 10−3

1050 × 2.5 × 10−10= 3.81 × 103

The scale of the Schmidt number is actually determined by the dynamic viscos-

ity and the diffusion coefficient, since the value of the density is always between

relatively narrow limits (see Eqn 3.47). On the other hand, when the tempera-

ture increases, the viscosity decreases and the diffusion coefficient increases, and

consequently their ratio – and also the Schmidt number – decreases, which is not

compensated by the decrease in density.

3.8 Dielectric properties

3.8.1 Radio-frequency and microwave heatingThe dielectric properties of foods are important if radio-frequency (often abbre-

viated to RF) or microwave heating is used. (Other names of this type of heating

are capacitive dielectric heating and capacitance heating.)

In dielectric heating, the foodstuff interacts with electromagnetic waves oscil-

lating at frequencies between 3 and 300 000 MHz. High-frequency heating is usu-

ally carried out at radio frequencies between 13.9 and 27 MHz and microwave

heating between 915 and 2450 MHz.

According to Manley (1998a,b,c),

there is an increased interest in the use of microwaves and radio-frequency energy to enhance

baking speed and efficiency. APV Baker has been offering microwave applications within

standard ovens to heat both dough pieces and biscuits later in the bake period (to encourage

more rapid drying). Sasib Bakery offers a radio-frequency application to speed drying in the

later parts of a conventional oven …RF-ovens are available in 25…85 kW modules. RF units have an overall efficiency of between

65 and 72% in terms of conversion of mains electrical consumption to transfer of RF energy

to the product …Microwave energy is used in the first zone to heat the dough piece rapidly, in the middle zones to

control leavening gas production and in later zones to increase the rate of moisture removal.

Microwave energy must be used in combination with conventional heating as this determines

the colouration and flavour development.

The amount of heat generated in dielectric heating depends on the dielectric

properties of the food such as the dielectric constant (𝜀) and the loss angle (𝛿).

These are both highly dependent on the food composition, the temperature and

the radiation frequency (or wavelength).

Dielectric heating generates heat directly inside the material exposed to the

electromagnetic waves. The conversion of electrical energy to heat results from

dielectric losses in the electrically non-conducting material, which is usually a

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86 Confectionery and chocolate engineering: principles and applications

poor thermal conductor. Dielectric heating depends on the interaction between

polar groups in the molecules of a non-conductive material and an alternating

electric field. The atomic carriers of the charges in such fluid and solid materials

are not able to move when an electric field E is imposed; instead, they can only be

slightly displaced from their initial positions. The effective force is proportional to

the electric field strength, and because of the displacement, negative and positive

surface charges arise at sites on the boundary. This phenomenon is quantified by

the polarization P, which is related to the electric field by the following equation:

P = (𝜀′r − 1)𝜀0E = D − 𝜀0E (3.63)

where P is the polarization vector (C/m2), 𝜀′r is the dielectric constant (>1),

𝜀0 is the dielectric constant of the vacuum (F/m), E is the electric field vector

(non-alternating) (V/m) and D is the dielectric displacement vector (C/m2).

D is defined in a vacuum by the Maxwell equation

D = 𝜀0E (3.64)

and 𝜀0 is defined by the Maxwell equations as

c = (𝜇0𝜀0)−1∕2 (3.65)

where c is the speed of light in vacuum=2.99792458× 108 m/s and 𝜇0

is the magnetic permeability of the vacuum, defined as equal to 4𝜋 ×10−7 N/A2 = 4𝜋 ×10−7 H/m (A= ampere and H=henry). Consequently,

𝜀0 =8.854187817×10−12 F/m.

If E is an alternating electric field, the dielectric constant becomes complex:

𝜀# = 𝜀′r − j𝜀′′r (3.66)

where j is the complex unit vector (=√−1). The dielectric loss factor 𝜀′′r expresses

the degree to which an externally applied electric field will be converted to heat:

𝛿 = 𝜀′′r ∕𝜀′r (3.67)

where 𝛿 is the dielectric loss, or loss tangent, and 𝜀′′r is the dielectric loss factor.

Both 𝜀′r and 𝜀′′r are dependent on the frequency of the alternating current (AC)

and also on the temperature. The loss tangent contains contributions from both

dielectric relaxation and electrical resistive heating, which dominates at lower

frequencies.

If the surface area of the plates of a capacitor is S (m2), the distance between

them is d (m) and the dielectric constant is 𝜀′r, then its capacitance is

C(F) = 𝜀0(F∕m)𝜀′r(S∕d)(m2∕m) (3.68)

If f (Hz) is the frequency of an alternating voltage U (V) and 𝛿 is the loss tangent,

then the power P is

P = 2𝜋fCU2 tan 𝛿 (3.69a)

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Engineering properties of foods 87

or

P(W∕m3) = 2𝜋𝜀0𝜀′rf (U∕d)2 tan 𝛿 ≈ 55.603 × 10−12𝜀′f (U∕d) tan 𝛿 (3.69b)

or

P (W∕cm3) ≈ 55.603 × 10−14𝜀′rf (U∕d) tan 𝛿 (3.70)

if d is in cm.

3.8.2 Power absorption: the Lambert–Beer lawThe Lambert–Beer law for power absorption gives

N(W ) = N0 exp (−2𝛼z) (3.71)

where N and N0 are the attenuated and the generated power, respectively, z is

the penetration depth (m) and 𝛼 is the attenuation factor (1/m), that is,

𝛼 = (2𝜋∕𝜆){(𝜀′r∕2)√(1 + tan2𝛿) − 1}1∕2 (3.72)

where 𝜆= c/f is the wavelength (m) (where c≈ 3×108 m/s is the velocity of light).

The wavelengths for frequencies of 27.12, 915 and 2450 MHz are

𝜆27.12 = (3 × 108m∕s)∕(27.12 × 106s−1) = 11.06m

𝜆915 = (3 × 108m∕s)∕(915 × 106s−1) = 0.328m

𝜆2450 = (3 × 108m∕s)∕(2450 × 106s−1) = 0.122m

If z= ze =1/2𝛼, then N=N0/e, where e=2.71… is the base of natural logarithms.

The penetration depth z can be calculated from Eqn (3.72):

z =(𝜆0

2𝜋

)(√𝜀′

𝜀′′

)(3.73)

where 𝜆0 is the vacuum wavelength, 𝜀′ is the real part of the complex dielectric

constant and 𝜀′′ is the imaginary part of the complex dielectric constant.

Microwave energy at 915 MHz penetrates more deeply than that at 2450 MHz

for the same material because

𝜆(915MHz) = (3 × 108m∕s)∕(915 × 106s−1) = 0.328m

and

𝜆(2450MHz) = (3 × 108m∕s)∕(2450 × 106s−1) = 0.122m

and the penetration depth is proportional to the vacuum wavelength. At the

extremes of the frequency range for dielectric heating (3 MHz and 30 GHz), the

corresponding penetration depths are 100 and 0.01 m, respectively.

The aforementioned relationship (3.73) also shows that infrared radiation,

for practical purposes, acts only on the surfaces of bodies because its wavelength

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88 Confectionery and chocolate engineering: principles and applications

is much shorter (e.g. 𝜆= 3×10−6 m at f=1014 Hz) than that of radio-frequency

radiation. Therefore infrared radiation from incandescent heaters is very often

used to provide intense heating for product colouring. The relationship described

in Eqn (3.72) is still valid, although both 𝜀′r and tan 𝛿 are dependent on the

frequency.

In industrial microwave heating units, the most commonly used frequencies

are 915 MHz and 2.45 GHz. A frequency of 5.8 GHz is increasingly being used for

special applications.

The most commonly used frequencies for radio-frequency heating are 13.56

and 27.12 MHz.

For further details, see Stammer and Schlünder (1992) and Grüneberg et al.

(1993).

3.8.3 Microwave and radio-frequency generators3.8.3.1 Microwave generators (magnetrons)The type of microwave generator most frequently used is the magnetron. Mag-

netrons were developed in the 1950s for radar applications and have been used

for microwave heating since the discovery of this application of high-frequency

waves.

Magnetrons are produced with output powers ranging from 200 W to 60 kW

or even higher. The majority of magnetrons are produced with output powers

between 800 and 1200 W for household microwave ovens. Magnetrons of very

low power are commonly used in medical applications, and magnetrons of high

power are used for industrial heating and in research.

Owing to the mass production of magnetrons with a power of about

800–1200 W, the price of such magnetrons is comparatively low. Therefore,

these magnetrons are also used for industrial heating applications.

During operation, magnetrons must be cooled to prevent overheating. Mag-

netrons with a power of up to about 2 kW are usually air cooled, while those

with a higher power are usually water cooled, requiring water recirculation units.

Those magnetrons also require the use of special protection equipment against

reflected power that could overheat and destroy the magnetron. Low-power

magnetrons are more robust and can be operated without protection equipment.

There are many other types of microwave generators, such as klystrons and

travelling wave tubes. However, none of these generator types are used for indus-

trial microwave heating as the costs are too high compared with magnetrons.

3.8.3.2 Radio-frequency generatorsRadio-frequency waves are usually generated by tube or semiconductor genera-

tors. Tube generators use a vacuum tube to generate the high-frequency waves.

Semiconductor generators are a comparatively new development for industrial

heating and have only limited output power. Tube generators can have an output

power of several 100 kW.

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Engineering properties of foods 89

Table 3.14 Dielectric properties of water.

Relative dielectricconstant (𝜺′r)

Relative dielectric lossconstant (𝜺′′)

Loss tangent(tan 𝜹)

Ice 3.2 0.0029 0.0009

Water (at 25 ∘C) 78 12.48 0.16 (=12.48/78)

In a radio-frequency heating unit, a high-frequency field is generated between

two or more electrodes. The shapes of the electrodes determine the shape of

the generated field. Although many electrode shapes are possible, two types of

electrodes are most commonly used, namely, rod electrodes and plate electrodes.

For heating, the lossy dielectric material is placed between or over the

electrodes. The electric field strength is determined by the applied voltage and

the distance between the electrodes. The minimum technically feasible distance

between the electrodes is determined by the applied voltage. With increasing

distance between the electrodes, the voltage required to maintain the electric

field strength also increases. The maximum distance between the electrodes and

thus the maximum product thickness are determined by the necessity to avoid

arcing between the electrodes.

Tables 3.14–3.16 show the dielectric constants of some substances that are of

interest in the confectionery industry. For the dielectric constant of cocoa but-

ter, see Fincke (1965). These data can be regarded as merely indicative, since

both 𝜀r and tan 𝛿 are dependent on the frequency used. Table 3.17 shows the

temperature and frequency dependence of tan 𝛿 of water.

Although a considerable body of published information exists on the dielec-

tric properties of many foodstuffs, because of the various factors describing the

electric field and the food that affect these properties, precise values for a par-

ticular product under a specific set of conditions can be obtained only by actual

measurements.

Table 3.15 Relative dielectric constants of some materials used in

confectionery practice at room temperature (indicative values).

Substance Relative dielectric constant

Air (dry) 1.000536

Cereals 3–5

Margarine, liquid 2.8–3.2

Sorbitol 33.5

Soy beans 2.8

Starch 3–5

Sucrose 3.3

Syrup 50

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90 Confectionery and chocolate engineering: principles and applications

Table 3.16 Relative dielectric constants of some vegetable oils at 20 ∘C and

their dependence on temperature.

Vegetable oil 𝜺(rel), 20 ∘C Range (∘C) (1/𝜺)(𝚫𝜺/𝚫t)

Arachis 3.051 0–100 −0.00313

Cottonseed 3.149 0–100 −0.00366

Linseed 3.192 0–100 −0.00385

Sunflower 3.11 0–100 −0.0034

Source: Kiss (1988).

Table 3.17 Temperature and frequency dependence of tan 𝛿 of water.

Temperature (∘C) 900 MHz 2450 MHz

15 0.07 0.17

55 0.03 0.07

95 0.02 0.04

Source: Adapted from Jeppson (1964).

The benefit of dielectric heating is that as the water content of the material

heated decreases, both the relative dielectric constant 𝜀r and the loss tangent

tan 𝛿 decrease. Consequently, the heat loading on material that is drying becomes

less and less. This process prevents excessive heating of the material, that is, this

operation can be described as gentle or considerate.

Dielectric drying lines, which consist of a transport band and a heating oven

above it, are made for industrial purposes (Vauck and Müller, 1994). The usual

technical data of such a drying line are length of band, 16 m; width of band, 0.7 m;

length of heating oven, 5 m; voltage, 7 kV; frequency, 15–19 MHz; throughput,

up to 400 kg/h; power consumption, 20 kW; source of radiant energy, tube gen-

erators; efficiency, 30–50%; and specific energy demand, c. 0.2–2 kW h/kg. The

power consumption can, however, reach 350 kW.

The main fields of application of dielectric drying lines are in the chemical

industry and in biotechnology. Since the process is relatively expensive, its use

in the confectionery industry is very limited at present.

3.8.4 Analytical applicationsThe dielectric properties of materials can give valuable information about their

composition. There is a relatively direct relationship between the dielectric

properties and the water content of a material – this is the basis of many

electronic moisture meters. The data provided by these measurements must be

compared with data obtained by absolute methods; for example, the calibration of

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Engineering properties of foods 91

measurements of the water content of cocoa powder using dielectric properties

may be done with results obtained by the Karl Fischer method. For confectionery

applications, see Minifie (1970); for near-infrared reflectance/transmittance

(NIR/NIT) investigations of cocoa and chocolate products, see Kaffka et al.

(1982a), Bollinger et al. (1999) and Schulz (2004); for investigations of proteins

using NIR/NIT and the Kjeldahl method, see Horváth et al. (1984); for investiga-

tions of water content, see Kaffka et al. (1990); for investigations of oil, protein,

water and fibre content, see Kaffka et al. (1982b), El-Rafey et al. (1988) and

Bázár (2008); and for investigations of wavelength optimization using the Polar

Qualification System (PQS), see Kaffka and Seregély (2002).

3.9 Electrical conductivity

3.9.1 Ohm’s lawWith foods that are conductors (e.g. sugar, whole egg, salt and dried milk), the

electrical conductivity is significantly dependent on the frequency of the electro-

magnetic field. Most foods, however, are poor conductors, and their conductivity

is essentially independent of the electromagnetic field.

The electrical conductivity is defined by Ohm’s law for direct current (DC):

E = IR (3.74)

where E is voltage (V), I is current (A) and R is resistance (Ω).

The electrical conductivity G is the inverse of the resistance:

G = 1R

(3.75)

It is measured in units of siemens (S), where

1S = s3A2

kgm2= A

V= 1

Ω

The specific resistance 𝛾 is defined as the resistance of a line of 1 mm2 cross section

and 1 m length, that is, its units are

[R][A][l]

= Ωmm2

m= 10−6Ω m = 10−6 m

S(3.76)

where specific resistance (Ωm)= 1/specific conductivity (S/m).

For AC, the electrical resistance can be expressed in units of 1/S=Ω too, but

in this case it is called the impedance Z and is of complex value:

Z = R + j𝜔L + 1j𝜔C

= R + j(𝜔L − 1

𝜔C

)(3.77)

where 𝜔=2𝜋f and R is the real (ohmic) part of the complex impedance Z. If |Z| is

the absolute value (in 1/S=Ω) of the complex number Z, then its reciprocal (in

S) is the absolute value of the complex conductivity.

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92 Confectionery and chocolate engineering: principles and applications

Materials can be classified by their conductivity into three classes:

• Conductors, such as metals, have a high conductivity. Electrolytes have either

a medium conductivity (good electrolytes, e.g. aqueous solutions of mineral

acids) or a low conductivity (poor electrolytes, e.g. dilute aqueous solutions

and water itself).

• Insulators, such as glass or a vacuum, have a low conductivity.

• Semiconductors: Their conductivity is generally intermediate but varies widely

under different conditions, such as exposure of the material to electric fields

or to light of certain frequencies.

3.9.2 Electrical conductivity of metals and electrolytes: theWiedemann–Franz law and faraday’s law

The various atomic mechanisms of electrical conduction result in differences in

the properties of matter.

Electrical conduction is closely connected to the movement of electrons. In

metals there is a very mobile electron cloud, which moves easily under the effect

of an electric field. Therefore, metals are excellent conductors of both electrons

and heat. (The high surface reflection of metals is also a result of their mobile

electrons.) If the temperature increases, the movement of the electrons becomes

more and more difficult, and consequently the conductivity decreases. In con-

trast, if the temperature of an electrolyte increases, the ions become more and

more mobile, and consequently its conductivity increases.

There is an important relationship between the thermal and electrical con-

ductivities of metals called the Wiedemann–Franz law. The ratio of the thermal

conductivity to the electrical conductivity of a metal is proportional to the tem-

perature. This relationship is based upon the fact that heat transport and electrical

transport both involve the free electrons in the metal. The thermal conduc-

tivity increases with the average particle velocity, since that increases the for-

ward transport of energy. However, the electrical conductivity decreases with

increasing particle velocity because collisions divert the electrons from the for-

ward transport of charge. This means that the ratio of the thermal to the electrical

conductivity depends upon the average velocity squared, which is proportional

to the temperature. According to the Wiedemann–Franz law,

L = 𝜆

GT= 2.45 × 10−8 W Ω∕K2 (3.78)

where L is the Lorenz number, 𝜆 is the thermal conductivity and G is the electrical

conductivity.

The Lorenz number is practically independent of the temperature and lies in

the range 2.3–3.2 for many metals.

The extension of the Wiedemann–Franz law to other kinds of materials is

questionable.

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Engineering properties of foods 93

For electrolytes, Faraday’s law states that

m = Qqn

MN

= 1F

QMn

(3.79)

where m is the mass of the substance produced at an electrode (in g), Q is the

total electric charge that has passed through the solution (in coulombs), q is

the electron charge= 1.602×10−19 C/electron, n is the valence of the substance

as an ion in solution (electrons/ion), F is Faraday’s constant= 96.485 C/mol,

M is the molar mass of the substance (g/mol) and N is the Avogadro num-

ber= 6.022×1023 ions/mol.

3.9.3 Electrical conductivity of materials used in confectioneryThe raw materials, the products and the semi-products of the confectionery

industry can be roughly separated into two groups:

Hydrophilic materials, which contain a hydrophilic continuous phase

Hydrophobic (or lipophilic) materials, which contain a hydrophobic continuous

phase

A hydrophilic phase can be regarded as a more or less concentrated aqueous

solution in which hydrophilic/lipophilic substances are dispersed. The base of

a lipophilic phase is a vegetable oil or fat in which the other ingredients are

dissolved or dispersed.

The electrical conductivity of such materials is determined by the following

facts:

• Hydrophilic materials are electrolytes, mostly poor electrolytes, the electrical

conductivity of which is dependent on the water activity.

• Hydrophobic materials (e.g. chocolate) are either good or poor insulators,

depending upon the amount of free ions, free fatty acids and so on.

Some typical conductivity values are given in Table 3.18 for both aqueous

solutions and fats/oils (see the entry for paraffin). Since the ohmic conductivity

of foods is low in general, measurement of the complex (ohmic+ inductive+capacitive) conductivity is mostly used, because this makes many-sided studies

of their properties possible.

3.9.4 Ohmic heating technologyThe study of the electrical properties of electrolytes (e.g. Kohlrausch’s rule) is

beyond the scope of the present work, and this topic may not seem impor-

tant from the point of view of present practice in the confectionery industry.

Nevertheless, we must take into account the fact that ohmic heating technology is

developing; see Fine (2007).

With ohmic heating, the food material, which serves as an electrical resistor,

is heated by passing electricity through it. At an atomic level, this use of elec-

tricity – or Joule heating – is the result of moving electrons colliding with atoms

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94 Confectionery and chocolate engineering: principles and applications

Table 3.18 Some typical electrical conductivities of materials.

Electrical conductivity

Metals

Silver 63.01×106 S/m at 20 ∘C (630 100 S/cm, the highest

electrical conductivity of any metal)

Copper 59.6× 106 S/m (20 ∘C)

Aluminium 37.8× 106 S/m (20 ∘C)

Electrolytes

Seawater 5 S/m

Drinking water 0.0005–0.05 S/m

Ultrapure water 5.5×10−6 S/m

Glycerol 2.2×10−3 S/m (0 ∘C); 12.3×10−3 S/m (21.3 ∘C)

Ethanol 3× 10−4 S/m

Sulphuric acid (30 m/m%, aqueous) 74 S/m

Insulators

Paraffin 10−16 S/m

Quartz 5× 10−15 S/m

Semiconductors

Germanium 1.1236× 106 S/m (0 ∘C)

Silicon 1.725×106 S/m

Graphite 12 S/m (0 ∘C)

Selenium 1.2×10−7 S/m

in the conductor, whereupon momentum is transferred to the atoms, increas-

ing their kinetic energy. This electrical energy is dissipated as heat, which results

in rapid, uniform heating throughout the product, producing a potentially far

higher-quality product than its canned counterpart. The heat generation is effec-

tive throughout the entire volume of the product and depends on the food’s

electrical properties (mainly the electrical conductivity). Unlike radiative tech-

niques (e.g. microwave heating), ohmic heating is not limited by the penetration

of waves; rather, heat is generated uniformly throughout the product exposed

to the electric field, if the conductivities of different parts of the product are

the same.

As a fluid represents an electrical resistance to a current, it can be heated

rapidly, and increases of 2 ∘C are possible within 1 s. The heating rate, however,

is dependent on the current used, together with the product’s physical chemistry

and electrical properties. The conductivity is also an important factor. Conduc-

tivity values change with both the temperature (as the temperature increases,

the conductivity increases and results in a gradual improvement in the heating

process over time) and the frequency of the current if AC is used.

The heating rate is also dependent on other parameters, such as the electric

field distribution and the size, shape and orientation of particulates in liquid

foods. A high solids content is desirable for effective ohmic heating because it

often results in faster heating. Ohmic heating is also a more efficient treatment

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Engineering properties of foods 95

for high-viscosity products and particulate foods (with particle sizes of up to 4 cm)

than are conventional heating techniques, which require time for heat penetra-

tion to occur to the centre of the material and in which particles heat up more

slowly than the fluid phase of the food. In addition, the lack of mechanical action

makes ohmic heating suitable for use with sensitive products.

In the past, one drawback of ohmic heating was that electrolytic reactions

could take place at the surface of the electrodes, leading to burning of the prod-

uct and corrosion if the electrodes were made of common food-grade metals.

The major electrolytic effect was dissolution of the metallic electrodes, which

could cause product contamination. To overcome this drawback, ohmic suppli-

ers now use more resistant electrodes (such as electrodes made of pure carbon),

use AC instead of DC and increase the frequency of the electric supply (no cor-

rosion takes place at high frequencies, especially at high current densities of

3500 A/m2). More significantly, owing to the variation in the performance of

electrical resistance heating from one product to another, the main disadvantage

of ohmic heating is that its application varies from product to product.

Despite this, a large number of potential future applications exist for ohmic

heating, including use in blanching, evaporation, dehydration, fermentation and

extraction. The development of non-acid sterilized food products is now closely

tracking the development of innovative aseptic packaging systems.

The prospects for ohmic heating in the confectionery industry cannot yet

be judged; however, the diversity of sweets makes possible the application of

up-to-date technologies. Furthermore, electricity is an environmentally friendly

source of energy, and therefore its use will be intensified.

3.10 Infrared absorption properties

The infrared absorption properties of foodstuffs are not easily described. Birth

(1976) discussed how light interacts with food materials and described the impor-

tant principles of normal surface reflection, body reflection and light scattering.

Surface reflection takes place, as the name implies, at the surface of a material

and is about 4% for most organic components. In the case of body reflection,

the light enters the material, becomes diffuse owing to scattering and under-

goes some absorption. The remaining light leaves the material close to where

it entered. Normal surface reflection produces the gloss or shine observed on

polished surfaces, while body reflection produces the colours and patterns that

constitute most of the information we obtain visually. For materials with a rough

surface, both the surface and the body reflection will be diffuse. Scattering is

the mechanism which redirects the radiant energy from its original direction of

propagation.

The optical characteristics of various media were also discussed theoretically by

Krust et al. (1962) and by Ginzburg (1969) using data from studies by Bolshakov

et al. (1976) of the optical characteristics of various materials and products. These

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96 Confectionery and chocolate engineering: principles and applications

studies demonstrated the necessity for taking account of scattered radiation dur-

ing measurement. As a first step, equations for short-wave radiation were deter-

mined using experimental transmission values for depths greater than 8 mm for

bread in a regression analysis (with no long-wave radiation remaining). As halo-

gen lamps (𝜆max = 1.12 μm) were used during these experiments, about 33% of

the total radiation, calculated from Planck’s equation, was absorbed in this wave-

length range, and therefore

qout

qin

= 0.33 exp(−1.6x) (3.80)

where qin is the input radiation energy flux, qout is the output radiation energy

flux and x is the penetration depth.

The equations for the long-wave (63% of the total radiation) penetration

curves were then calculated by subtracting the calculated transmission values

shown earlier from the experimental transmission values for the total radiation:

qout

qin

= 63 exp (−6.6x) (3.81)

The total penetration curves describing the experimentally measured transmis-

sion values are therefore given by

qout

qin

= 33 exp (−1.6x) + 63 exp (−6.6x) (3.82)

A summation of the coefficients gives 96% total absorption for the radiation.

This is in agreement with the theoretical value, as the surface reflection for most

organic materials is about 4%.

3.11 Physical characteristics of food powders

3.11.1 Classification of food powdersFood powders are a large group of different kinds of powders that have little

in common, except for being used as (or in) foods. In the confectionery indus-

try, the most important raw materials in the powder state are sucrose, wheat

flour, milk powder, soy flour, gelatin, pectin, agar-agar and starch; among the

finished products, cocoa powder and various pudding powders should be men-

tioned. Many mixtures in the powder state are made during production too. Even

this incomplete enumeration indicates the importance of this topic.

The classification criteria for food powders may, therefore, vary for the purpose

of convenience or according to any particular practical application. Peleg (1983)

provided a classification of powders by:

• Use (flour, sweeteners, etc.)

• Major chemical component (starchy, sugar, etc.)

• Process (ground, spray dried, etc.)

• Size (fine, coarse)

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Engineering properties of foods 97

• Moisture sorption pattern (extremely hygroscopic, moderately hygroscopic,

etc.)

• Flowability (free-flowing, cohesive, etc.)

This classification demonstrates the difficulties of treating food powders as a

group at a level of generalization that will not make the analysis too vague and

consequently impractical. Furthermore, some of the more interesting and poten-

tially useful criteria, for example, hygroscopicity and flowability, are not easy to

quantify because they represent the combined effect of different sorts of physical

and physicochemical phenomena. The composition and properties of many food

powders may vary to different degrees and may also change with time. There-

fore, it is not uncommon that a free-flowing powder, for example, may become

sticky during storage or that a relatively non-hygroscopic powder (e.g. salt) may

become highly hygroscopic in the presence of impurities. Realizing these prob-

lems, and with the understanding that exceptions to the discussion are not only

possible but also sometimes unavoidable, this chapter is an attempt to evaluate

the factors that determine or influence the physical properties of food powders,

with special emphasis on their specific or unique characteristics.

The physical properties of powders are usually characterized at two levels, that

of the individual particles and that of the bulk powder. Although it is self-evident

that the bulk properties are primarily influenced by the properties of the particles,

the relationship between the two is by no means simple and involves external

factors such as the system geometry and the mechanical and thermal history

of the powder. The bulk properties of fine powders, always interdependent, are

determined by the physicochemical properties of the material (e.g. composition

and moisture content); the geometry, size and surface characteristics of the indi-

vidual particles; and the history of the system as a whole. The shape of the

container can affect flowability, and the powder density usually increases as a

result of vibration, for example. Numerical values assigned to such properties

therefore ought to be regarded as useful only under the conditions under which

they were determined or as indicators of the order of magnitude only.

3.11.2 Surface activitySince the phenomenon of water vapour sorption in food has been extensively

studied and discussed in the literature, it need not be discussed here. Less infor-

mation is available on the capacity of many kinds of food surfaces to adsorb

fine solid particles or to interact with other particles and equipment surfaces.

These interactions are not limited to particles of the same or similar chemical

species, although there is evidence to suggest that surface affinity can differ con-

siderably between materials (e.g. in the case of certain anticaking agent–powder

systems). The mechanisms by which particle surfaces interact are also of sev-

eral different kinds, including liquid bridging by surface moisture or melted fat,

electrostatic charge (as in dust), molecular forces and the surface energy of crys-

talline materials. Detailed theoretical discussions and mathematical analyses of

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98 Confectionery and chocolate engineering: principles and applications

such interactions and their implications in powder technology have been pub-

lished by Rumpf (1961), Pietsch (1969) and Zimon (1969).

3.11.3 Effect of moisture content and anticaking agentsIn general, moisture sorption is associated with increased cohesiveness, due

mainly to interparticle liquid bridges. Therefore, especially in the case of hygro-

scopic food powders, a higher moisture content ought to result in a lowering

of the loose bulk density, as indeed is the case for powdered sugar and salt, for

example, see Table 3.19. It should be mentioned, however, that this decrease

will only be detected in freshly sieved or flowing powders, where these same

interparticle forces are not allowed to cause caking of the mass.

Another notable exception to this trend is in the case of fine powders that are

very cohesive even in their dry form (e.g. baby formula and coffee creamer). In

such cases it appears that the bed array has reached its maximum openness at a

low moisture content, and therefore a further lowering of the density becomes

impossible. It is also worth remembering that excessive moisture levels, especially

in powders containing soluble crystalline compounds (such as sugars or salt),

may result in liquefaction of the powder and consequently in an increase in its

density. At this stage the powder most probably has already lost its utility, and

therefore this phenomenon has little practical importance.

Anticaking agents (or flow conditioners) are supposed to reduce interparticle

forces, and, as such, they are expected to increase the bulk density of powders

(Peleg and Mannheim, 1973). It has been observed, though, that there may be an

optimal concentration beyond which the effect will diminish (Nash et al., 1965)

or will be practically unaffected by the conditioner concentration (Hollenbach

et al., 1982).

It can also be observed that for a noticeable effect on the bulk density (i.e. an

increase of the order of 10% or more), the agent and the host particles must have

surface affinity. Otherwise, the particles of the agent may segregate and, instead

of reducing the interparticle forces, will only fill the interparticle space. It seems,

however, that there is very little information on the exact nature of these surface

interactions and the mechanism by which they affect the bed structure. Examples

of the effects of moisture and anticaking agents on the bulk properties of selected

food powders are given in Tables 3.19 and 3.20 (Peleg, 1983). The value of b in

these tables is the constant in the equation

𝜌B = a + b log 𝜎N (3.83)

where 𝜌B is the bulk density, 𝜎N is the applied stress and a and b are constants.

3.11.4 Mechanical strength, dust formation and explosibilityindex

Many solid food materials, especially when dry, are brittle and fragile. Their hard-

ness on the Mohs scale is of the order of 1–2 (Carr, 1976).

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Engineering properties of foods 99

Table 3.19 Effect of moisture content on the mechanical characteristics of selected food

powders.

PowderMoisture

(%)

Loosebulk

density(g/cm3)

Compressibility(valueof b)

Cohesion(g/cm2)

Angle ofinternalfriction

(∘)a References

Powdered salt

(100/200 mesh)

Dry 1.26 0.02 0 40 Moreyra and

Peleg (1981)

0.6 0.78 0.12 50 36

Powdered

sucrose

(60/80 mesh)

Dry 0.62 0.152 10 39 Peleg and

Mannheim

(1973)

0.1 0.5 0.185 14 37

Starch Dry 0.81 0.12 6 33 Peleg (1971)

18.5 0.69 0.15 13 30

Baker’s yeast 8.4 0.52 0.08 14 42 Dobbs et al.

(1982)

13 0.49 0.26 TCb TCb

aDetermined by a Jenike flow factor tester at consolidation levels of 0.2–0.5 kg/cm3.bTC indicates that the powder was too cohesive for measurement by the flow factor tester.

Source: Peleg (1983). Reproduced with permission from Springer.

Table 3.20 Effect of anticaking agents on the bulk density and compressibility of selected food

powders.

Powder AgentConcentration

(%)Loose bulk

density (g/cm3)Compressibility

(value of b) References

Sucrose None 0 0.7 0.066 Hollenbach

et al. (1982)

Ca stearate 0.5 0.87a 0.039a

Silicon dioxide 0.5 0.75a 0.052a

Ca3(PO4)2 0.5 0.76a 0.044a

Gelatin

(powdered)

None 0 0.68 0 Peleg (1971)

Al silicate 1 0.7 0.016

Cornstarch None 0 0.62 0.109 Hollenbach

et al. (1982)

Ca stearate 1 0.59 0.099

Silicon dioxide 1 0.67 0.077a

Ca3(PO4)2 1 0.61 0.062a

Soy protein None 0 0.27 0.04 Hollenbach

et al. (1982)

Ca stearate 1 0.27 0.041

Silicon dioxide 1 0.27 0.036

Ca3(PO4)2 1 0.31a 0.024a

aSignificant change relative to the untreated powder.

Source: Peleg (1983). Reproduced with permission from Springer.

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100 Confectionery and chocolate engineering: principles and applications

Since, particularly for small objects, surface or shape irregularities are normally

associated with mechanical weakness (e.g. due to stress concentrations), dry food

particles have a tendency to wear down or disintegrate. Mechanical attrition of

food powders usually occurs during handling and processing, when the parti-

cles are subjected to impact and frictional forces. The result is frequently a dust

problem that may also develop into a dust explosion hazard.

The incidence of dust explosions depends mainly on the dust particle size,

the dust-to-air ratio and the availability of a triggering spark. Carr (1976) listed

potentially explosive agricultural dusts and ranked them according to their

explosibility in the following descending order: starch (50), sugar (13.2), grain

(9.2), wheat flour (3.8), wheat (2.5), skimmed milk (1.4), cocoa (1.4) and coffee

(≪0.1). (The numbers in parentheses are the explosibility index, where a severe

hazard is denoted by an index of ≥10, a strong hazard by 1–10, a moderate

hazard by 0.1–1 and a weak hazard by <0.1.)

Other implications of dust in the food industry include human health and

safety, plant and equipment maintenance and material loss.

When the size of the particles produced through mechanical attrition is larger

than that of dust particles, the process can still influence the product’s bulk den-

sity or cause a segregation problem that may affect the product’s appearance, as

in the case of instant coffee.

3.11.5 CompressibilityPowders can be compacted in two ways: by tapping, that is, by the application

of vibration (which may occur during transport or handling, during storage in

tall bins, as a result of vibrating the powder in order to increase the weight in a

given container or as a result of vibrating the dosing equipment for the purpose of

tabletting, as in the case of some soups and candies), and by mechanical compres-

sion. The stresses that develop in storage are usually a few orders of magnitude

smaller than those applied in tabletting and similar forming operations.

3.11.5.1 TappingAccording to Sone (1972), for a variety of food powders, the relationship between

the volume reduction fraction 𝛾n and the number of taps n is given by

𝛾n =V0 − Vn

V0

= abn1 + bn

(3.84)

or, in linearized form,n𝛾n

= 1ab

+ na

(3.85)

where V0 is the initial volume, Vn is the volume after n taps and a and b are

constants.

The constant a in this equation represents the asymptotic level of the volume

change or, in other words, the level that will be obtained after a large number of

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Engineering properties of foods 101

taps or a long time of vibration:

limx→∞

𝛾n = a (3.86)

The constant b represents the rate at which the compaction is achieved, that is,

1/b is the number of vibrations necessary to reach half of the asymptotic change.

The intersection with the ordinate is 1/ab. Consequently, both constants can be

determined from Eqn (3.85).

3.11.5.2 Compaction under compressive loadAccording to Gray (1968) the main modes, or mechanisms, by which a powder

bed deforms are:

• Spatial rearrangement of particles (without deformation of the particles)

• Filling of interparticle voids by deformation (mainly plastic) of particles

• Filling of voids by fragmentation of particles

The relative contribution of each mechanism depends mainly on the properties

of the particles (e.g. size, shape and hardness), the magnitude of the applied

pressure and the stress distribution within the compacted specimen.

Therefore, the compressibility pattern of a given powder may be totally differ-

ent in different load ranges. At the low end of the pressure range, that is, for a

normal stress of the order of up to 10–50 N/cm2, the first mechanism seems to be

dominant, and, with few exceptions, such as brittle coffee agglomerates and fatty

powders, most of the change in density is due to structural rearrangement of the

bed. The original structure of both cohesive and non-cohesive powders is greatly

influenced by the presence of interparticle forces. Therefore, it is expected that an

open structure supported by such forces will readily collapse under small stresses,

resulting in a high apparent compressibility in such a stress range. This has indeed

been observed in a large variety of food powders (Peleg and Mannheim, 1973;

Moreyra and Peleg, 1981; Peleg et al., 1982; Peleg, 1983).

The compressibility under small loads is a sensitive index of the cohesiveness of

a powder (Carr, 1976) and can be used to detect potential flow problems. In this

low stress range, the compressive deformability of food powders can be described

by Eqn (3.83). The constant b in that equation has been called the compressibility.

Its values for selected food powders are listed in Tables 3.19 and 3.20 (Peleg,

1983). It should be mentioned that Eqn (3.83) is dimensionally not correct.

3.11.6 Angle of reposeThe angle of repose (Fig. 3.1) is an indispensable parameter in the design of

systems for the processing, storage and conveying of powders. Its actual magni-

tude, however, depends on the way in which the powder heap is formed (e.g.

the impact velocity), and therefore published values of the angle are not always

comparable (Brown and Richards, 1970).

For cohesive powders, the measurement of this angle is sometimes difficult

because of the irregular shapes that heaps can assume. The angle of repose is

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102 Confectionery and chocolate engineering: principles and applications

Fall fromfixed height Bed rupture

Rotary drum(Instantaneous

angle)

α α

α

Figure 3.1 Angle of repose 𝛼. Source: Peleg (1983). Reproduced with permission from Springer.

sometimes confused with the angle of internal friction. Although its magnitude is

certainly influenced by frictional forces (especially in free-flowing powders), it is

also affected by interparticle attractive forces – a factor that becomes dominant in

wet and cohesive powders. Mainly for this reason, the angle of repose (regardless

of how it is measured) can be used as a rough indicator of flowability.

According to Carr (1976), angles of repose of up to about 35∘ indicate free

flowability, 35–45∘ some cohesiveness, 45–55∘ cohesiveness (loss of free flowa-

bility) and 55∘ and above very high cohesiveness and very limited flowability, if

at all.

3.11.7 FlowabilityDespite a few superficial similarities, the flowability of liquids and of powders is dif-

ferent physical phenomena.

The main distinctions are as follows:

1 The flow rate of powders (Fig. 3.2), in contrast to that of liquids, is practically

independent of the height h (i.e. the head) of the powder above the aperture if

h is more than about 2.5 times the aperture diameter D (Brown and Richards,

1970).

2 Powders can resist appreciable shear stresses. Once compacted, under their

own weight or by external pressure, they can also form mechanically stable

structures (e.g. arches) that will halt flow altogether despite the existence of

a head.

For these reasons, treatment of a powder’s gravitational flowability must be

based on theories of solid mechanics (Jenike, 1964) and not on hydrodynamics.

The general principle on which such analyses are based is that, from a physical

point of view, powder flow is equivalent to failure of a solid in shear.

In ideal free-flowing powders or granular materials, the resistance to flow

is primarily through friction, and therefore flowability evaluation is fairly

straightforward. In cohesive powders (as in the case of most food powders),

interparticle forces are enhanced by compaction (e.g. through an increase in

the number of contact points), with the result that the compact can develop

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Engineering properties of foods 103

Dp

DD

Q

Q

h

θ

PowderIf h > 2.5D

Q = ConstantLiquid

Q = const. D2h1/2

Figure 3.2 Flow rate of powders and of liquids. D= aperture diameter; h=head height above

aperture; Dp = typical size of granules; Q= volume flux of stored material. Source: Peleg

(1983). Reproduced with permission from Springer.

appreciable mechanical strength. Therefore, under even a small pressure, many

food powders may cause serious flow problems. For cohesive powders, the

system geometry (e.g. the bin angle and aperture diameter) plays a decisive role

in establishing the flow regime, that is, mass or funnel flow, and its rate and

stability. A detailed description and analysis of the methodology involved can be

found in, for example, the work of Jenike (1964).

In the case of cohesive food powders, internal friction has very little influence

on flowability. Most food powders have an angle of internal friction of the order

of 30–45∘ (Peleg, 1983), and it usually decreases slightly as moisture is absorbed.

This is mainly because of a reduction in the surface roughness of the particles

through dissolution and lubrication. It is obvious that this reduction in inter-

nal friction does not result in improved flowability. Further details are given in

Charm (1971, p. 113–114).

A comprehensive discussion of topics such as the flow of powders and the

storage of powders in silos has been given by Schulze and Schwedes (1993).

3.11.8 CakingMany food powders, especially those containing soluble components or fats, tend

to agglomerate spontaneously when exposed to a moist atmosphere or elevated

storage temperatures. This phenomenon can result in anything from small soft

aggregates that break easily to rock-hard lumps of variable size or solidification of

the whole powder mass. In most cases, the process is initiated by the formation of

liquid bridges between particles that can later solidify by drying or cooling. This

mechanism, known as humidity caking (Fig. 3.3), was schematically described by

Burak (1966).

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104 Confectionery and chocolate engineering: principles and applications

Moisture sorption or heating

Dry Wet

Surface

Continuedsorption or melting

Attraction Fusion

Caked(hard)

Cohesive(sticky)Cohesive

(sticky)Free

flowing

Drying or cooling

Continueddrying or cooling

Caked (hard)

Caked(sticky)

Re-wetting

Equilibration

Drying orcooling

Figure 3.3 Schematic representation of the most common caking mechanisms in food

powders. Source: Peleg (1983). Reproduced with permission from Springer.

Incidentally, the attraction stage shown in Figure 3.3 is not a hypothetical

stage. It can actually be observed that moisture absorption is accompanied by

shrinkage of the powder.

3.11.8.1 Source of liquid bridges in food productsThe source of the liquid bridges in food powders is sticky or liquefied particle

surfaces, produced mainly by the following effects:

• Melting of fats: This mechanism has practically no importance in confectionery

practice.

• Moisture sorption, accidental wetting or moisture condensation, which causes

dissolution of the surface and/or the presence of a liquid film around the par-

ticles.

• Liquefaction of the surface itself as a result of the temperature at which amor-

phous sugars become thermoplastic being exceeded, without the addition of

external moisture. [A detailed study of the physicochemical aspects of this

phenomenon was reported by To and Flink (1978) and Flink (1983).] This

temperature, also known as the sticky point, has a strong dependency on the

powder’s moisture content. The sticky point is especially low for fruit juice

powders, and this is the main reason for their physical instability. This tem-

perature can easily be exceeded in other sugar-rich powders (e.g. onion and

certain spices) during grinding (and therefore refrigerated mills are recom-

mended in such cases) and during storage when the temperature or moisture

is not tightly controlled.

• Liberation of absorbed moisture when amorphous sugars crystallize. A notable

example is the crystallization of lactose in milk powders (Berlin et al., 1968),

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Engineering properties of foods 105

one of the main reasons for a variety of instantization processes; see also Flink

(1983).

According to Kargin (1957), glucose glass sorbs water only on the surface,

owing to the low diffusivity of water in the glass. As the surface hydrates, a

saturated solution forms and the glass softens, giving higher water diffusion. In

tightly packed sugar glasses, water sorption is a surface phenomenon, and on the

usual weight basis, sorption will be higher the higher the specific area.

Lees (1968) described the graining of boiled sweets, which is a result of recrys-

tallization of amorphous sugar. According to Lees, seeding studies at low humid-

ity indicated that the induction period could be related to the formation of nuclei.

The course of recrystallization was measured by the loss of water from the sample

and by X-ray diffraction. For further details, see Lees (1968).

Makower and Dye (1956) studied the recrystallization of spray-dried sucrose

occurring during storage at various relative humidities. An induction period prior

to the start of recrystallization, which depended on the relative humidity, was

noted.

Guilbot and Drapron (1969) gave moisture sorption isotherms for amorphous

and crystalline sugars. Crystalline sugars begin to sorb after a minimum level of

water activity aw is reached, while amorphous sugars sorb at any water activity.

Crystalline maltose first starts sorbing water at aw =0.25 and immediately forms

the monohydrate. Amorphous maltose sorbs from aw greater than zero and

appears to recrystallize at aw = 0.52, at which time it loses water down to the

monohydrate level. Tests on a series of amorphous sugars showed all of them

to have approximately the same isotherm, at least up to their recrystallization

points, probably indicating that the same sites (—OH groups) are available for

uptake of water for all sugars. As these sugars recrystallized, they lost water to

become their respective hydrates, although an anhydrous sugar would lose all

the previously sorbed water. At high enough aw, the sugars eventually go into

solution.

Guilbot and Drapron also observed that the temperatures for solid–liquid tran-

sitions of amorphous sugars were much lower than the melting temperatures

of the respective crystalline sugars. The similarity of this transition temperature

(collapse temperature) for the various amorphous sugars tested indicated that

their bonding energy and degree of bonding were similar in the amorphous state.

Sloan and Labuza (1974) also presented many sorption isotherms, including

those for amorphous and crystalline sucrose. Amorphous sucrose begins sorbing

water at aw = 0.10, with a major rise in moisture content at aw = 0.30. Crys-

talline sucrose remains essentially dry (i.e. with a moisture content of about

0) until about aw =0.84 and then begins to absorb considerably, meeting the

amorphous-sucrose sorption curve at about aw = 0.90. The isotherms do not

reflect any recrystallization effect, which probably means that the time was too

short for recrystallization to occur.

Roth (1976, 1977) demonstrated that mechanical crushing of sugar crystals

produces an amorphous surface capable of recrystallization after sorbing water.

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106 Confectionery and chocolate engineering: principles and applications

Measurements showed that the amorphous layer on the surface comprised about

2% of the sugar mass. Recrystallization of sucrose was noted at aw =0.42 at 20 ∘C,

at which point there were caking and liquefaction due to recrystallization. Sub-

sequent isotherms for the recrystallized sucrose were normal for the crystalline

material and were repeatable, indicating no further change after the recrystal-

lization had been completed.

Simatos and Blond (1975) noted that freeze-dried sucrose adsorbed water at

high rates, while a glass produced from the melt was slow to sorb water, this

being due to the difference in specific surface areas of the two samples. Dif-

ferential thermal analysis of freeze-dried sucrose showed a glass transition at

45 ∘C, devitrification at 91 ∘C and melting of a crystalline phase at 180 ∘C. Glassy

sucrose produced from the melt had a glass transition at about 60 ∘C and a shal-

low, broad melting peak at about 160 ∘C. Simatos and Blond concluded that

freeze-dried sucrose contains sucrose nuclei that crystallize upon rewarming,

these crystals then melting at the normal melting point. X-ray diffraction did

not indicate a crystalline structure, but electron diffraction revealed some orga-

nization in freeze-dried sucrose. The size of the structured regions must be small,

and it could be questioned whether these are crystal nuclei, small crystals or parts

of organized regions in the glass.

The onset and progression of the caking phenomenon do not necessitate liq-

uefaction of whole particles or the whole powder bed. It is enough that only part

of the surface becomes wet to initiate agglomeration. Furthermore, the intensity

and the spread of the phenomenon within a given bed depend on the moisture

absorption rate, the rate of diffusion of moisture into the interior of the particles

and the rate of penetration of moisture into the bed. The hardness of the aggre-

gates will depend on the material – crystalline, glassy or fatty – and on the tempe-

rature history of the particles, including the temperature range and the frequency

of fluctuations. It can also happen that because of insufficient drying or because

of mixing of ingredients with different moisture contents, caking will occur only

after moisture equilibration inside the package.

The meanings of the terms caking tendency and caking intensity are fairly vague.

Despite this limitation, however, it can be shown that most powders that are

known to be cohesive (in terms of bulk properties and flowability) also tend to

cake readily, especially if under static pressure (Peleg and Mannheim, 1973).

3.11.9 Effect of anticaking agentsAnticaking agents (also known as flow conditioners, glidants and free-flowing

agents) are very fine powders (particle size 1–4 μm) of an inert or fairly inert

chemical substance that are added to powders with a much larger particle size in

order to inhibit caking and improve flowability. In studies of sucrose and onion

powders, Peleg and Mannheim (1973) showed that such agents were effective

(in both roles) in only a limited relative humidity range. The explanation is that

coverage of the host particle surfaces by particles of the agent is sufficient to

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Engineering properties of foods 107

reduce interparticle attraction and perhaps to interfere with the continuity of

liquid bridges. The presence of agent particles is not sufficient, however, to cover

moisture sorption sites. Therefore, if moisture sorption is not disturbed, liquid

bridges will eventually be formed and caking will occur as if the agent were not

present.

Additional aspects of the use of anticaking agents in food and other pow-

ders are discussed by, for example, Nash et al. (1965), Burak (1966), Peleg and

Mannheim (1973), Carr (1976) and Hollenbach et al. (1982).

3.11.10 SegregationSegregation of particles occurs when particles with different properties are dis-

tributed preferentially in different parts of a bed. The main reasons for segre-

gation are differences in particle size, density, shape and resilience. However,

in practice, differences in particle size are by far the most important factor. Seg-

regation usually occurs when free-flowing powders having a significant range

of particle sizes are exposed to vibration or other types of mechanical motion.

Under such conditions, the smaller particles migrate to the bottom of the bed so

that their concentration decreases as a function of height in the bed. The phe-

nomenon is not limited to mixtures of particles of different types. It can and does

occur in chemically uniform powders whenever significant size differences exist.

The segregation phenomenon is particularly noticeable when the powder con-

tains a considerable amount of fines (e.g. colourants in drink powders and fines

at the bottom of an instant-coffee jar).

In the case of cohesive powders, segregation of fines is less likely to occur. The

reason is that in such powders, the fines usually adhere to the surface of the

larger particles to form what are known as ordered mixtures (Yeung and Hersey,

1979; Egermann, 1980).

For further details, see Molerus (1993) and Mak and Kelly (1976).

Further reading

Arana, I. (2012) Physical Properties of Foods-Novel Measurement Techniques and Applications, CRC

Press, Taylor & Francis Groups Ltd.

Barton, A.F.M. (1991) CRC Handbook of Solubility Parameters and Other Cohesion Parameters, 2nd

edn, CRC Press, Boca Raton, FL.

Bálint, Á. (2001) Prediction of physical properties of foods for unit operations. Periodica Polytech-

nica Chemical Engineering, 45, 35–40.

Beaton, C.F. and Hewitt, G.F. (1989) Physical Property Data for the Design Engineer, Hemisphere

Publishing, New York.

Berk, Z. (2009) Food Process Engineering and Technology, Elsevier, Academic Press.

Boethling, R.S. and Mackay, D. (2000) Handbook of Property Estimation Methods for Chemicals, Envi-

ronmental and Health Sciences, Lewis Publishers, CRC Press LLC, Boca Raton, FL.

Cropper, W.H. (1998) Mathematical Computer Programs for Physical Chemistry, Springer, New York.

Eszterle, M. (1993) Molecular structure and specific volume of pure sucrose solutions. Zuck-

erindustrie, 118 (6), 459–464.

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108 Confectionery and chocolate engineering: principles and applications

Figura, L.O. and Teixeira, A.A. (2007) Food Physics: Physical Properties, Measurement and Applica-

tions, Springer, New York.

Francis, B., Hastings, W.R. and Jeans, P.A. (1962) Pilot Scale High Frequency Biscuit Baking

with Particular Reference to the Checking of Hard Sweet Biscuits. BBIRA, Report 63.

Fricke, B.A., Bryan, R. and Becker, P.E. (2001) Evaluation of thermophysical property models

for foods. HVAC & R Research, 7 (4), 311–330.

Hayes, G.D. (1987) Food Engineering Data Handbook, Longman Science and Technology, Harlow.

Hewitt, G.F. (ed.) (1992) Handbook of Heat Exchanger Design, Begell House, New York.

Koral, T. (2004): Radio Frequency Heating and Post-Baking - A maturing Technology that can

still offer significant benefits, Biscuit World, magazine by Crier Media Group/Adsales Associates

(UK), 4(7), 1–6.

Kress-Rogers, E. and Brimelow, C.J.B. (2001) Instrumentation and Sensors for the Food Industry,

CRC Press, Boca Raton, FL.

Krizhanoskiy, I.S., Leppo, R.M. and Chernatyin, G.A. (1968) Calculation of the heat-, energy-

and water resources in the confectionery industry (in Russian). Khlebopekar-naya i Konditer-

skaya Promyshlennost, 12 (5), 25–28.

Lawson, R., Miller, A.R. and Thacker, D. (1986) Heat Transfer in Biscuit Baking, Part I: The Effects

of Radiant Energy on Semi-sweet Biscuits. C&CFRA (FMBRA), Report 132.

Lewis, M.J. (1996) Physical Properties of Foods and Food Processing Systems, Woodhead Publishing,

Cambridge.

Lienhard, J.H. IV, and Lienhard, J.H. V, (2005) A Heat Transfer Textbook, 3rd edn, Phlogiston Press,

Cambridge, MA.

Lyman, W.J., Reehl, W.F. and Rosenblatt, D.H. (1982) Handbook of Chemical Property Estimation

Methods: Environmental Behavior of Organic Compounds, McGraw-Hill, New York.

McKenna, B.M. (1990) Solid and Liquid Properties of Foods, A bibliography, Centre for Food Science

University College, Dublin.

Murra, F., Zhang, L. and Lyng, J.G. (2009) Radio frequency treatment of foods: review of recent

advances. Journal of Food Engineering, 91 (4), 297–508.

Noel, T.R., Parker, R., Ring, S.M. and Ring, S.G. (1999) A calorimetric study of structural relax-

ation in a maltose glass. Carbohydrate Research, 319, 166–171.

Ottenhof, M.-A., MacNaughtan, W. and Farhat, I.A. (2003) FTIR study of state and phase tran-

sitions of low moisture sucrose and lactose. Carbohydrate Research, 338, 2195–2202.

Parker, A., Vigouroux, F. and Reed, W.F. (2000) Dissolution kinetics of polymer powders. AIChE

Journal, 46 (7), 1290–1299.

Povey, M.J.W. and Mason, T.J. (1998) Ultrasound in Food Processing, Blackie Academic & Profes-

sional, London.

Rahman, M.D.S. (1995) Food Properties, CRC Press, Taylor & Francis Groups Ltd.

Raznjavic, K. (1996) Handbook of Thermodynamic Tables, 2nd edn, Begell House, New York.

Reid, R.C. and Sherwood, T.K. (1966) The Properties of Gases and Liquids – Their Estimation and

Correlations, McGraw Hill, New York, NY.

Rohsenow, W.M., Hartnett, J.P. and Cho, Y.I. (eds) (1998) Handbook of Heat Transfer, 3rd edn,

McGraw-Hill, New York.

Sahin, S. and Sumnu, S.G. (2006) Physical Properties of Foods, Springer.

Sethna, J.P. (2011) Chapter 12: Continuous phase transitions, in Statistical Mechanics-Entropy,

Order Parameters, and Complexity, Clarendon Press, Oxford.

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CHAPTER 4

The rheology of foods and sweets

4.1 Rheology: its importance in the confectioneryindustry

The rheological properties of sweets play an important role both in engineering

calculations for the manufacture of sweets and in the evaluation of the quality

of sweets.

Heat and mass transfer processes are strongly influenced by the rheological

properties (viscosity, yield stress, etc.) of sweets. On the other hand, the textural

characteristics of sweets are of paramount importance. A study of the rheological

properties of sweets demands a thorough knowledge of rheology because sweets,

as a consequence of their great variety, are typical examples of fluids that require

complex rheological models to represent them.

4.2 Stress and strain

Rheology is the science of the flow and deformation of matter, and therefore a

good understanding of stress and strain is an essential prerequisite for a study of

rheology.

4.2.1 Stress tensorStress, defined as a force per unit area and usually expressed in pascals (Pa ≡

N∕m2), may be tensile, compressive (=negative tensile) or shear. Nine separate quan-

tities are required to completely describe the state of stress in a material.

A small elementary cube (Fig. 4.1) may be considered in terms of Cartesian

coordinates (x, y and z or, in another notation, x1, x2 and x3). Stresses are indicated

by 𝜎ij, where the first subscript refers to the normal to the face upon which the

force acts and the second subscript refers to a direction tangential to the face if

i≠ j; if i= j, both superscripts refer to the normal direction. Therefore, 𝜎11 is a

normal (tensile or compressive) stress acting in the plane perpendicular to x1, in

the direction of x1, and 𝜎23 is a shear stress acting in the plane perpendicular to x2,

in the direction of x3. Normal stresses are considered to be positive where they

act outward (acting to create a tensile stress) and negative where they act inward

(acting to create a compressive stress).

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109

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110 Confectionery and chocolate engineering: principles and applications

σzz

σyy

σxx

τyz

τzy

τxyτyx

τzx

τxz

z

y

x

Figure 4.1 Typical stresses on a cube.

Stress components may be summarized as a stress tensor written in the form of

a matrix:

t = 𝜎ij =⎡⎢⎢⎣

𝜎11 𝜎12 𝜎13

𝜎21 𝜎22 𝜎23

𝜎31 𝜎32 𝜎33

⎤⎥⎥⎦

(4.1)

Another notation for a stress tensor is

Φij =⎡⎢⎢⎣

𝜎11 𝜏12 𝜏13

𝜏21 𝜎22 𝜏23

𝜏31 𝜏32 𝜎33

⎤⎥⎥⎦

(4.2)

This latter notation emphasizes the difference between the normal stresses (𝜎ii)

and the shear stresses (𝜏 ij, i≠ j). Thus, the usual notation for a yield stress is 𝜏0

because it is a kind of shear stress – in general, 𝜎 is used for the notation of

both normal and shear stresses; however, 𝜏 is used for notating shear stresses

exclusively. Also, a common notation is 𝜎ii = 𝜎i, so, for example, 𝜎11 = 𝜎1, which

relates to the diagonal elements of the tensor.

The basic laws of mechanics can be used, by considering the moments about

the axes under equilibrium conditions, to prove that the stress matrix (𝜎ij or Φij)

is symmetrical:

𝜎ij = 𝜎ji (4.3)

that is,

𝜎12 = 𝜎21

𝜎31 = 𝜎31

𝜎32 = 𝜎23

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The rheology of foods and sweets 111

meaning that here are only six (6= 9−3) independent components in the stress

tensor represented in Eqn (4.1).

4.2.2 Cauchy strain, Hencky strain and deformation tensorStrain is a consequence of a stress in the normal direction (i.e. a tensile or com-

pressive stress).

Let us consider a specimen of initial length L0 which is extended to a length

L= L0 + 𝛿L. Since this deformation is small, that is, infinitesimal (𝛿L), it may be

thought of in terms of the Cauchy strain (also called the engineering strain):

𝜀C = 𝛿LL0

= LL0

− 1 (4.4)

However, for large deformations, the Hencky strain (also called the true strain) is

commonly used; this is determined by evaluating an integral from L0 to L:

𝜀H =∫

L

L0

dLL

= ln

(LL0

)(4.5)

The choice of which strain measure to use is largely a matter of convenience,

and one can be calculated from the other:

𝜀H = ln(1 + 𝜀C) (4.6)

Since the Taylor series of ln(1+ 𝜀C) is

𝜀H = ln(1 + 𝜀C) = 𝜀C −(𝜀C)2

2+

(𝜀C)3

3, etc. (if 0 ≤ 𝜀C < 1)

the Cauchy and Hencky strains are approximately equal at small strains: 𝜀H ≈ 𝜀C.

Evidently, 𝜀H and 𝜀C are dimensionless ratios.

The Hencky (true) strain is important in food engineering.

Another type of deformation commonly found in rheology is simple shear (or

simple shear strain) as a consequence of a shear stress. This can be illustrated

by considering a rectangular bar of height h. The lower surface is stationary and

the upper surface is displaced linearly by an amount equal to 𝛿L. Each element is

subject to the same level of deformation, so the size of the element is not relevant.

The angle of shear, 𝛾, may be calculated as

tan 𝛾 = 𝛿Lh

(4.7)

For small deformations, the angle of shear (in radians) is equal to the shear strain

(also symbolized by 𝛾), that is, tan 𝛾 = 𝛾.A related strain tensor can also be expressed in matrix form

𝜀ij =⎡⎢⎢⎣

𝜀11 𝜀12 𝜀13

𝜀21 𝜀22 𝜀23

𝜀31 𝜀32 𝜀33

⎤⎥⎥⎦

(4.8)

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112 Confectionery and chocolate engineering: principles and applications

r ′r

x

0

A ′

B′

B

A

u(x + r)

u(x)

Figure 4.2 Interpretation of the strain tensor.

which includes the strains in both the normal direction (the diagonal positions

in the matrix) and the tangential direction.

For an interpretation of the strain tensor, let us consider Figure 4.2. In a defor-

mation experiment, for example, a tensile test, AB changes to A′B′. In a small

vicinity of the point A, that is, for small deformations, a Taylor expansion can be

used:

u(x+ r) = u(x) + D(x)r oru(x+ r) − u(x)

r= D(x) = du

dr

where D(x) is a derivative tensor (the gradient tensor or strain tensor). In detail,

D(x) = dudx

= [uij] =⎡⎢⎢⎣

(𝜕ux∕𝜕x) (𝜕ux∕𝜕y) (𝜕ux∕𝜕z)(𝜕uy∕𝜕x) (𝜕uy∕𝜕y) (𝜕uy∕𝜕z)(𝜕uz∕𝜕x) (𝜕uz∕𝜕y) (𝜕uz∕𝜕z)

⎤⎥⎥⎦

For small deformations, the symmetric deformation tensor can be used:

E = 𝜀ij = (1∕2)(D + DT)

or, in detail,

E = 𝜀ij =⎡⎢⎢⎣

𝜀11 𝛾12∕2 𝛾13∕2

𝛾21∕2 𝜀22 𝛾23∕2

𝛾31∕2 𝛾32∕2 𝜀33

⎤⎥⎥⎦

(4.9)

where DT is the transposed matrix of D, that is, (D)ij = (DT)ji, and, for the mixed

entries, 𝛾 ij = 𝛾 ji (i≠ j).

The following motion function is important for studying deformations:

x = a(t) + R(t)D(t)X (4.10)

where t is the time coordinate, x=x(X, t) is a vector describing the motion of a

point P0, a(t) is a vector describing translation, R(t) is a tensor describing rotation,

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The rheology of foods and sweets 113

D(t) is a tensor describing deformation without rotation and X is the material (or

Lagrange) coordinates (in three dimensions).

If there is no rotation, the following holds:

D = E + I (4.11)

where I is the unit tensor:

I =⎡⎢⎢⎣

1 0 0

0 1 0

0 0 1

⎤⎥⎥⎦

(4.12)

If there is no translation, it follows from Eqn (4.10) that

x = RD = dR (4.13)

where d is another form of the deformation tensor. The equation RD=dR is a

result of the polar decomposition theorem of Cauchy; for further details, see Verhás

(1985, Appendix F5). The product RD means rotation+ deformation, and dRmeans deformation+ rotation; in general, RD≠DR for products of matrices (the

matrix product is not commutative in general).

According to the polar decomposition theorem, every tensor T can be

decomposed into a product of an isometric tensor M and a symmetric tensor Sor R: T=MS=RM, where the isometric property is defined by the equation

v= (Mr)2 = r2, where v and r are vectors (isometric means measure-conservative).

Equation (4.10) describes the motion around a point P0. However, in order to

study the change of volume around the point P0, let us consider the equation

dV = j dV0 = det R det D dV0 (4.14)

where j is the Jacobian determinant (0< j<∞):

j =⎡⎢⎢⎣

(𝜕x1∕(𝜕X1) (𝜕x1∕(𝜕X2) (𝜕x1∕(𝜕X3)(𝜕x2∕(𝜕X1) (𝜕x2∕(𝜕X2) (𝜕x2∕(𝜕X3)(𝜕x3∕(𝜕X1) (𝜕x3∕(𝜕X2) (𝜕x3∕(𝜕X3)

⎤⎥⎥⎦

(4.15)

A constant value of j represents the fact that the material cannot be annihilated.

Since det R= 1, the following holds from Eqn (4.14):

dV = det D dV0 (4.16)

Let us define the factor 𝜆V = (det D)1/3; we can then write

D0 =(

1𝜆V

)D and d0 =

(1𝜆V

)d (4.17)

4.2.3 Dilatational and deviatoric tensors: tensor invariantsBoth the stress and the strain tensors can be broken down into two tensors: the

dilatational and the deviatoric tensor.

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114 Confectionery and chocolate engineering: principles and applications

If we introduce the notation q= (V′ −V)/V for the specific volume change, the

following holds:

q ≈ 𝜀11 + 𝜀22 + 𝜀33 = tr 𝜀ij (4.18)

The average specific strain can be expressed as

𝜀∗ =tr 𝜀ij

3(4.19)

For a pure volume change,

DDil = 𝜀∗I (4.20)

where DDil is the dilatational tensor and I is the unit tensor.

For a pure deformation,

DDev = 𝜀ij − 𝜀∗I (4.21)

In detail,

DDev = 𝜀ij − 𝜀∗ =⎡⎢⎢⎣

𝜀11 − 𝜀∗ 𝛾12∕2 𝛾13∕2

𝛾21∕2 𝜀22 − 𝜀∗ 𝛾23∕2

𝛾31∕2 𝛾32∕2 𝜀33 − 𝜀∗

⎤⎥⎥⎦

(4.22)

This decomposition is not done simply for its own sake: Hamann (1983) noted

that it may be important in the study of material failure because some foods, par-

ticularly those that are incompressible, may not be sensitive to volume-changing

stresses but may be very sensitive to shape-changing stresses. For example, but-

ter and gelled egg white, which are nearly incompressible, are unaffected by

hydrostatic pressure (the deviatoric part is practically zero); however, if they are

deformed in terms of shape (the deviatoric part is not zero), they eventually

break. Shear stresses are deviatoric, and if we have the condition called pure

shear, the overall effect is a change in shape with negligible change in volume.

A decomposition of the stress tensor similar to Eqn (4.21) can also be given:

TDil = 𝜎∗I (4.23)

TDev = 𝜎ij − 𝜎∗I (4.24)

4.2.3.1 Scalar invariants of a tensorIn the theory of tensors of second rank, the eigenvalue problem is important; this

means the solution of the equation

AI = 𝜆I or (A − 𝜆I) = 𝟎 (4.25)

where A= [Aij] is a tensor of second rank, I is the unit tensor, 0 is the zero tensor

and 𝜆 is a scalar.

By calculating det(A− 𝜆I)= 0, the following equation can be obtained:

𝜆3 − S1𝜆2 + S2𝜆 − S3 = 0 (4.26a)

where the scalar invariants of the tensor A are

S1 = A11 + A22 + A33 = tr A (4.26b)

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The rheology of foods and sweets 115

S2 = (A11A22 − A12A21) + (A11A33 − A13A31) + (A22A33 − A23A32) (4.26c)

S3 = A11A22A33 = det A (4.26d)

Some further important relationships are

S1 = 𝜆1 + 𝜆2 + 𝜆3

S2 = 𝜆1𝜆2 + 𝜆1𝜆3 + 𝜆2𝜆3 = 12(tr A)2 − 1

2(tr A2)

S3 = 𝜆11𝜆22𝜆33 = 13(tr A3) − 1

2(tr A2)tr A + 1

6(tr A)3 (4.27a)

where 𝜆1, 𝜆2 and 𝜆3 are the solutions of Eqn (4.24), called the eigenvalues of the

tensor A.

The eigenvalues can be used to represent the normal stresses of the tensor Ain the form

A =⎡⎢⎢⎣

𝜆1 0 0

0 𝜆2 0

0 0 𝜆3

⎤⎥⎥⎦

(4.27b)

The normal stresses and the scalar invariants are important in the theory of

plasticity.

It is relevant to note that in the case of a symmetric tensor, the characteristic

equation (Eqn 4.26a) always has three real roots; furthermore, the eigenvectors

corresponding to them are orthogonal to each other.

4.2.4 Constitutive equationsEquations that show a relationship between stress (𝜎ij) and strain (𝜀ij) are called

rheological equations of state or constitutive equations. In the case of complex materi-

als, these equations may include other variables such as time, temperature and

pressure. The word rheogram refers to a graph of a rheological relationship, for

example, strain versus stress (for solids) or shear rate versus shear stress (for

fluids; see later).

Rheometry investigates the rheological properties of materials under special

conditions for which the rheological equations can be applied in a relatively

simplified, possibly scalar, form, for example, a flow curve (shear stress vs.

shear rate).

4.3 Solid behaviour

4.3.1 Rigid bodyThe definitive equation for a rigid (or Euclidean) body is

d = I (4.28)

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116 Confectionery and chocolate engineering: principles and applications

that is, for a rigid body, no deformation takes place during its movement.

(Euclidean geometry can be interpreted as a physical theory dealing with

the motion of rigid bodies.) In other words, the condition for deformation is

d− I≠0.

4.3.2 Elastic body (or Hookean body/model)When a force is applied to a solid material and the resulting stress versus strain

curve is a straight line through the origin, the material obeys Hooke’s law. This

relationship may be stated for shear stress and shear strain as

𝜎12 = 𝜇𝛾 (4.29)

where 𝜇 (in Pa) is the shear modulus.

Hookean materials do not flow and are linearly elastic. The stress remains

constant until the strain is removed, and the material then returns to its original

shape. Sometimes shape recovery, though complete, is delayed by atomic-level

processes. This time-dependent, or delayed, elastic behaviour is known as

elasticity.

Hooke’s law can be used to describe the behaviour of many solids (e.g. steel,

eggshell, dry pasta and hard candy) when they are subjected to small strains, typi-

cally such that 𝛾12 <0.01. Large strains often produce brittle fracture or non-linear

behaviour.

The behaviour of a Hookean solid may be investigated by studying the uniax-

ial compression of a cylindrical sample (Fig. 4.3). If a material is compressed so

that it experiences a change in length and radius, such that h0 → (h0 − 𝛿h) and

R0 → (R0 + 𝛿R), then the normal stress and strain may be calculated as follows

(assuming that the vertical direction in the figure is denoted by x2):

𝜎22 = F

𝜋R20

(4.30)

𝜀C = 𝛿hh0

(4.31)

where the absolute value of 𝛿h is used.

From Eqns (4.30) and (4.31), Young’s modulus, E (Pa), also called the modulus

of elasticity, can be determined:

E =𝜎22

𝜀C

(4.32)

If the deformations are large, the Hencky strain 𝜀H should be used to calculate

the strain, and the stress calculation should be adjusted for the increase in radius

caused by the compression:

𝜎22 = F𝜋(R0 + 𝛿R)2

(4.33)

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The rheology of foods and sweets 117

R0

h0

F

δh < 0

δR > 0

Figure 4.3 Uniaxial compression of a cylindrical sample.

In the case of axial compression, if the deformation is large, not only the normal

strain in the x2 direction but also the tangential shear strains in the x1 and x3

directions should be taken into account.

A critical assumption in these calculations is that the sample remains cylindri-

cal in shape. For this reason, lubricated contact surfaces are often recommended

when materials such as food gels are tested.

Young’s modulus may also be determined by flexural testing of beams; for a

detailed description, see Steffe (1996).

In addition to Young’s modulus, Poisson’s ratio 𝜈 can be defined from compres-

sion data:

𝜈 = lateral strainaxial strain

=𝛿R∕R0

|𝛿h∕h0|(4.34)

where the absolute value of 𝛿h is used.

Poisson’s ratio may range from 0 to 0.5. Typically, 𝜈 varies from 0.0 for rigid-like

materials containing large amounts of air to near 0.5 for liquid-like materials.

Values from 0.2 to 0.5 are common for biological materials, with 0.5 representing

an incompressible substance such as potato flesh. Tissues with a high level of

cellular gas, such as apple flesh, have values closer to 0.2. Metals usually have

values of Poisson’s ratio between 0.25 and 0.35; see Steffe (1996, p. 9).

If a material is subjected to a uniform change in external pressure, it may expe-

rience a volume change. These quantities are used to define the bulk modulus K:

K(Pa) = change in pressure∕volumetric strain (4.35)

that is, the pressure causes a change in volume that is related to the original value

of the volume.

The bulk modulus of dough is approximately 106 Pa, while the value for steel

is 1011 Pa. Another common property, the bulk compressibility, is defined as the

reciprocal of the bulk modulus.

The definitive equation for a Hookean body is

t = ⌊(d − I) (4.36)

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118 Confectionery and chocolate engineering: principles and applications

where ⌊ is a tensor function. If our study is limited to isotropic media, the fol-

lowing well-known form of Hooke’s law is obtained:

t = 2𝜇(d − I) + 𝜆 tr(d − I)I (4.37)

where 𝜇 and 𝜆 are the Lamé parameters. If tr(d− I)= tr E≈ 0, that is, the volume

change is small, then Eqn (4.37) is simplified; see Eqn (4.29).

In the case of incompressibility,

div E = tr E = 0 (4.38)

(Definitions: modulus= stress/strain; compliance= strain/stress, that is, modu-

lus= 1/compliance.)

The following elastic moduli are used for characterizing homogeneous

isotropic materials: E=Young’s modulus, 𝜇= shear modulus, 𝜈 = Poisson’s

ratio, K= bulk modulus (which is an extension of Young’s modulus to three

dimensions), 𝜆=first Lamé parameter and M= P-wave modulus (uninteresting

from our point of view).

When two material constants describing the behaviour of a Hookean solid are

known, the others can be calculated using theoretical relationships. For example,

the first Lamé parameter can be calculated from

𝜆 = K − 2𝜇

3(4.39)

Numerous experimental techniques applicable to food materials may be used

to determine Hookean material constants. The methods include testing in ten-

sion, in compression and in torsion; see Dally and Riley (1965), Polakowski and

Kipling (1966) and Mohsenin (1986).

The Hookean properties of some typical materials have been published; see

Lewis (1987) [cited by Steffe (1996, Appendix 6.5)].

4.3.3 Linear elastic and non-linear elastic materialsBoth linear elastic materials and non-linear elastic materials (such as rubber)

return to their original shape when the stress is removed. Food may be solid in

nature but not Hookean. A comparison of curves for linear elastic (Hookean),

elastoplastic and non-linear elastic materials (Fig. 4.4) shows a number of simi-

larities and differences.

An elastoplastic material has a Hookean-type behaviour below the yield stress

(𝜎0) but flows to produce permanent deformation above that value. Margarine

and butter, at room temperature, may behave as elastoplastic substances. The

method of investigation of this type of material, as a solid or as a fluid, depends

on whether the shear stress is above or below 𝜎0. It is worth noting, however,

that typical elastic materials, such as steel and rubber, also have a yield stress,

although it has a very high value and the elastic (linear) section in Figure 4.4 is

much steeper than in the case of foods.

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The rheology of foods and sweets 119

Fluid

Non-linear e

lastic

Ela

stic

(H

ooke

an)

Shear

str

ess,

σ 12

Yieldstress,

σ0

Deformation, γ

Figure 4.4 Deformation curves for linear elastic (Hookean), elastoplastic and nonlinear elastic

materials.

Furthermore, to fully distinguish fluid-like from solid-like behaviour, the char-

acteristic time of the material and the characteristic time of the deformation

process involved must be considered simultaneously. The Deborah number, pro-

posed by Reiner, has been defined to address this issue (see Steffe, 1996, p. 332).

Food rheologists also find the failure behaviour of solid food (particularly brit-

tle materials and firm gels) to be very useful because such data sometimes corre-

late well with the conclusions of human sensory panels (Kawanari et al., 1981;

Hamann, 1983; Montejano et al., 1985).

A typical characteristic of brittle solids is that they break when given a small

deformation. Hamann (1983) summarized an evaluation of the structural fail-

ure of solid foods in compression, torsion and sandwich shear modes. The jagged

force–deformation relationships of crunchy materials may offer alternative tex-

ture classification criteria for brittle or crunchy foods (Ulbricht et al., 1995; Peleg

and Normand, 1995).

4.3.4 Texture of chocolateTscheuschner (2008) investigated the texture of chocolate with an Instron-type

instrument (from Kögel u.a.). If the height of a sample body of cylindrical form

is H0 and the reduction under the effect of compression is ΔH, the compression

can be defined by the ratio K=ΔH/H0. If the cross-sectional area of the probe

body is A and the force of compression is F, then the pressure of compression

can be defined by P=F/A. If Fm is the maximum force needed for breaking the

sample, then the solidity with respect to biting can be defined by Pm = Fm/A.

By studying plots of P versus K, it can be observed that the curves, starting

from the origin, go through a maximum value which provides a measure of the

biting solidity for the given conditions (recipe, temperature etc.); the value of P

finally decreases. The typical range of P is 0–2.5× 106 Pa and that of K is 0–30%.

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120 Confectionery and chocolate engineering: principles and applications

If the velocity of compression is increased, the maximum of P (Pm) is displaced

to higher values of K.

According to Tscheuschner’s study, there is a linear relationship between the

sensory biting solidity IB and the instrumentally measured solidity Pm, which has

the form IB = 1.03Pm + 0.91.

Moreover, he determined that, at constant values of compression and temper-

ature, the decrease in the height h(t) of the sample as a function of the time t

of melting gives a linear plot of h(t) versus t. If the duration of melting is fixed

(e.g. 20 min), then the values hA for this time interval are characteristic of the

melting of the chocolate. When this measured behaviour of chocolate was com-

pared with the sensory behaviour (characterized by IM) in the mouth, a linear

relationship was found: IM = 0.9hA + 0.14.

Both IB and IM may provide a basis for classifications of sensory quality. For

further details, see Tscheuschner (2008).

4.4 Fluid behaviour

4.4.1 Ideal fluids and Pascal bodiesThe model of ideal fluids is based on Pascal’s theorem, according to which no

shear stress evolves during the movement of ideal fluids. Consequently, the

Cauchy stress tensor t is simplified to a spherical tensor:

t = −pI (4.40)

where p is the scalar pressure and I is the unit tensor.

The other principal equation expresses the incompressibility of ideal fluids. If

the equation of continuity is

d𝜌

dt+ 𝜌 div v = 0 (4.41)

where 𝜌 is the fluid density and v is the velocity vector of the fluid, then the

following holds for an incompressible fluid:

div v = 0 andd𝜌

dt= 0 → 𝜌 = 𝜌(t) = constant (4.42)

Equations (4.40) and (4.42) determine the flow properties of ideal fluids, or

Pascal bodies.

4.4.2 Fluid behaviour in steady shear flow4.4.2.1 Simple steady shear flow: Newtonian fluidsTo interpret the deformation rate, let us consider the time derivative of the defor-

mation tensor E= 𝜀ij = (1/2)(D+DT):

V(t,x) = dEdt

=d(u∕r)

dt= 1

2(D + DT) (4.43)

where D= dv/dx, that is the velocity gradient.

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The rheology of foods and sweets 121

For isotropic fluids, the constitutive equation of a Newtonian body (or model)

can be given as

t = 2𝜂(Grad v)S + (𝜂V div v − p)I (4.44)

where t is the stress tensor (Pa), 𝜂 is the shear viscosity (Pa s), (Grad v)S is the

symmetric part of the velocity gradient tensor (s−1), 𝜂V is the volumetric viscosity

(Pa s), div v is the divergence of the velocity (s−1) and p is the static pressure (Pa).

For a Newtonian model, the velocity gradient tensor can be given in the form

Grad v =⎡⎢⎢⎣

0 𝜀′ 0

0 0 0

0 0 0

⎤⎥⎥⎦

(4.45)

where 𝜀′ ≡ d𝜀/dt is the shear rate.

Every asymmetric tensor can be constructed from a symmetric and an anti-

symmetric tensor; when this is done for Grad v, we obtain

⎡⎢⎢⎣

0 𝜀′ 0

0 0 0

0 0 0

⎤⎥⎥⎦=⎡⎢⎢⎣

0 𝜀′∕2 0

𝜀′∕2 0 0

0 0 0

⎤⎥⎥⎦

symmetric tensor

+⎡⎢⎢⎣

0 𝜀′∕2 0

−𝜀′∕2 0 0

0 0 0

⎤⎥⎥⎦

antisymmetric tensor

In Eqns (4.36) and (4.43), only the symmetric tensor is taken into account. If

the fluid is incompressible (div v= 0), the static pressure can also be neglected

(p= 0), and then the stress tensor has the form

t =⎡⎢⎢⎣

0 𝜂𝜀′ 0

𝜂𝜀′ 0 0

0 0 0

⎤⎥⎥⎦

(4.46)

If only a single component differs from zero, the well-known equation of a

flow curve is obtained,

𝜏12 = 𝜂𝜀′ (4.47)

Let us consider Cauchy’s equation of motion, which is an application of New-

ton’s second law to continua:

𝜌dvdt

= Div t + 𝜌f (4.48)

On the left side of Eqn (4.48), we have (mass× acceleration)/volume; on the

right side, we have forces acting on the surface/volume (Div t)+ forces acting in

the volume/volume. If the value of t in Eqn (4.44) is substituted into Eqn (4.48),

we obtain

𝜌dvdt

− 𝜌f − grad p − 𝜂 div grad v = 0 (4.49)

assuming that the fluid is incompressible (div v=0, i.e. 𝜂V can be neglected).

Equations (4.41) and (4.49) are the Navier–Stokes equations in a simpler form.

Fluids may be studied by subjecting them to continuous shearing at a constant

rate. Ideally, this can be accomplished using two parallel plates with a fluid in the

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122 Confectionery and chocolate engineering: principles and applications

Area

Force

Velocity

profile

h

u = 0

u

x1

x2Figure 4.5 Velocity profile of fluid between

parallel plates. Source: Steffe (1996). Reproduced

with permission from Steffe.

gap between them (Fig. 4.5). The lower plate is fixed and the upper one moves

at a constant velocity u, which can be thought of as an incremental change in

position L divided by a small interval of time t, that is, 𝛿L/𝛿t. A force per unit area

on the plate is required for motion, resulting in a shear stress 𝜎21 on the upper

plate, which, conceptually, could also be considered to be a layer of fluid.

The flow described earlier by Equations 4.46 and 4.47 is steady simple shear, and

the shear rate (also called the strain rate) is defined as the rate of change of strain:

𝛾 ′ ≡d𝛾

dt= d

dt

(𝛿Lh

)= u

h(velocity gradient) (4.50)

Other symbols for the shear rate are 𝜕v/𝜕r (where r is the radius of a tube) and D.

This experimental arrangement is a realization of Newton’s original defini-

tion of viscosity, which may be applied to streamline (laminar) flow between parallel

plates:

𝜂 = 𝜂(𝛾 ′) =𝜎21

𝛾 ′(4.51)

where 𝜎21 is an element of the stress tensor.

In steady, simple shear flow the coordinate system may be oriented parallel

to the direction of flow so that the stress tensor given by Eqns (4.1) and (4.4)

reduces to

𝜎ij =⎡⎢⎢⎣

𝜎11 𝜎12 0

𝜎21 𝜎22 0

0 0 𝜎33

⎤⎥⎥⎦

(4.52)

Methods of applying this definition for different types of viscometer are

described by, for example, Steffe (1996, Chapter 1).

Spreading (of creams or spreads) and brushing operations are frequently found

in the food industry. In this case, the maximum shear rate can be estimated from

the velocity u of the brush or knife divided by the thickness z of the coating:

𝛾 ′max = uz

(4.53a)

The idea of ‘maximum speed divided by gap size’ can be useful for estimating the

shear rates found in particular applications such as brush coating (Steffe, 1996).

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The rheology of foods and sweets 123

The shear rate induced by mixing can be calculated by the Metzner–Otto

method (Metzner and Otto, 1957) according to the formula

𝛾 ′ = Kn (4.53b)

where n is the revolution rate (in s−1) and K is the Metzner–Otto constant. For

details of the determination of K, see Windhab (1993).

Simple shear flow is called viscosimetric flow. It includes

• axial flow in a tube;

• rotational flow between concentric cylinders;

• rotational flow between a cone and a plate;

• torsional flow (and also rotational flow) between parallel plates.

In viscosimetric flow, three shear-rate-dependent material functions, collec-

tively called viscometric functions, are needed to completely establish the state of

stress in the fluid, since they contain all the elements of the stress tensor given

by Eqns (4.45) and (4.53). These may be described as

the viscosity function,

𝜂 = 𝜂(𝛾 ′) =𝜎21

𝛾 ′(𝜎21 = 𝜎12) (4.54)

the first normal-stress coefficient,

Φ1 = Φ1(𝛾 ′) =𝜎11 − 𝜎22

(𝛾 ′)2=

N1

(𝛾 ′)2(4.55)

and the second normal-stress coefficient,

Φ2 = Φ2(𝛾 ′) =𝜎22 − 𝜎33

(𝛾 ′)2=

N2

(𝛾 ′)2(4.56)

The first normal-stress difference N1 = 𝜎11 − 𝜎22 is always positive and is

assumed to be approximately 10 times greater than the second normal-stress

difference N2 = 𝜎22 − 𝜎33.

Measurement of N2 is difficult; fortunately, the assumption that N2 =0 is usu-

ally satisfactory. The ratio N1/𝜎12, known as the recoverable shear (or recoverable

elastic strain), has proven to be a useful parameter in modelling die swell phe-

nomena in polymers (Tanner, 1988).

Some data on the N1 values of fluid foods have been published (Table 4.1).

If a fluid is ideally Newtonian,

• 𝜂(𝛾 ′) is a constant and equal to the Newtonian viscosity; and

• the first and second normal-stress differences (N1 and N2) are zero.

As 𝛾 ′ approaches zero, elastic fluids tend to display Newtonian behaviour.

Table 4.2 shows several shear-rate regions that are important in food process-

ing.

Sharma and McKinley (2012) give an empirical rule for computing the first

normal-stress difference from steady shear viscosity data for concentrated poly-

mer solutions and melts.

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124 Confectionery and chocolate engineering: principles and applications

Table 4.1 Values of steady shear and normal-stress differences.a

Product K (Pan) n K′ (Pa sm) m

Apple butter 222.90 0.145 156.03 0.566

Panned frosting 355.84 0.117 816.11 0.244

Honey 15.39 0.989

Ketchup 29.10 0.136 39.47 0.258

Marshmallow cream 563.10 0.379 185.45 0.127

Mayonnaise 100.13 0.131 256.40 −0.048

Mustard 35.05 0.196 65.69 0.136

Peanut butter 501.13 0.065 3785.00 0.175

Stick butter 199.29 0.085 3403.00 0.393

Stick margarine 297.58 0.074 3010.13 0.299

Squeezable margarine 8.68 0.124 15.70 0.168

Tub margarine 106.68 0.077 177.20 0.358

Whipped butter 312.30 0.05? 110.76 0.476

Whipped cream 422.30 0.05 363.70 0.418

aThe constants K and n are those of the Ostwald–de Waele model, 𝜎 =K(𝛾 ′)n;

N= 𝜎11 − 𝜎22 =K′(𝛾 ′)m.

Source: Steffe (1996). Reproduced with permission from Steffe.

Table 4.2 Shear rates typical of familiar materials and

processes.

Process/situation Shear rate (s−1)

Extrusion, pipe flow 1–1000

Dough sheeting, dip coating 10–100

Mixing/stirring 10–1000

4.4.2.2 Classification of rheological behaviourClassifying fluids is a valuable way to conceptualize fluid behaviour. However,

we do not mean to imply that the types of behaviour noted in Figures 4.6–4.8

are mutually exclusive.

Every type of model is characterized by two plots:

• deformation (𝜀) versus time (t); and

• deformation (𝜀) versus stress (𝜏) for elastic deformation (Fig. 4.6); in addition,

there is a plot of shear rate (𝜕𝜀/𝜕t) versus shear stress (𝜏) (called the flow curve)

for plastic (Fig. 4.7) and viscous (Fig. 4.8) deformation.

All three types of rheological behaviour (elastic, plastic and viscous) are ideally

manifested in the so-called ideal bodies (the ideal Hookean, ideal Bingham and

ideal Newtonian bodies), for which both plots are linear. The plastic models have

the typical characteristic that in a plot of 𝜕𝜀/𝜕t versus 𝜏, the curve (or, in the case

of an ideal Bingham body, the line) does not start from the origin but from a

value 𝜏0, called the yield stress.

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The rheology of foods and sweets 125

ε

t

ε

t

ε

t

ε

τ

ε

τ

ε

τ

Hookeanbody

(Ideal)

Non-Hookeanbody

Reversible

Figure 4.6 Types of elastic deformation.

ε

t

Plastoelastic Viscoplastic(Ideal Bingham body)

Plastic(non-elastic)

ε

t

ε

t

ττ

𝜕ε/𝜕t𝜕ε/𝜕t

τ

𝜕ε/𝜕t

Figure 4.7 Types of plastic deformation.

Among the plastic and viscous models, there are types which also have elastic

properties under the usual technological circumstances. It is, however, worth

emphasizing that under extreme conditions (e.g. a sudden, very strong stress),

even such typical viscous media as water behave as elastic rather than viscous

materials.

A further classification of the various models emphasizes the time-

independent/dependent or shear-thinning/thickening behaviour of a fluid,

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126 Confectionery and chocolate engineering: principles and applications

ε

t t

ViscoelasticIdeal

(Newton body)Viscous

(non-elastic)

ε ε

t

ττ

𝜕ε/𝜕t𝜕ε/𝜕t

τ

𝜕ε/𝜕t

Figure 4.8 Types of viscous deformation.

and the ‘mixing’ of these behaviours; for example, a material showing elastic

behaviour (such as dough) may simultaneously show shear thinning and

time-dependent behaviour. Other factors, such as ageing, may also influence

the rheological behaviour.

In the following sections, mathematical models are presented, which describe

the rheological behaviour of various types of fluid.

4.4.2.3 Mathematical models for inelastic fluids4.4.2.3.1 Time-independent material functions for viscous and plastic

fluidsThe elastic behaviour of many fluid foods is small or can be neglected (materials

such as dough are an exception), leaving the viscosity and plasticity function as

the main area of interest.

The ideal Newton model can be described by the equation

𝜏 = 𝜂D (4.57)

where 𝜏 is the shear stress (Pa), 𝜂 is the dynamic viscosity (Pa s)= constant and

D is the shear rate (s−1).

In the case of generalized Newton models, 𝜂 depends on the shear rate or shear

stress.

Fluids that have a yield stress 𝜏0 ≥ 0 are called Bingham fluids, in general. The

flow curve can be described by the equation

𝜏 = 𝜂Pl𝛾′ + 𝜏0 (4.58)

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The rheology of foods and sweets 127

Shear rate (s–1)0

0

Yield

stressShear

str

ess (

Pa)

Shear thinning

Shear thinning

Shear thickening

Bingham fluids

(Ideal)

(Ideal)

Newtonianfluids

Figure 4.9 Flow curves for typical time-independent fluids. The flow curves of Newtonian and

Bingham fluids are straight only in the ideal case; otherwise, they are convex or concave.

where 𝜂Pl is the plastic (or Bingham) viscosity (Pa s), which is constant in the

case of an ideal Bingham body.

In the case of generalized Bingham fluids, 𝜂Pl is not constant but is dependent on

the shear rate or shear stress.

Figure 4.9 demonstrates the flow curves of Newtonian and Bingham fluids;

both types may show either shear-thinning or shear-thickening behaviour. The

flow curves of Newtonian and Bingham fluids are straight only in the ideal case;

in other cases, they are convex or concave.

One of the mathematical models used to describe the behaviour of certain

types of generalized Newtonian fluids and generalized Bingham fluids is the

Herschel–Bulkley model [or Herschel–Bulkley–Porst–Markowitsch–Houwink

(HBPMH) or generalized Ostwald–de Waele model],

𝜏 = KDn + 𝜏0 (4.59)

where K (>0) is the consistency coefficient, n (>0) is the flow behaviour

index and 𝜏0 (≥0) is the yield stress. One special case of the Herschel–Bulkley

model is the Ostwald–de Waele (or power-law) model, where 𝜏0 =0, that is

the Ostwald–de Waele fluid is a type of Newtonian fluid. The Herschel–Bulkley

model is appropriate to many fluid foods. K is commonly called the viscosity (𝜂)

or the plastic viscosity (𝜂Pl).

Shear-thinning and shear-thickening behaviour of time-independent Newtonian

and Bingham fluids can be distinguished by the following relations (where the

shear rate is denoted here by D):

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128 Confectionery and chocolate engineering: principles and applications

• 𝜕𝜂/𝜕D> 0 corresponds to shear-thickening behaviour, or dilatancy – there is a

convex flow curve of 𝜏 versus D;

• 𝜕𝜂/𝜕D< 0 corresponds to shear-thinning, or pseudo-plastic, behaviour – there

is a concave flow curve.

For further details, see Langer and Werner (1981), Ellenberger et al. (1984),

Tebel and Zehner (1985), Henzler (1988), Grüneberg and Wilk (1992), Schmer-

witz (1992), Schnabel and Reher (1992) and Steffe (1996, Appendix 2).

4.4.2.3.2 Apparent viscosityThe apparent viscosity has a precise definition. It is, as in Eqn (4.51), the shear

stress divided by the shear rate:

𝜂app = 𝜂app(D) =𝜏21

D

(= 𝜏

D

)(4.60)

(Later, we shall sometimes use the notation 𝜏21 ≡ 𝜏.)

For Herschel–Bulkley fluids, the apparent viscosity is determined in a like man-

ner from Eqns (4.59) and (4.60). Therefore,

𝜂app = 𝜏

D= KDn−1 +

𝜏0

D(4.61)

During flow, materials that show shear-thinning behaviour may exhibit three

distinct regions:

The lower Newtonian region, where the apparent viscosity 𝜂0, called the limiting

viscosity at zero shear rate, can be regarded as constant as the shear rate is

varied. The lower Newtonian region may be relevant in problems involving

low shear rates, such as those related to the sedimentation of fine particles in

fluids.

The middle region, where the apparent viscosity 𝜂 changes with shear rate

(decreasing for shear-thinning fluids) and the power-law equation is a suit-

able model for the phenomenon. The middle region is most often examined

when the performance of food-processing equipment is considered.

The upper Newtonian region, where the slope of the curve 𝜂∞, called the limiting

viscosity at infinite shear rate, can again be regarded as constant as the shear

rate is varied.

When the flow of an Ostwald–de Waele fluid in a tube is studied, the so-called

consistency variables are defined:

P(Pa) =ΔpR

2Land V (s−1) = 4Q

R3𝜋(4.62)

where R (m) and L (m) are the radius and length, respectively, of the tube, Δp

(Pa) is the pressure difference between the two ends of tube and Q (m3/s) is the

flow rate.

The usual V versus P plot is of the form presented in Figure 4.10, where

tan 𝛼 = 1𝜂0

and tan 𝛽 = 1𝜂∞

(4.63)

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The rheology of foods and sweets 129

β

α

P

V

Figure 4.10 Shear-thinning behaviour of an Ostwald–de Waele fluid represented by a plot of

the consistency variables.

4.4.2.3.3 Time-dependent material functions of plastic and viscousfluids

Time-dependent materials are considered to be inelastic with a viscosity function,

which depends on time. The response of the substance to a stress is instantaneous,

and the time-dependent behaviour is due to changes in the structure of the material

itself.

In contrast, the time-dependent effects found in viscoelastic materials arise

because the response of the stress to an applied strain is not instantaneous and

is not associated with a structural change in the material. Also, the timescale of

thixotropy may be quite different from the timescale associated with viscoelas-

ticity. The most characteristic effects are usually observed in situations involving

short process times.

Real materials may be both time-dependent and viscoelastic.

Materials with time-dependent characteristics may exhibit either a decreasing

or an increasing shear stress (and apparent viscosity) with time at a fixed rate of

shear. Both phenomena can be described by the following relations (where the

shear rate D is constant):

• (𝜕𝜏/𝜕t)D > 0 for fluids with time-thickening behaviour and

• (𝜕𝜏/𝜕t)D < 0 for fluids with time-thinning behaviour.

Table 4.3 shows the terminology that is used for fluids with time-dependent

behaviour. For example, thixotropy may be observed when the rotor of a rota-

tional viscosimeter turns at a constant angular velocity (D= shear rate∼ d𝜔/dt),

while the measured values relating to the shear stress decrease continuously.

Irreversible thixotropy, called rheomalaxis (or rheodestruction), is common in

food products and may be a factor in evaluating the yield stress as well as in the

general flow behaviour of a material. (‘Antithixotropy’ and ‘negative thixotropy’

are synonyms for ‘rheopexy’.)

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130 Confectionery and chocolate engineering: principles and applications

Table 4.3 Terminology used for fluids with time-

dependent behaviour.

Change Time-thinning Time-thickening

Reversible Thixotropy Rheopexy

Irreversible Rheomalaxis

(rheodestruction)

Rheoretrogradation

The thixotropy of many fluid foods may be described in terms of the

sol–gel transition phenomenon. This terminology could apply, for example, to

starch-thickened baby food or to yogurt. After being manufactured and placed

in a container, these foods slowly develop a three-dimensional network and may

be described as gels. When they are subjected to shear (by standard rheological

testing or by mixing with a spoon), the structure is broken down (the gel→ sol

transition) and the material reaches a minimum thickness, where it exists in the

sol state. In foods that show reversibility, the network is rebuilt and the gel state

is reobtained. Irreversible materials remain in the sol state. When a material is

subjected to a constant shear rate, the shear stress will decay over time. During

a rest period, the material may completely recover, partially recover or not

recover any of its original structure, leading to a high-, medium- or low-torque

response, respectively, in the sample.

Thixotropic behaviour is common in the confectionery industry; for example,

before dosing, filling masses are mixed thoroughly in order to obtain the correct

viscosity. The structural changes caused by mixing can be linked, for example, to

recrystallization, and then breaking and/or solution of large crystals, in the case

of fondant used as an ingredient.

Torque decay data may be used to model irreversible thixotropy by adding a struc-

tural decay parameter 𝜆 to the Herschel–Bulkley model to account for breakdown

(Tiu and Boger, 1974):

𝜏 = 𝜆{KDn + 𝜏0} (4.64)

where 𝜆= 𝜆(t), the structural parameter, is a function of time. 𝜆= 1 before the

onset of shearing (t= 0), and an equilibrium value 𝜆E <𝜆 is obtained after com-

plete breakdown as a result of shearing, which means irreversibility.

The decay of the structural parameter with time may be assumed to obey a

second-order equation,d𝜆dt

= −k1(𝜆 − 𝜆E)2 (4.65)

where k1 is the rate constant, which is a function of shear rate. From Eqns (4.52),

(4.53), (4.61) and (4.64),

𝜆 = 𝜏

KDn + 𝜏0

= 𝜂D

KDn + 𝜏0

≡ 𝜂A (4.66)

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The rheology of foods and sweets 131

Table 4.4 Viscosity data.

𝜼 (Pa s) Time (s)

10 0

9 10

8.3 20

where A≡D/{KDn + 𝜏0}= constant (since D and 𝜏0 are constant). Taking into

account Eqns (4.65) and (4.66), we can write

d𝜆dt

= Ad𝜂

dt= −k1(𝜆 − 𝜆E)2 = −k1A2(𝜂 − 𝜂E)2 (4.67)

where 𝜆(t)→ 𝜂(t) and 𝜆E → 𝜂E.

After integrating the differential equations (4.53) and (4.67) with respect to 𝜂,

the result is1

𝜂 − 𝜂E

= 1𝜂0 − 𝜂E

+ Bt (4.68)

where 𝜂0 is the initial value of the apparent viscosity calculated from the initial

shear stress and shear rate (for t=0 and 𝜆= 1), and B= k1A.

Using Eqn (4.68), a plot of 1/(𝜂 − 𝜂E) versus t, at a particular shear rate, can

be made to obtain B. This is done for numerous shear rates and the resulting

information is used to determine the relation between B and 𝛾 ′ and the relation

between k1 and 𝛾 ′.

This method supposes also that K (=viscosity) is constant with time at a given

shear rate, that is the change of the ratio denoted by A can be neglected.

Example 4.1The data for viscosity as a function of mixing time listed in Table 4.4 were

obtained.

By applying Eqn (4.68), 𝜂E and B (Pa s2)−1 are calculated as follows:

Eqn I∶ 19 − 𝜂E

= 110 − 𝜂E

+ 10B

Eqn II∶ 18.3 − 𝜂E

= 110 − 𝜂E

+ 20B

Eqn II − Eqn I∶ 18.3 − 𝜂E

− 19 − 𝜂E

= 10B = 19 − 𝜂E

− 110 − 𝜂E

that is1

8.3 − 𝜂E

+ 110 − 𝜂E

= 29 − 𝜂E

→ 𝜂E = 4.33 Pa s

and, with substitution from Eqn I,

B = 0.00377 … (Pa s2)−1

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132 Confectionery and chocolate engineering: principles and applications

4.4.2.4 Yield stress phenomenaAn important characteristic of Bingham plastic materials is the presence of a yield

stress 𝜎0 (another common notation is 𝜏0), which represents a finite stress required

to achieve flow. Below the yield stress, the material exhibits solid-like characteris-

tics: it stores energy at small strains, and does not level out under the influence

of gravity to form a flat surface. This characteristic is very important in process

design and quality assessment for materials such as butter, yogurt and spreads,

and also for dipping in chocolate or any other fatty mass. The yield stress is a

practical, but idealized, concept.

4.4.2.4.1 Thickness of a falling filmThe yield stress is important in the covering of centres, for example covering with

chocolate mass. Let us consider a wall which has an angle 𝛼 to the vertical. The

shear stress gradient affecting an infinitesimally thick layer of chocolate mass is

d𝜏yz

dy= 𝜌g cos 𝛼 (4.69)

where z is a coordinate directed along the wall, z⟂ y, 𝜌 is the density of the falling

film and g is the gravitational constant (9.81 m/s2).

To integrate Eqns (4.25) and (4.69) between the boundaries of the film, we

take 𝜏 =𝜏0 from 0 to a, and then a variable value of 𝜏 from a to y. Although

the flow curve most commonly used for chocolate mass is the Casson equation

(discussed later), we use here the general form for a Bingham fluid for simplicity

(see Eqn 4.58), d𝜏=d𝜏0 (=0)+𝜂(dvyz/dy)dy, which holds also for a Casson body:

a+y

0d𝜏 = 𝜏0 + ∫

y

a𝜂

dvyz

dydy = a𝜌g cos 𝛼 +

y

a𝜂

dvyz

dydy (4.70)

The flow starts where 𝜏 = 𝜏0 (i.e. y= a), which means the following in the case of a

vertical wall parallel to the z direction (since z⟂ y, 𝛼 = 0, and therefore cos 𝛼 = 1):

𝜏0 = 𝜌ga (4.71)

where a is the thickness of the film.

For further details, see Szolcsányi (1972, pp. 191–194) and Lásztity (1987a,

p. 267).

Example 4.2The yield stress (or yield value) of couverture chocolate is 𝜎0 =10 Pa;

𝜌= 1.2×103 kg/m3. The thickness of chocolate cover will be (see Eqn 4.60)

a =𝜎0

𝜌g= 10

1.2 × 103 × 9.81(m) = 0.849 mm

The yield stress 𝜏0 may be defined as the minimum stress required to initiate flow.

Although the existence of a yield stress has been challenged, there is little doubt

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The rheology of foods and sweets 133

from a practical standpoint that 𝜎0 is an engineering reality, which may strongly

influence process engineering calculations.

There are many ways to evaluate the yield stress for fluid-like substances

(Steffe, 1996, p. 35). Cheng (1986) has written an excellent review of the yield

stress problem, and has also described a concept of static and dynamic yield stresses

that has great practical value in the rheological testing of fluid foods.

Many foods, such as starch-thickened baby food (Steffe and Ford, 1985),

thicken during storage and exhibit irreversible thixotropic behaviour when

stirred before consumption. Chemical changes (e.g. starch retrogradation) cause

a weak gel structure to form in the material during storage. This structure is

sensitive and is easily disrupted by movement of the fluid. The yield stress

measured on an undisturbed sample is the static yield stress. The yield stress of a

completely broken down sample, often determined from extrapolation of the

equilibrium flow curve, is the dynamic yield stress (Fig. 4.11).

Equilibriumflow curve

Staticyield stress

Dynamicyield stress

Shear

str

ess

Shear rate

Figure 4.11 Static and dynamic yield stresses. Source: Steffe (1996). Reproduced with

permission from Steffe.

The static yield stress may be significantly higher than the dynamic yield stress.

If the material recovers its structure during a short period of time (which is

uncommon in food products), then a rate parameter may be used to fully describe

the rheological behaviour.

The idea of a static and a dynamic yield stress can be explained by assuming

that there are two types of structure in a thixotropic fluid (Cheng, 1986):

• One structure is insensitive to shear rate and serves to define the dynamic yield

stress associated with the equilibrium flow curve.

• A second structure, the weak structure, forms over a certain period of time when

the sample is at rest.

Combined, the two structures cause a resistance to flow which determines the

static yield stress.

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134 Confectionery and chocolate engineering: principles and applications

Yoo et al. (1995) defined a new dimensionless number, the yield number:

Yield number =static yield stress

dynamic yield stress(4.72)

An important issue in the measurement of yield stress, particularly from a

quality control standpoint, is reproducibility of the experimental data. This is

critical when one is comparing the overall characteristics of products made on

different production lines or in different plants.

4.4.2.4.2 Bingham fluidsBingham fluids have a yield stress, and in certain circumstances they behave

both like solids (elastic and/or plastic behaviour if 𝜏 ≤ yield stress) and like fluids

(if 𝜏 > yield stress). Various theoretical descriptions of the solid→plastic→fluid

transitions make use of a threshold value denoted by f, which characterizes the

plastic state. This value is called the yield stress (discussed earlier). f is usually

expressed in terms of the scalar invariants of the stress tensor T: f= f(t1, t2, t3). In

the plastic state,

f (t1, t2, t3) ≥ 0 (4.73)

It is known from experiment that f is independent (or nearly independent)

of the first scalar invariant (t1 = tr T), that is the deviatoric stress (the shearing

effect) essentially determines the value of f: f= f(t2, t3). If, also, the effect of t3 can

be neglected, the Huber–von Mises criterion is obtained:

f = TDev ⋅ TDev −2(𝜎F)2

3= 0 (4.74)

where ⋅ denotes the scalar product of the deviatoric tensor TDev with itself, and

𝜎F is a material property. Equation (4.74), written in detail, is

f = (𝜎y − 𝜎z)2 + (𝜎z − 𝜎x)2 + (𝜎x − 𝜎y)2 + 6(𝜎2xy + 𝜎2

yz + 𝜎2zx) −

2(𝜎F)2

3= 0 (4.75)

Taking the Huber–von Mises criterion (Eqns 4.74 and 4.75) into account, the

constitutive equation of a generalized Bingham fluid can be written as

V =(

12𝜂

)[1 −

√2∕3

TDev ⋅ TDev

𝜎F

]TDev (4.76)

where V is the shear rate tensor and 𝜂 is the dynamic viscosity.

Tresca’s criterion can be easily represented by means of Mohr circles (Fig. 4.12).

The abscissa is the stress 𝜎 in the normal direction, the ordinate is the shear stress

𝜏, and j1 < l2 < l3 are the eigenvalues of the stress tensor T. Tresca’s criterion is

defined by the equation

𝜏cr =l3 − l1

2(4.77)

that is the critical value of the shear stress is equal to the radius of largest semi-

circle (see Fig. 4.12).

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The rheology of foods and sweets 135

τ

σ1

τcr

σ2σ3

σ

Figure 4.12 Representation of Tresca’s criterion by means of Mohr circles.

Example 4.3A stress tensor is given by its elements (in Pa) as follows:

𝜎ij =⎡⎢⎢⎣

4 5 0

5 4 0

0 0 4

⎤⎥⎥⎦

A. Let us calculate the Huber–von Mises criterion according to Eqn (4.75):

f = (4 − 4)2 + (4 − 4)2 + (4 − 4)2 + +6(52 + 02 + 02) − 2(𝜎F)2∕3 = 0

𝜎F = 15 Pa

It can be seen that this calculation is very easy.

B. Let us calculate the Tresca criterion according to Eqn (4.77), which uses the

roots (l3; l1) of the characteristic equation of the stress tensor.

For obtaining the characteristic equation, the following determinant has to be

calculated:

0 = det𝜆 − 4 5 0

5 𝜆 − 4 0

0 0 𝜆 − 4

= (𝜆 − 4)[(𝜆 − 4)2 − 0 × 0] − 5[5(𝜆 − 4) − 0 × 0] + 0 =

= (𝜆 − 4)(𝜆 − 4)2 − 25(𝜆 − 4) = (𝜆 − 4)[(𝜆 − 4 + 5)(𝜆 − 4 − 5)

= (𝜆 + 1)(𝜆 − 4)(𝜆 − 9)

(The roots of characteristic equation are denoted by 𝜆 in general.)

The roots are: l1 =−1; l2 = 4; l3 = 9.

𝜏cr = (l3 − l1)∕2 = (9 + 1)∕2 = 5 Pa

The two criteria usually do not differ so much. In theoretical calculations the

Huber–von Mises criterion is prefered.

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136 Confectionery and chocolate engineering: principles and applications

4.4.2.4.3 Recent studies on yield stressBarnes (1999) gives an account of the development of the idea of a yield stress

for solids, soft solids and structured liquids from the beginning of this century

to the present time. Around 1980, commercial versions of the new generation

of electrically driven controlled-stress rheometers began to appear, based on air

bearings that greatly reduced friction, but now using the so-called drag-cup elec-

trical motors that allowed controlled stresses to be more easily applied, but still

independent of rotation speed. Along with these features came new ways of

measuring smaller and smaller rotation and rotation rates. The latest optical-disc

technology now means that rotation rates as low as 10−8 rad s−1 (∼1 rev in

20 years) can be measured! This has opened up a new range of previously unob-

tainable flow behaviour for structured liquids which seemed to have a yield stress.

Access to these ultra-low shear-rate regions is now called creep testing, by analogy

to the testing of solids under similar low-deformation- rate, long-time conditions;

albeit solids creep testing is usually performed in extension rather than in shear.

Figure 4.13 shows a typical log(viscosity) versus. log(shear stress) plot demon-

strating the yield phenomenon which was recognized by Barnes (1995).

In Barnes’ experience, the best way to describe the curve from 10−3 s−1 and

above is by using the Sisko model or if it is easier, then one of the models

(Bingham, Casson, Herschel–Bulkley models etc.) with a yield stress can be used.

If the stress tensor is known, the Huber-von Mises criterion, see Example 4.3, or

the Tresca criterion can be used for calculating the yield stress.

Shear stress (Pa)101

102

103

104

105

106

107

102 103

Viscosity (Pa s)

Figure 4.13 Sketch of a log(viscosity) versus log(shear stress) plot according to Barnes (1999),

which shows the steep increase of viscosity by decreasing the shear stress. Source: Barnes et al.

(1989). Reproduced with permission from Elsevier.

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The rheology of foods and sweets 137

4.4.2.5 Dependence of dynamic viscosity on temperature and pressure4.4.2.5.1 Dependence on temperatureThe following relationship can be derived on the basis of Eyring’s theory for pure

liquid chemical substances:

𝜂 = A exp( U

RT

)(4.78)

where A is a constant, U is the activation energy of the viscosity, R is the universal

gas constant and T is the temperature (K). The activation energy of diffusion is

equal to that of viscosity, and hence

𝜂 = A exp( U

RT

)= kT

D𝛿(4.79)

where D is the diffusion constant, k is the Boltzmann constant and 𝛿 is the dis-

tance between neighbouring layers of the fluid.

Equation (4.78) gives good agreement with empirical results close to the nor-

mal boiling point; however, in a broad region, a plot of ln 𝜂 versus 1/T is not

linear.

The following rule can be applied to estimate U:

U =ΔHevap

2.45(4.80)

where ΔHevap is the latent heat of evaporation. For further details, see Liszi

(1975).

For the temperature region t=28–100 ∘C, the viscosity versus temperature

function of (crystal-free) cocoa butter (CB) has been given by Tscheuschner

(1993a) as

𝜂 = 5.7 × 10−7 exp(3533.7

T

)(Pa s) (4.81)

If we consider an unknown viscosity 𝜂 at any temperature T and a reference

viscosity 𝜂r at a reference temperature Tr, the constant A can be eliminated from

Eqn (4.78), and the resulting equation can be written in logarithmic form:

ln

(𝜂

𝜂r

)=(E

R

)(1T− 1

Tr

)(4.82)

Steffe (1996, Appendices 6.14) gives data on activation energies for fruit juices

and various egg products (Ostwald–de Waele fluids); the range of the values is

1.2–14.2 kcal/g mol at 50 ∘C (1 kcal= 4.1868 kJ).

4.4.2.5.2 Dependence on pressureThe activation energy U for viscosity and diffusion consists of two parts: one

is the energy that is needed for the creation of a new ‘hole’, and the other is

the potential that has to be passed through by a molecule in order to reach a

neighbouring hole. If an external pressure P acts on a liquid, then additional

work is needed because not only the cohesive forces but also this pressure has

to be compensated. If the volume of a hole v0 is regarded as independent of the

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138 Confectionery and chocolate engineering: principles and applications

external pressure P, then an additional amount of work Pv0 will be added to the

activation energy U; consequently, the following relation will be valid for the

pressure dependence:

𝜂 = 𝜂0 exp

(Pv0

kT

)(4.83)

where 𝜂0 is the dynamic viscosity of the fluid at P≈0 (a very small pressure). See

also Stephan and Lucas (1979) and Lucas (1981).

The effects of shear rate and temperature can be combined into a single expres-

sion (Harper and El Sahrigi, 1965):

𝜂 = f (T; 𝛾 ′) = KT exp( E

RT

)(𝛾 ′)m−1 (4.84)

where m is the average value of the flow behaviour index based on all tempera-

tures and KT is a constant at a given temperature T.

The effects of temperature and concentration C on the apparent viscosity at a

constant shear rate can be combined into a single relationship (Vitali and Rao,

1984; Castaldo et al., 1990):

𝜂 = f (T;C) = CBKTC exp( E

RT

)(4.85)

where KTC is a constant at a given temperature T and concentration C, and B is

an exponent. The three constants KTC, E and B must be determined from exper-

imental data.

The effects of shear rate, temperature and concentration (or moisture content) can

also be combined into a single expression (Mackey et al., 1989):

𝜂 = f (T; 𝛾 ′;C) = KT𝛾 ′;C exp( E

RT+ BC

)(𝛾 ′)m−1 (4.86)

where the influence of shear rate is given in terms of a power-law function. The

parameters KT𝛾 ′;C, m, E and BC cannot be given an exact physical interpretation

because the sequence of steps used in determining them influences the magni-

tude of the constants. The parameters of the equation may be determined using

stepwise regression analysis with the assumption that interaction effects (such as

the temperature dependence of m and BC) can be neglected.

The rheological behaviour of fluid foods is complex and is influenced by

numerous factors. The time–temperature history and strain history may be

added to Eqn (4.43) to form a more comprehensive equation; see Dolan et al.

(1989), Mackey et al. (1989), Morgan (1989) and Dolan and Steffe (1990). This

is applicable to protein- and starch-based dough and slurry systems.

4.4.3 Extensional flow4.4.3.1 Shear-free flowViscometric flow may be defined as that type of flow which is indistinguishable

from steady simple shear flow. Pure extensional flow, which yields an extensional

viscosity, does not involve shearing and is sometimes referred to as ‘shear-free’

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The rheology of foods and sweets 139

flow. (In the published literature, ‘elongational viscosity’ and ‘Trouton viscosity’

are common synonyms for ‘extensional viscosity’.)

Many food-processing operations involve extensional deformation, and the

molecular orientation caused by extension, compared with shear, can produce

unique food products and behaviours.

The reason why shear and extensional flow have a different influence on

rotational behaviour is that flow fields orient long molecules of high molecu-

lar weight. In shear flow, the preferred orientation corresponds to the direction of

flow; however, the presence of a differential velocity across the flow field encour-

ages molecules to rotate, thereby reducing the degree of stretching induced in

molecular chains.

However, in extensional flow, the situation is very different. The preferred

molecular orientation is in the direction of the flow field because there are no

competing forces to cause rotation. Hence, extensional flow will induce the

maximum possible stretching of the molecules, producing a tension in the chains

that may result in a large resistance to deformation (compared with the case of

shear flow). Stiffer molecules are oriented more quickly in an extensional flow

field. This phenomenon may be a factor in the choice of the thickening agent for

pancake syrup: stringiness can be reduced, while maintaining thickness, when

stiffer molecules are selected as additives. Reduced stringiness leads to what can

be called a clean ‘cut-off’ after syrup is poured from a bottle. An example of a

stiff molecule is the rod-like biopolymer xanthan; this can be compared with

sodium alginate and carboxymethyl cellulose, which exhibit a random coil-type

conformation in solution (Padmanabhan and Bhattacharya, 1993, 1994).

Extensional flow is an important aspect of food process engineering and is

prevalent in many operations, such as dough processing. Sheet stretching and

extrudate drawing provide good examples of extensional flow (Fig. 4.14).

The converging flow into dies such as those found in single- and twin-screw

extruders involves a combination of shear and extensional flow; the extensional

component of deformation is illustrated in Figure 4.14. In the analysis of converg-

ing flow in a die, the pressure drop across the die can be separated into shear and

extensional components. Converging flow may also be observed when a fluid is

sucked into a pipe or a straw, and when food is spread with a knife.

One of the most common examples of extensional flow is seen when a filled

candy bar or a fruit-filled pastry is pulled apart. Extensional deformation is also

present in calendering (Fig. 4.14), a standard operation performed with dough

sheeting. Gravity-induced sagging (see Fig. 4.14 again) also involves extensional

deformation. This may be observed in the cut-off apparatus associated with

fruit-filling systems for pastry products. Extensional flow in this situation is

undesirable because it may contribute to inconsistent levels of filling or an

unsightly product appearance due to smeared filling. Bubble growth from the

production of carbon dioxide during dough fermentation, extrudate expansion

caused by vaporization of water, and squeezing to achieve spreading of a product

also involve extensional deformation. Extensional flow is also a factor in die

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140 Confectionery and chocolate engineering: principles and applications

Sheetstretching Extruder die

Calendering

Gravity-induced sagging

Squeezing

Bubble growth

Figure 4.14 Various ways of shaping dough using extensional flow.

swell and in mixing, particularly dough mixing with ribbon blenders (Steffe,

1996). This shows that extensional viscosity plays an important role in many

fields of confectionery practice.

4.4.3.2 Extensional viscosityAlthough extensional viscosity is clearly a factor in food processing, the use of

this rheological property in the engineering design of processes and equipment is

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The rheology of foods and sweets 141

still at an early stage of development. Extensional flow is also an important factor

in the human perception of texture with regard to the mouthfeel and swallowing

of fluid foods and fluid drugs.

Extensional viscosity has been measured for various food products. First of

all, Trouton’s investigations (Trouton, 1906a,b) and Leighton et al. (1934) should

be mentioned. Extensional viscosity plays an essential function in extrusion and

in calendering, which are important operations in both the food and the plastic

industry.

Rheological measurements of food doughs have certainly been carried out

for many years in the food industry. The farinograph, amylograph and Braben-

der torque rheometer are some of the instruments that have been used to pro-

vide an indication of the deformation characteristics of doughs. Data from the

Chopin Alveograph, a common dough-testing device in which a spherical bub-

ble of material is formed by inflating a sheet, can be interpreted in terms of a

biaxial extensional viscosity (Launay and Buré, 1977; Faridi and Rasper, 1987).

Doughs have also been evaluated by subjecting them to uniaxial extension (de

Bruijne et al., 1990).

However, although these instruments have proved to be quite useful for

obtaining qualitative information about the properties of doughs, they do not

give these properties in quantities defined in engineering or scientific units. This

is because the flow field created in these devices is usually so complicated that

basic material properties cannot be obtained (Baird, 1983).

4.4.3.3 Types of extensional flow

There are three basic types of extensional flow (Fig. 4.15):

• During uniaxial extension, material is stretched in one direction (x1) with a cor-

responding size reduction in the other two directions (x2 and x3); for example,

a cube is stretched into a prism of square cross-section (x2 = x3). This is truly

uniaxial, because the extension occurs only in one direction, and there is a

contraction in the other two directions.

• In planar extension, material is stretched in the x1 direction with a corresponding

decrease in thickness (in the x2 direction), while the width (in the x3 direction)

remains unchanged.

• Biaxial extension appears similar to uniaxial compression, but it is usually

thought of as a flow which produces a radial tensile stress, for example when

a column of circular cross-section is compressed.

4.4.3.3.1 Uniaxial extension

For a material of constant density in uniaxial extension, the velocity distribution in

Cartesian coordinates, described using the Hencky strain rate, is

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142 Confectionery and chocolate engineering: principles and applications

Planar extension

Uniaxial extension

Biaxial extension

Figure 4.15 The basic types of extensional flow.

u1 = 𝜀′Hx1 (extension) (4.87)

u2 = −𝜀′Hx2

2(contraction) (4.88)

u3 = −𝜀′Hx3

2(contraction) (4.89)

where 𝜀′H > 0 is the Hencky shear rate. If the direction of stretching is x1, then

a size reduction (equal to half of the stretching) takes place in the x2 and x3

directions.

Pure extensional flow does not involve shear deformation; therefore, all the

shear stress terms are zero:

𝜎12 = 𝜎13 = 𝜎12 = 0 (4.90)

The stress is also axisymmetric:

𝜎22 = 𝜎33 (4.91)

This results in one normal-stress difference that can be used to define the tensile

extensional viscosity:

𝜂E =𝜎11 − 𝜎22

𝜀′H=𝜎11 − 𝜎33

𝜀′H(4.92)

Materials are said to be tension-thinning (or extensionally thinning) if 𝜂E

decreases with increasing 𝜀′H. They are tension-thickening (or extensionally

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The rheology of foods and sweets 143

thickening) if 𝜂E increases with increasing 𝜀′H. These terms are analogous to the

shear-thinning and shear-thickening used previously to describe changes in the

apparent viscosity with shear rate.

4.4.3.3.2 Biaxial extensionThe velocity distribution produced by a uniaxial compression that causes a biaxial

extensional flow can be expressed in Cartesian coordinates as

u1 = 𝜀′Bx1 (extension) (4.93)

u2 = −2𝜀′Bx2 (contraction) (4.94)

u3 = 𝜀′Bx3 (extension) (4.95)

Since 𝜀′H = 2𝜀′B(> 0), biaxial extension can actually be viewed as a form of ten-

sile deformation. Uniaxial compression, however, should not be viewed as being simply

the opposite of uniaxial tension, because the tendency of molecules to orient themselves is

stronger in tension than in compression (Steffe, 1996).

Axial symmetry allows the aforementioned equations to be rewritten in cylin-

drical coordinates (z= axial direction, r= radial direction and 𝜃 = angle of rota-

tion):

uz = −2𝜀′Bz (compression) (4.96)

ur = 𝜀′Br (extension) (4.97)

u0 = 0 (no rotation) (4.98)

The biaxial extensional viscosity is defined in terms of the normal-stress differ-

ence and the strain rate:

𝜂B =𝜎11 − 𝜎22

𝜀′B=𝜎11 − 𝜎33

𝜀′B

=𝜎zz − 𝜎rr

𝜀′B=

2(𝜎zz − 𝜎rr)𝜀′H

(4.99)

where 𝜎zz and 𝜎rr are the corresponding diagonal elements of the stress tensor in

cylindrical coordinates.

4.4.3.3.3 Planar extensionIn planar extension, the velocity distribution is

u1 = 𝜀′Hx1 (extension) (4.100)

u2 = −𝜀′Hx2 (contraction) (4.101)

u3 = 0 (no change) (4.102)

This type of flow produces two distinct stress differences: (𝜎11 − 𝜎22) and

(𝜎11 − 𝜎33). The planar extensional viscosity is defined in terms of the more

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144 Confectionery and chocolate engineering: principles and applications

easily measured of these two stress differences:

𝜂P =𝜎11 − 𝜎22

𝜀′H(4.103)

It is difficult to generate planar extensional flow, and experimental tests of this

type are less common than those involving tensile or biaxial flow.

4.4.3.4 Relation between extensional and shear viscositiesThe following limiting relationships between the extensional and shear viscosi-

ties can be expected for non-Newtonian fluids at small strains (Walters, 1975;

Petrie, 1979a,b; Dealy, 1994):

lim𝜀′H→0

𝜂E(𝜀′H) = 3 lim𝛾 ′→0

𝜂(𝛾 ′) → 𝜂E = 3𝜂 (4.104)

lim𝜀′B→0

𝜂B(𝜀′B) = 6 lim𝛾 ′→0

𝜂(𝛾 ′) → 𝜂B = 6𝜂 (4.105)

lim𝜀′H→0

𝜂P(𝜀′H) = 4 lim𝛾 ′→0

𝜂(𝛾 ′) → 𝜂P = 4𝜂 (4.106)

The values relating to the special case of Newtonian fluids are indicated by the

sign ‘→’, where 𝜂 is the Newtonian viscosity in steady shear flow.

These latter three equations can be used to verify the operation of extensional

viscometers. Clearly, however, a Newtonian fluid must be extremely viscous to

maintain its shape and give the solid-like appearance required in many exten-

sional flow tests (Steffe, 1996).

Reliable relationships for non-Newtonian fluids at large strains have not been

developed.

Trouton (1906a,b) established a mathematical relationship between tensile

extensional viscosity and shear viscosity. Data for extensional and shear vis-

cosities are often compared using a dimensionless ratio known as the Trouton

number Tr, where

Tr =extensional viscosity

Shear viscosity(4.107)

Since the extensional and shear viscosities are functions of different strain

rates, a conventional method of comparison is needed to remove ambiguity.

Based on a consideration of viscoelastic and inelastic fluid behaviour, Jones et al.

(1987) proposed the following conventions for computing Trouton numbers for

uniaxial and planar extensional flow:

Truniaxial =𝜂E(𝜀′H)

𝜂(√

3𝜀′H)(4.108)

Trplanar =𝜂P(𝜀′H)𝜂(2𝜀′H)

(4.109)

meaning that shear viscosities (𝜂) are calculated at shear rates equal to√

3𝜀′H for

uniaxial extension and 2𝜀′H for planar extension.

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The rheology of foods and sweets 145

Using similar considerations, Huang and Kokini (1993) proposed the following

convention for the case of biaxial extension:

Trbiaxial =𝜂B(𝜀′B)

𝜂(√

12𝜀′B)(4.110)

The Trouton ratio for a Newtonian fluid may be determined from Eqns

(4.96)–(4.98). Any departures from these numbers are due to viscoelastic mate-

rial behaviour. Experimental results may produce considerably higher values.

For example, Peck et al. (2006) measured the following Trouton numbers in

roller extrusion of biscuit doughs for uniaxial extension as a function of die

entry angle: for short doughs, 45–124 (die entry angle 60∘) and 51–141 (45∘)and for hard doughs, 89–108 (60∘) and 100–133 (45∘). These Trouton numbers

were calculated on the basis of power-law parameters, obtained using the

Gibson equation (see Chapter 14).

For further studies, see Steffe (1996, Chapter 4); for further discussion of sim-

ple extension, see Leblans and Scholtens (1986) and for methods of measuring

extensional viscosity, see Cheremisinoff (1988, pp. 991–1059).

4.4.3.4.1 A critical discussion concerning extensional viscosityPetrie’s review issues (Petrie, 2006) arise from the practical problem that viscosity

(in shear or extension) is a material property defined for steady, spatially uniform

flows while for practical applications where extensional viscosity is important,

flows are never steady and spatially uniform. This has lead to use of the concept

of a ‘transient extensional viscosity’ and use of a variety of approximations and

averaging techniques. According to Petrie the use of the term ‘transient exten-

sional viscosity’ or its equivalent has led to confusion on a number of occasions.

Unless the term is used in a very clear and restricted way, it should not be used

at all.

Another issue concerns the connection between extensional and shear flow

properties. The ‘Trouton ratio’, defined as 𝜂E/𝜂 is 3 for a Newtonian fluid and

there are corresponding ratios for biaxial extensional flows. For viscoelastic flu-

ids, this result will generally hold in the limiting case of very small rates of strain,

but otherwise nothing can be said without a specific constitutive equation.

4.4.4 Viscoelastic function and the idea of fading memoryof viscoelastic fluids

4.4.4.1 Viscoelastic phenomena and the fading memoryViscoelastic fluids simultaneously exhibit obvious fluid-like (viscous) and

solid-like (elastic) behaviour, however, these substantial properties are changing

in time according to monotone-decreasing functions. The idea of fading memory

related to the phenomena of viscoelastic fluids (stress relaxation, creep and

recovery) was first expressed by Boltzmann; also see Appendix 3.3.2.

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146 Confectionery and chocolate engineering: principles and applications

The manifestations of this behaviour due to a high elastic component can

be very strong and can create difficult problems in process engineering design.

These problems are particularly prevalent in the plastics-processing industry but

are also present in the processing of foods such as doughs, particularly those

containing large quantities of wheat protein. Figures 4.16–4.19 illustrate several

viscoelastic phenomena (Steffe, 1996).

During mixing or agitation, a viscoelastic fluid may climb an impeller shaft in

a phenomenon known as the Weissenberg effect. This can be observed in the home

mixing of cake or chocolate brownie batter.

When a Newtonian fluid emerges from a long, round tube into the air, the

emerging jet will normally contract. The normal-stress differences present in a

viscoelastic fluid, however, may cause jet expansion. This behaviour contributes

to the challenge of designing extruder dies to produce the desired shape of many

pet, snack and cereal foods. In addition, highly elastic fluids may exhibit a tubeless

siphon effect. This phenomenon is well known in the confectionery industry in

relation to dosing fillings that show elastic behaviour (although they are not

actually sucked up). A drop of filling does not separate from the dosing head, and

Impeller Impeller

(b)(a)

Figure 4.16 The Weissenberg effect: a viscoelastic fluid may climb an impeller shaft. (a)

Newtonian fluid and (b) viscoelastic fluid. Source: Steffe (1996). Reproduced with permission

from Steffe.

(b)(a)Vacuum Vacuum

Figure 4.17 The tubeless siphon effect. Under the effect of a vacuum, a viscoelastic fluid may

pull a fibre. (a) Newtonian fluid and (b) viscoelastic fluid. Source: Steffe (1996). Reproduced

with permission from Steffe.

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The rheology of foods and sweets 147

(b)(a)

Figure 4.18 A viscoelastic fluid may produce jet expansion.

(a) Newtonian fluid and (b) viscoelastic fluid. Source: Steffe

(1996). Reproduced with permission from Steffe.

Stop

Recoil

(a) (b)

Figure 4.19 Recoil phenomenon of a viscoelastic fluid. (a) Newtonian fluid and (b) viscoelastic

fluid. Source: Steffe (1996). Reproduced with permission from Steffe.

thus the head ‘pulls a fibre’ from the drop. Various fillings with an aqueous base

frequently contain a gelling agent in order to fix the water content; however, this

gives a certain amount of elasticity to the filling. The fibre pulled by the dosing

head causes problems because, for example, a chocolate cover cannot perfectly

close a praline.

A recoil phenomenon where tensile forces in a fluid cause particles to move

backwards (snap back) when the flow is stopped may also be observed in vis-

coelastic fluids. A summary of the behaviour of viscoelastic polymer solutions in

various flow situations has been given by Boger and Walters (1993).

4.4.4.2 Importance of large deformations in food rheologyIn process engineering, data on viscoelasticity may be very helpful in understand-

ing various problems. When materials are tested in the linear range, material

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148 Confectionery and chocolate engineering: principles and applications

functions do not depend on the magnitude of the stress, the magnitude of the

deforming strain or the rate of application of the strain. If the behaviour is linear,

an applied stress will produce a proportional strain response. The linear range of

testing is determined from experimental data. Testing can easily enter the nonlin-

ear range if excessive strains (usually >1%) or high deformation rates are applied

to a sample.

The importance of large-deformation (nonlinear) behaviour in food rheology,

however, should not be overlooked. Many processes, such as mastication and

swallowing, are accomplished only with very large deformations. The collection

of viscoelastic data relevant to this type of problem involves testing in the nonlin-

ear range of behaviour. These data may be useful in attacking practical problems;

however, from a fundamental standpoint, they can only be used for comparative

purposes, because the theoretical complexity of nonlinear viscoelasticity makes

it impractical for most applications.

Elastic behaviour may be evaluated using viscometric methods to deter-

mine the normal-stress differences found in steady shear flow. Alternatively,

viscoelastic material functions may be determined from experiments involving

the application of unsteady-state deformations. In general, these dynamic

testing techniques may be divided into two major categories: transient and

oscillatory.

Transient methods include tests of start-up flow, cessation of steady shear flow,

step strain, creep and recoil. In oscillatory testing, samples are deformed by the

application of a harmonically varying strain, which is usually applied over a sim-

ple shear field.

In a creep test, the material is subjected to a constant stress and the corre-

sponding strain is measured as a function of time, 𝛾(t) (in %/100%). The data

are often plotted in terms of the shear creep compliance

J (m2∕N) = J(t) = 𝛾

𝜎constant

(4.111)

versus time.

In a step-strain test, commonly called a stress relaxation test, a constant strain

is applied to the test sample and the changing stress over time, 𝜎(t), is measured.

The data are commonly presented in terms of a shear stress relaxation modulus

G = G(t) = 𝜎

𝛾constant

(4.112)

versus time.

Data from creep and stress relaxation tests can also be described in terms of

mechanical (spring and dashpot) analogues; see Polakowski and Kipling (1966),

Sherman (1970), Mohsenin (1986) and Barnes et al. (1989).

4.4.4.3 Mechanical analogues for describing viscoelastic behaviourMassless mechanical models, composed of springs and dashpots, are useful for

conceptualizing rheological behaviour. A spring is considered to be an ideal solid

element obeying Hooke’s law,

𝜎 = Gy (4.113)

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The rheology of foods and sweets 149

Figure 4.20 Maxwell model (series connection).

Newton

Hooke

Figure 4.21 Kelvin model (parallel connection).

Newton

Hooke

and a dashpot is considered to be an ideal fluid element obeying Newton’s law,

𝜎 = 𝜇𝛾 ′ (4.114)

where 𝜎 is the stress (Pa), G is the elasticity modulus (Pa), 𝛾 is the strain (a ratio,

i.e. a dimensionless number), 𝛾 ′ is the shear rate (s−1) and 𝜇 is the dynamic

viscosity (Pa s).

Springs and dashpots can be connected in various ways to portray the

behaviour of viscoelastic materials; however, the combination of elements is not

unique, because many different combinations can be used to model the same set

of experimental data. The most common mechanical analogues of rheological

behaviour are the Maxwell (Fig. 4.20) and Kelvin (or Kelvin–Voigt) models

(Fig. 4.21).

4.4.4.3.1 Stress relaxation – the Maxwell modelA wide range of behaviour may be observed in stress relaxation tests. No relax-

ation would be observed in an ideal elastic material, while an ideal viscous sub-

stance would relax instantaneously. Viscoelastic materials relax gradually, with

the end point depending on the molecular structure of the material being tested:

the stress in a viscoelastic solid decays to an equilibrium stress (𝜎E >0), but the

residual stress in a viscoelastic liquid is zero.

Stress relaxation data are commonly presented in terms of a stress relaxation

modulus (see Eqn 4.113)

G = f (t) = 𝜎

𝛾constant

(4.115)

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150 Confectionery and chocolate engineering: principles and applications

If the material is perfectly elastic, the relaxation modulus is equal to the shear

modulus.

The Maxwell model (Fig. 4.20), which contains a Hookean spring in series with

a Newtonian dashpot, has frequently been used to interpret stress relaxation data

for viscoelastic liquids, particularly polymeric liquids. The total shear strain in a

Maxwell fluid element is equal to the sum of the strain in the spring and the

dashpot:

𝛾 = 𝛾spring + 𝛾dashpot (4.116)

By differentiating Eqn (4.116), and taking into account Eqns (4.77) and (4.79),

the following equation is obtained:

dy

dt= 𝛾 ′ = 1

Gd𝜎dt

+ 𝜎

𝜇(4.117)

or

𝜎 + 𝜆reld𝜎dt

= 𝜇𝛾 ′ (4.118)

where the relaxation time (also called the characteristic time) is defined as

𝜆rel =𝜇

G(4.119)

Although an exact definition of 𝜆rel is difficult, it can be thought of as the time it

takes a macromolecule to be stretched out when deformed.

The aforementioned equations have been presented in terms of shear deforma-

tion. If testing is conducted in uniaxial tension or compression, then the relaxation

time can be thought of in terms of an extensional viscosity 𝜂Ex and Young’s mod-

ulus E.

The Maxwell model is useful in understanding stress relaxation data. Consider

a step-strain (stress relaxation) experiment where there is a sudden application

of a constant shear strain 𝛾0. When the strain is constant, the shear rate is equal

to zero (𝛾 ′ = 0), and Eqn (4.118) becomes

𝜎 + 𝜆reld𝜎dt

= 0 (4.120)

This equation may be integrated using the initial condition that 𝜎 = 𝜎0 at t= 0;

after evaluating the integral,

𝜎 = 𝜎0 exp

(− t𝜆rel

)(4.121)

Equation (4.121) describes the gradual relaxation of the stress (from 𝜎0 to

zero) after the application of a sudden strain. The relationship provides a means

of determining the relaxation time: 𝜆rel is the time it takes for the stress to decay

to 1/e (approximately 36.8%) of its initial value.

Experimental data show that the Maxwell model does not account for the

stress relaxation behaviour of many viscoelastic materials, because it does not

include an equilibrium stress 𝜎E. This problem may be addressed for numerous

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The rheology of foods and sweets 151

foods by constructing a model that consists of a combination of various elements

in series or parallel coupling. This concept can be generalized to determine a

relaxation spectrum for a viscoelastic material (Ferry, 1980).

Peleg and Normand (1983) noted two major problems in collecting stress

relaxation data for foods:

1 When subjected to large deformations, foods usually exhibit nonlinear vis-

coelastic behaviour.

2 Natural instability and biological activity make it difficult to determine equi-

librium mechanical parameters.

To overcome these difficulties, Peleg and Normand suggested that stress relax-

ation data should be calculated as a normalized stress (a normalized force term

is also acceptable) and fitted to the following linear equation:

𝜎0t

𝜎0 − 𝜎= k1 + k2t (4.122)

where 𝜎0 is the initial stress, 𝜎 is the decreasing stress at time t, and k1 (s) and

k2 are constants. The reciprocal of k1 represents the initial decay rate (s−1), and

k2, which is dimensionless, is a hypothetical value of the asymptotic normalized

force. The Equation (4.122) can be used also for stress relaxation modulus (G)

instead of stress (𝜎). An important requirement is that the Equation (4.122) must

not be applied for t= 0, i.e., for the initial point, because 𝜎0 × 0/(𝜎0 − 𝜎0)=0/0

(undefined).

4.4.4.3.2 Creep and recovery – the Kelvin modelIn a creep test, an instantaneous stress is applied to the sample and the change

in strain (called the creep) is observed over time. When the stress is released,

some recovery may be observed as the material attempts to return to the orig-

inal shape. These tests can be particularly useful in studying the behaviour in

constant-stress environments such as those found in levelling, sedimentation and

coating applications, where gravity is the driving force. Creep experiments can

also be conducted in uniaxial tension or compression.

Viscoelastic materials (e.g. bread dough) can exhibit a nonlinear response to

strain and, owing to their ability to recover some structure as a result of storing

energy, show a permanent deformation less than the total deformation applied

to the sample. This strain recovery, or creep recovery, is also known as ‘recoil’

and may be investigated in terms of a recoil function (Dealy, 1994).

The starting point for developing a mechanical analogue describing creep

behaviour is the Kelvin model (Fig. 4.21), which contains a spring connected in

parallel with a dashpot. When this system is subjected to shear strain, the spring

and dashpot are strained equally; see Eqn (4.116).

The total shear stress (𝜎) caused by the deformation is the sum of the individual

shear stresses which, using Eqns (4.113) and (4.114), can be written as

𝜎 = Gy + 𝜇𝛾 ′ (4.123)

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152 Confectionery and chocolate engineering: principles and applications

Differentiating Eqn (4.123) with respect to time (where G is constant) yields

1G

d𝜎dt

= 𝛾 ′ + 𝜆retd𝛾 ′

dt(4.124)

where the retardation time 𝜆ret =𝜇/G is unique for any substance, and d𝛾/dt= 𝛾 ′

(see Eqn 4.117). If the material were a Hookean solid, the retardation time would

be zero and the maximum strain would be obtained immediately on the appli-

cation of the stress: the achievement of the maximum strain in a viscoelastic

material is delayed (or retarded). The retardation time can be thought of in terms

of the extensional viscosity 𝜂Ex and Young’s modulus E if the testing is conducted

in uniaxial tension or compression.

In creep, where the material is allowed to flow after being subjected to a con-

stant shear stress, that is d𝜎/dt= 0, the solution to Eqn (4.124) is

𝛾 = f (t) =(𝜎0

G

)[1 − exp

(− t𝜆ret

)](4.125)

showing that the initial strain is zero (𝜎0 =0 at t= 0). Equations (4.93) and

(4.125) predict a strain that asymptotically approaches the maximum strain

(𝜎0/G) associated with the spring. 𝜆ret is the time taken for the delayed strain to

reach approximately 63.2% (1− 1/e) of the final value. Materials with a large

retardation time reach their full deformation slowly.

The Kelvin model (Fig. 4.21) shows excellent elastic retardation (Fig. 4.22),

but it is not generally enough to model creep in many biological materials. The

solution to this problem is to use the Burgers model (Fig. 4.23), which is a Kelvin

and a Maxwell model placed in series.

τ0

t1(a)

(b)

t

τ

t1 t

γ∞

γ

γ1

Figure 4.22 Response of a Kelvin fluid to a constant stress 𝜏0.

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The rheology of foods and sweets 153

Figure 4.23 The Burgers model: a Kelvin and a Maxwell

model coupled in series.

Maxwell

KelvinG1

G0

σ

σ

μ0

μ1

Data following this mechanical analogue show an initial elastic response due to

the free spring, a retarded elastic behaviour related to the parallel spring–dashpot

combination, and Newtonian-type flow after long periods of time due to the free

dashpot:

𝛾 = f (t) =(𝜎0

G

)+(𝜎0

Gl

)[1 − exp

(− t𝜆ret

)]+𝜎0t

𝜇0

(4.126)

where 𝜆ret =𝜇1/Gl, the retardation time of the Kelvin portion of the model.

The Burgers model can also be expressed in terms of the creep compliance by

dividing Eqn (4.126) by the constant stress 𝜎0:

J (Pa−1) = 𝛾

𝜎0

= J(t) = 1G

+(

1Gl

)[1 − exp

(− t𝜆ret

)]+ t𝜇0

(4.127)

where J0 = 1/G (t=0) is the instantaneous compliance, J1 is the retarded com-

pliance, 𝜆ret is the retardation time (=𝜇1/Gl) of the Kelvin component and 𝜇0 is

the Newtonian viscosity of the free dashpot. The sum of J0 and J1 is called the

steady-state compliance.

When creep experiments are conducted, controlled-stress rheometers allow

the strain recovered when the constant stress is removed to be measured. The

complete creep and recovery curve may be expressed using the Burgers model.

When calculated as a compliance, the creep is given by Eqn (4.127) for 0< t< t1,

where t1 is the time when the constant stress is removed.

At the beginning of creep (t= 0), there is an instantaneous change J= J0 in

the compliance (where J0 =1/G) due to the spring in the Maxwell portion of the

model. Then, the Kelvin component produces an exponential change (if t< 0,

then 0< (1/Gl)[1− exp(−t/𝜆ret)]→1/Gl) in the compliance related to the retar-

dation time. After sufficient time has passed, the independent dashpot generates

a purely viscous response (t/𝜇0) since the other additive terms (1/G+ 1/Gl) do

not change any more for practical purposes.

If necessary, additional Kelvin elements can be added to the Burgers model

to represent the experimental data better. Mathematically, this idea can be

described by the equation

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154 Confectionery and chocolate engineering: principles and applications

J = J(t) = J0 +∑

i

Ji exp

(− t𝜆ret

)+ t𝜇0

, i = 1,2, … ,m (4.128)

where m is the total number of Kelvin elements in the model, each having a

unique retarded compliance and retardation time. A simple linearized model has

been suggested by Peleg (1980) to characterize the creep of biological materials:

tJ= k1 + k2t (4.129)

where t is the time (s), J is the compliance function (Pa−1), and k1 (Pa s) and k2

(Pa) are constants.

The Eqn. (4.128) is so-called exponential polinom-both the Maxwell and

the Kelvin models which are built from more elementary rheological elements

lead to mathematically similar equations related to relaxation/retardation stress,

modulus or compliance. The approximation e−kt (1−kt) provides the possibility

of linearizations proposed by Peleg and Normand (1983), see Eqn. (4.122) and

by Peleg (1980), see Eqn. (4.129).

4.4.4.4 Analogy between rheological models and electrical networksOn the basis of the Kirchhoff laws, an analogy (denoted by ‘∼’) can be established

between rheological and electrical networks in the following way:

Hooke model ∼ electrical resistance

that is

Hooke′s law ∼ Ohm′s law (4.130)

𝜎 =G𝛾 ∼ I= (1/R) U

𝜎 ∼ I (electrical circuit)

G∼1/R (R= electrical resistance)

𝛾 ∼U (electrical potential)

Newton model ∼ electrical capacitor (4.131)

that is

𝜎 =𝜇𝛾 ′ ∼ I= C (dU/dt)

𝛾 ∼U

𝛾 ′ = d𝛾/dt∼ dU/dt

𝜇∼C

This analogy facilitates the analysis of rheological models. For further details,

see Foster (1924, 1932), Guillemin (1935, 1950) and Verhás (1985).

4.4.4.5 Series and parallel coupling of models: relaxation functionsVerhás (1985) showed that for series and parallel coupling, respectively, the fol-

lowing simple relationships hold:

M1(k1)SM2(k2)▸M1,2(k1,2), where 1∕k1,2 = 1∕k1 + 1∕k2 (4.132)

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The rheology of foods and sweets 155

and

M1(k1)PM2(k2)▸M1,2(k1,2), where k1,2 = k1 + k2 (4.133)

In these relationships, M denotes the model (Hooke, Newton or coupled); ki is

a characteristic of the model (e.g. G for the Hooke model or 𝜂 for the Newton

model); i (=1 or 2) is an index related to the model; S and P denote serial and

parallel coupling, respectively; and▸ indicates the resultant model after coupling.

For example, for serially coupled Newton models,

N1(𝜂1)SN2(𝜂2)▸N1,2(𝜂1,2)

where 1/𝜂1,2 = 1/𝜂1 + 1/𝜂2.

Evidently, for serial coupling, 𝜎 =∑

𝜎i, and for parallel coupling, 𝛾 =∑

yi.

In addition, Verhás (1985) showed that

• if 2 K models or two Maxwell models, with equal relaxation times, are coupled

in parallel or in series, respectively, the resultant Kelvin model or Maxwell

model also has this common relaxation time.

• For any Maxwell model, a Kelvin model can be found which is equivalent to

it, and vice versa.

This generalization of rheological models leads to the notion of a relaxation

function,𝜎(t) = 𝛾0Ψ(t) (4.134)

where 𝜎(t) is the stress (Pa) as a function of time t, 𝛾0 is the deformation when

t=0, and Ψ(t) is the relaxation function (Pa). The clear meaning of Ψ(t) is the

stress remaining in the body after time t, after a sudden deformation of unit size.

A detailed survey of mechanical models of food has been given by

Tscheuschner (1993b). By using fractional calculus a comprehensive discussion

of the creep, relaxation and viscosity properties of basic rheological models is

given by Mainardi (2010), Mainardi and Spada (2011). For further details, see

Appendix 3.

4.4.5 Oscillatory testingIn oscillatory instruments, samples are subjected to a harmonically varying stress

or strain. This testing procedure is the most common dynamic method for study-

ing the viscoelastic behaviour of food. The results are very sensitive to chemical

composition and physical structure, so they are useful in a variety of applications,

including evaluation of gel strength, monitoring starch gelatinization, studying

glass transition phenomena, observing protein coagulation or denaturation, eval-

uating curd formation in dairy products, studying the melting of cheese, studying

texture development in bakery and meat products, shelf-life testing, and corre-

lation of rheological properties with human sensory perception. Food scientists

have found oscillatory testing instruments to be particularly valuable tools for

product development work.

Oscillatory testing may be conducted in tension, bulk compression or shear.

Typical commercial instruments operate in the shear deformation mode, and

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156 Confectionery and chocolate engineering: principles and applications

this is the predominant testing method used for food. A shear strain may be

generated using parallel-plate, cone-and-plate or concentric cylinder fixtures.

Dynamic testing instruments may be divided into two general categories:

controlled-rate instruments, where the deformation (strain) is fixed and the

stress is measured, and controlled-stress instruments, where the stress amplitude

is fixed and the deformation is measured. Both produce similar results. The

emphasis in this section is on fluid and semi-solid foods.

In oscillatory tests, materials are subjected to a deformation (in controlled-rate

instruments) or a stress (in controlled-stress instruments), which varies

harmonically with time. Sinusoidal simple shear is typical. To illustrate the

concept, consider two rectangular plates oriented parallel to each other

(Fig. 4.24).

The lower plate is fixed and the upper plate is allowed to move back and forth

in a horizontal direction. Assume that the sample being tested is located between

the plates of a controlled-rate device. Suppose the strain in the material between

the plates is a function of time defined by

𝛾 = 𝛾0 sin(𝜔t) (4.135)

where 𝛾0 is the amplitude of the strain, equal to L/h when the motion of the

upper plate is L sin(𝜔t); 𝜔= 2𝜋𝜈 is the angular frequency expressed in rad/s, and

𝜈 is the frequency expressed in hertz (cycles/s).

For example, if the two plates in Figure 4.24 are separated by a distance

of h=1.5 mm and the upper plate is moved by L= 0.3 mm from the centre

line, then the maximum strain amplitude may be calculated as 0.2 or 20%

(𝛾0 = L/h=0.3/1.5= 0.2). This can be regarded as a large deformation.

Using a sine wave for the strain input results in a periodic shear rate, found by

taking the derivative of Eqns (4.100) and (4.135):

d𝛾

dt= 𝛾 ′ = 𝛾0𝜔 cos(𝜔t) (4.136)

For a small strain amplitude (in the linear viscoelastic region, 𝜎 ∼ 𝛾), the follow-

ing shear stress is produced by the strain input:

𝜎 = 𝜎0 sin(𝜔t + 𝛿) (4.137)

h

L

L sin(ωt)

Oscillating plate

Stationary plate

Figure 4.24 Oscillatory strain between rectangular plates. Source: Steffe (1996). Reproduced

with permission from Steffe.

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The rheology of foods and sweets 157

where 𝜎0 is the amplitude of the shear stress (not to be confused with the yield

stress symbolized by 𝜎0 or 𝜏0 in earlier sections), and 𝛿 is the phase lag or phase

shift (also called the mechanical loss angle) relative to the strain. The time period

associated with the phase lag is equal to 𝛿/𝜔.

Dividing both sides of Eqn (4.137) by 𝛾0 yields

𝜎

𝛾0

=(𝜎0

𝛾0

)sin(𝜔t + 𝛿) (4.138)

The results of small-amplitude oscillatory tests can be described by plots of the

amplitude ratio 𝜎0/𝛾0 and the phase shift 𝛿 as frequency-dependent functions.

However, the shear stress output produced by a sinusoidal strain input is usually

written as

𝜎 = G′𝛾 +(

G′′

𝜔

)𝛾 ′ (4.139)

where G′ is the shear storage modulus and G′′ is the shear loss modulus. In addition,

these two moduli can be expressed as

G′ =(𝜎0

𝛾0

)cos 𝛿 (4.140)

and

G′′ =(𝜎0

𝛾0

)sin 𝛿 (4.141)

G′𝛾0 may be interpreted as the component of the stress in phase with the strain;

G′′𝛾0 may be interpreted as the component of the stress 90∘ out of phase with

the strain.

Some additional frequency-dependent material functions are as follows:The complex modulus G*,

G∗ =𝜎0

𝛾0

=√

G′2 + G′′2 (4.142)

The absolute value of the viscosity, 𝜂*,

𝜂∗ = G∗

𝜔=√𝜂′2 + 𝜂′′2 (4.143)

the components of which are the dynamic viscosity 𝜂′,

𝜂′ = G′′

𝜔(4.144)

and the complex viscosity 𝜂′′,

𝜂′′ = G′

𝜔(4.145)

Using Eqns (4.104) and (4.106), Eqns (4.99) and (4.101) can be expressed as

𝜎 = G′𝛾 + 𝜂′𝛾 ′ (4.146)

which represents the material behaviour well because it clearly indicates the elas-

tic (G′𝛾) and viscous (𝜂′𝛾 ′) nature of the substance.

The tangent of the phase shift or phase angle (tan 𝛿) is also a function of

frequency:

tan 𝛿 = G′′

G′ (4.147)

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158 Confectionery and chocolate engineering: principles and applications

This parameter is directly related to the energy lost per cycle divided by the

energy stored per cycle. Values of tan 𝛿 for typical food systems (dilute solutions,

concentrated solutions and gels) have been given by Steffe (1996, pp. 325–326).

The Maxwell model of a fluid is often used to interpret data from the dynamic

testing of polymeric liquids. If the strain input is harmonic (see Eqns 4.135 and

4.136), Eqn (4.136) can be substituted into Eqn (4.120), and the resulting dif-

ferential equation can be solved to produce a number of frequency-dependent

rheological functions for Maxwell fluids:

G′ =G𝜔2𝜆2

rel

1 + 𝜔2𝜆2rel

(4.148)

G′′ =G𝜔𝜆rel

1 + 𝜔2𝜆2rel

(4.149)

𝜂′ = 𝜂

1 + 𝜔2𝜆2rel

(4.150)

tan 𝛿 = G′′

G′ = 1𝜔𝜆rel

(4.151)

where 𝜆rel is the relaxation time of the Maxwell fluid and is equal to 𝜇/G.

Looking at experimental data may allow the material constants of the Maxwell

model to be evaluated from the asymptotes: as 𝜔 goes to zero, 𝜂′ goes to 𝜂; and

as 𝜔 goes to infinity, G′ goes to G.

For further details of the dynamic testing of foods, see, for example, Sherman

(1983), Stastna et al. (1986) and van Vliet (1999), as well as Appendix 3.

4.4.6 ElectrorheologySteffe (1996, Section 1.11) discussed the topic of electrorheology, sometimes

called the Winslow effect (Winslow, 1947), which refers to changes in the rhe-

ological behaviour due to the imposition an electric field on a material. Elec-

trorheological fluids are dispersions of solid particles, typically 0.1–100 μm in

diameter, in an insulating (non-conducting) oil. An example, milk chocolate,

was discussed by Steffe (1996). At low shear rates, in the absence of an electric

filed, the particles are randomly distributed, and many electrorheological flu-

ids show near-Newtonian behaviour. With the application of an electric field,

the particles become polarized, causing particle alignment across the electrode

gap and creating an enhanced, fibre-like structure. The application of a voltage

causes some materials to develop high yield stresses, which can be so high that

flow ceases, effectively transforming the material from a liquid to a solid.

The dielectric properties of chocolate are well known, although barely studied,

and are worthy of more interest.

4.4.7 MicrorheologyIn microrheology, the local and bulk mechanical properties of a complex fluid are

extracted from the motion of probe particles embedded within it. The motion

of probe particles is measured using either video or laser tracking techniques.

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The rheology of foods and sweets 159

The motion of probe particles is measured using either video or laser tracking

techniques. Video analysis of trajectories of tracer particles can yield a complete

characterization of the linear viscoelasticity of fluid. This idea was given a firm

foundation by Mason and Weitz (1995) by using the well-known Stokes–Einstein

equation: D= kBT/(6𝜋𝜂a), where D is the diffusion coefficient of a particle, 𝜂 [Pa s]

is the bulk viscosity (the single parameter that describes a Newtonian fluid) and

a is the radius of the colloidal particle. Particle motion is either thermally induced

(passive methods) or driven externally (active methods) and interpreted to yield

the viscoelastic modulus (Kasza et al., 2007).

In either case, when the embedded particles are much larger than any struc-

tural size of the material, particle motions measure the macroscopic stress relax-

ation; smaller particles measure the local mechanical response and also probe

the effect of steric hindrances caused by local microstructure. The use of small

colloidal particles theoretically extends the accessible frequency range by shifting

the onset of inertial effects to the megahertz regime; in practice, the measurable

frequency range varies with the details of the experimental apparatus.

Microrheology indicates a family of methods; the most common experiments

involve video-particle tracking, magnetic or laser tweezers and atomic force

microscopic methods. A common classification is as follows:

• Passive microrheology methods : dynamic light scattering (DLS), diffusive

wave spectroscopy (DWS), video-particle tracking (one- or two particle

microrheology).

• Active microrheology methods: magnet bead microrheology (or mag-

netic tweezers), optical tweezers measurements, atomic force microscopy

techniques.

For a comprehensive discussion of the methods of microrheology, see MacIn-

tosh and Schmidt (1999), Gardel et al. (2005), Cicuta and Donald (2007), Squires

and Mason (2010). For applications in food science, see Scheffold et al. (2003),

Chen et al. (2010a,b), and for applications in cell biology, see Verdier (2003),

Kasza et al. (2007), Wirtz (2009), Kollmannsberger (2009), Jun (2009), Allan

(2012).

In the field of microrheology of biological fluids and cells, see Fabry et al.

(2001), Waigh (2005), Savin (2006, 2007).

4.5 Viscosity of solutions

When a polymer is dissolved in a solvent, there is a noticeable increase in the

(dynamic) viscosity of the resulting solution. The viscosities of pure solvents and

solutions can be measured, and various values calculated from the resulting data:

Relative viscosity = 𝜂rel =𝜂solution

𝜂solvent

(4.152)

Specific viscosity = 𝜂sp = 𝜂rel − 1 (4.153)

Reduced viscosity = 𝜂red =𝜂sp

C(4.154)

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160 Confectionery and chocolate engineering: principles and applications

Inherent viscosity = 𝜂inh = ln(𝜂red

C

)(4.155)

Intrinsic viscosity = 𝜂int = limC→0

(𝜂sp

C

)≡ [𝜂] (4.156)

where C is the volume or mass concentration of the solution.

Using these concepts for the well-known Einstein equation,

𝜂solution = 𝜂solvent(1 + 2.5Φ) (4.157)

where Φ is the volume concentration of solid spheres in a solution, the value of

which must be small, we can derive

𝜂rel = 1 + 2.5Φ (4.158)

𝜂sp = 2.5Φ (4.159)

𝜂red = 2.5 = 𝜂int (4.160)

If Φ is small enough,

ln 𝜂rel ≈ 𝜂sp (4.161)

If Φ is measured in g/100 ml, and the swelling of the polymer is taken into

account by a factor s, then from the Einstein equation,

[𝜂] = 0.025sΦ (4.162)

The Einstein equation can be used to describe the viscosity properties of emul-

sions too (discussed later).

The intrinsic viscosity has great practical value in molecular-weight determi-

nations of high polymers, using the equation

[𝜂] = KMa (4.163)

where M is the molecular weight of the polymer, a= 0.7–1 (according to

Staudinger, a=1), and K is a constant characterizing the monomer of the

polymer and the solvent. If a≠ 1 (the general case), Eqn (4.163) is called the

Mark–Houwink equation. For details, see Erdey-Grúz and Schay (1954), Sun

(2004) and Section 5.3.1 of this book.

The viscosities of solutions are useful in understanding the behaviour of some

biopolymers, including aqueous solutions of locust bean gum, guar gum and car-

boxymethyl cellulose (Rao, 1986). The intrinsic viscosities of numerous protein

solutions have been summarized by Rha and Pradipasena (1986).

For further details, see Krieger (1983) and Sun (2004).

Example 4.4From a practical viewpoint, a 20 m/m% aqueous sucrose solution can be

regarded as dilute – the molar ratio of sucrose is 0.0132 merely as calculated

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The rheology of foods and sweets 161

in Example 3.2. According to Junk and Pancoast (1973), the dynamic viscosity

𝜂 of such a sucrose solution is 1.957 cP=1.957×10−3 Pa s, and its density is

1.06655 g/ml (at 20 ∘C).

Let us calculate the viscosity of this solution with the help of Eqn (4.158),

given that at 20 ∘C the viscosity of water 𝜂0 is 1.002×10−3 Pa s and the density

of water 𝜌0 is 0.998 g/ml.

In this case, the volume of 100 g of sucrose solution is (100/1.06655) ml=93.76 ml, and the volume of 80 g of water is (80/1.002) ml=79.84 ml. Conse-

quently, the volume ratio of sucrose is

Φ= 93.76 − 79.8493.76

= 0.1485

According to the Einstein equation (4.157),

𝜂solution = 𝜂water(1 + 2.5Φ) = 1.002 × 10−3 Pa s (1 + 2.5 × 0.1485)

= 1.374 × 10−3 Pa s

The difference is (1.957−1.374)/1.957= 29.8%.

4.6 Viscosity of emulsions

4.6.1 Viscosity of dilute emulsionsVery dilute emulsions exhibit a Newtonian viscosity, and this is often defined in

terms of the viscosity 𝜂0 of the continuous phase and the droplet volume fraction

Φ by using the equation proposed by Einstein (Eqn 4.158). Equation (4.159) is

valid provided

• the droplets behave as solid, rigid spheres;

• they are large with respect to the size of the molecules of the continuous phase;

• there is no hydrodynamic interaction between the droplets; and

• slippage does not occur at the oil/water interface.

The increase in viscosity above the value 𝜂0 results from energy dissipation

when droplets of an immiscible liquid are introduced into the continuous phase,

and the flow pattern of the latter phase is then modified in the vicinity of the

droplets.

The limitations on the applicability of Eqn (4.158) are often satisfied by very

dilute emulsions, particularly if the droplet size does not exceed a few microns

and the droplets are enveloped by an elastic or viscoelastic film of adsorbed emul-

sifier molecules. However, when the adsorbed emulsifier film is fluid, as with

ionic emulsifiers, Eqns (4.157) and (4.159) have to be modified to allow the

transmission of normal and tangential components of stress across the interface

and into the droplets (Taylor, 1932). This produces fluid circulation within the

droplets and reduces the distortion of the flow pattern in the continuous phase

around the droplets. Equations (4.158) now becomes

𝜂rel = 1 +2.5{𝜂i + (2∕5)𝜂0}Φ

𝜂i + 𝜂0

(4.164)

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162 Confectionery and chocolate engineering: principles and applications

Non-Newtonianflow

Newtonianflow

Φcrit Φ

ηref

Phase inversion

Figure 4.25 Phase inversion of an emulsion (relative viscosity vs. volume concentration of

solid).

where 𝜂i is the viscosity of the liquid forming the drops. The validity of Eqn

(4.164) has been confirmed by viscosity studies with a large number of O/W

emulsions.

4.6.2 Viscosity of concentrated emulsionsFor very dilute emulsions, 𝜂rel increases linearly as Φ increases. For more con-

centrated emulsions, Φ exerts a greater influence and the viscosity changes from

Newtonian to non-Newtonian. The non-Newtonian character is initially pseu-

doplastic, but in very concentrated systems it may become plastic and exhibit

viscoelasticity. Very often the influence of 𝜂rel is as portrayed in Figure 4.25,

with 𝜂rel increasing almost exponentially to a maximum value just prior to emul-

sion inversion, where a critical value of Φ (Φcrit) is exceeded. A phase inversion

experiment was discussed in Section 2.1.4 (see also Mohos, 1982). A detailed

discussion of phase inversion is given in Chapter 5.10.

When Φ increases beyond the limit of validity of Eqns (4.122) and (4.158), the

distorted flow patterns around the droplets draw closer together and eventually

overlap. The resulting hydrodynamic interaction leads to an increased 𝜂rel. This

effect has been represented in many different forms, but they usually reduce to

a power series in Φ,

𝜂rel = 1 + 2.5Φ + bΦ2 + cΦ3 + · · · (4.165)

provided the droplets behave as discrete spheres; b and c are constants. Many

different values of b, between 0 and 10 for O/W and W/O emulsions, have been

quoted in the literature, but there are very few values for c.

The hydrodynamic interaction between spherical droplets on opposite sides of

a hypothetical spherical enclosure and separated by a distance f can be defined

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The rheology of foods and sweets 163

by a coefficient 𝜆, where

𝜆 =1 − D∕2f

D∕2f(4.166)

and D is the droplet diameter. This equation is valid provided D/2f lies between

0.5 and 1. Therefore, the hydrodynamic interaction depends both on the size of

the droplets and on the distance between them. The latter will also be influenced

by droplet size in that, at constant Φ, the value of f will decrease as D decreases.

The sharp increase in viscosity, which is observed in more concentrated emul-

sions, can be explained by applying lubrication theory to calculate the viscous

dissipation of energy (Frankel and Acrivos, 1967).

The viscosity of concentrated emulsions at high shear rates such that the

droplets are completely deflocculated can often be satisfactorily described by the

relation𝜂∞

𝜂0

= exp( 2.5Φ

1 − kΦ

)(4.167)

where k depends on the hydrodynamic interaction between droplets and

increases as the droplet size decreases (Saunders, 1961). This equation has the

same form as that proposed by Mooney (1951), with k now being described as a

geometric crowding factor such that 1.35< k<1.91.

When expanded, Eqn (4.167) gives a power series (a geometric series with a

quotient kΦ) in Φ similar to Eqn (4.165).

Practical emulsions are never monodisperse with respect to droplet size, and

the characteristics of the size distribution influence the rheological properties.

The model represented by Eqn (4.167) can be extended to emulsions containing

an i-modal size distribution, and the product of the relative viscosities of the

various size fractions in the continuous phase at the same volume concentration

gives the resultant relative viscosity:

𝜂rel =∏

i

exp

(2.5Φi

1 − kiΦi

)(4.168)

The viscosity of an emulsion can also be related to the droplet size distribution

by an alternative relation (Djakovic et al., 1976),

𝜂 = SK − B (4.169)

where K is the rate of change of viscosity with respect to the specific surface S,

so that

K = d𝜂

dS(4.170)

and B is a constant.

4.6.3 Rheological properties of flocculated emulsionsFollowing preparation, the droplets in emulsions flocculate and the size of the

aggregates so formed increases with storage time. These aggregates immobilize

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164 Confectionery and chocolate engineering: principles and applications

liquid from the continuous phase within the voids between the droplets, so that

when the emulsion is examined in a viscometer at low shear rates such that the

aggregate structure is not seriously damaged, an anomalously high viscosity is

exhibited. When the shear rate is increased, the aggregate size is progressively

reduced, as is the volume of the continuous phase immobilized. The effect of

aggregation on viscosity can be demonstrated by a simple procedure in which an

emulsion is first stirred vigorously or subjected to a high shear rate and is then

examined at a low shear rate (Mooney, 1946; Sherman, 1967).

In emulsions stabilized by emulsifiers with not too high a molecular weight,

van der Waals attraction forces are primarily responsible for the bonds between

droplets in the aggregates. This gives rise to viscoelastic properties in the

near-stationary state. When a small shear stress is applied to the emulsion, the

resulting time-dependent strain leads to creep compliance–time behaviour; see

the earlier discussion of the Kelvin fluid. The values of the various parameters

decrease as the mean droplet size increases, with the precise influence of droplet

size varying from one parameter to another. It is noteworthy that in the case

of emulsions with a relatively small mean droplet size, small changes in the

mean size can produce substantial changes in the magnitudes of the viscoelastic

parameters. For further details, see Sherman (1983, pp. 405–437).

When freshly prepared emulsions are stored at ambient temperature, the

droplets flocculate and coalesce for some time before there is visible separa-

tion of the disperse phase. At the same time, the rheological properties alter

significantly, provided no other processes are associated with storage.

Measurements made at high shear rates on W/O and O/W emulsions with

medium to high concentrations of disperse phase indicate a sharp decrease of vis-

cosity with storage time. This is associated with an increasing mean droplet size.

The kinetics of droplet coalescence are defined by

Nt = N0 exp(−Ct) (4.171)

where Nt and N0 are the numbers of droplets per millilitre of emulsion at time

t and initially, respectively, and C is the rate of droplet coalescence. For further

details, see Tscheuschner (1993b).

4.7 Viscosity of suspensions

According to Scott Blair (1969), Hatschek proposed the following equation for

the viscosity of concentrated suspensions:

𝜂susp = 11 − (ΦK)1∕3

(4.172)

where Φ is the ratio of volume suspended to total volume and K is the volumi-

nosity factor, which takes into account the swelling due to the solvent attaching

to the suspended phase and increasing the volume of the particles.

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The rheology of foods and sweets 165

Roscoe (1952) proposed the following equation for a suspension of uniformly

sized particles in high concentration,

𝜂sus =𝜂solv

(1 − 1.35Φ)2.5(4.173)

and, for a suspension of diversely sized particles in high concentration,

𝜂sus =𝜂solv

(1 − Φ)2.5(4.174)

Oldroyd (1959) dealt with various cases of deformation of disperse systems:

slow, steady rates; variable, small rates; and finite rates. In addition, he discussed

various forms of the Einstein equation (Eqn 4.158) and differential equations

describing more complicated rheological properties.

Example 4.5Let us calculate the approximate value of Φ for the fat-free suspended frac-

tion of a chocolate that contains about 35 m/m% cocoa butter, and estimate the

(dynamic) viscosity of this chocolate mass if the viscosity of cocoa butter 𝜂c.butter

is about 0.03 Pa s. The density of chocolate is 1.235 g/ml and that of cocoa butter

is 0.91 g/ml.

100 g chocolate has a volume of 100∕1.235 = 80.97 ml

35 g cocoa butter has a volume of 35∕0.91 = 38.46 ml

If we assume that no voluminosity needs to be taken into account, the volume

of fat-free components is the difference between the aforementioned volumes:

Φ = 80.97 − 38.4680.97

= 0.525

Using Eqn (4.173),

𝜂chocol. =𝜂c.butter

(1 − 1.35Φ)2.5= 0.03

0.0458= 0.655 Pa s

Using Eqns (4.139) and (4.174),

𝜂chocol. =𝜂c.butter

(1 − Φ)2.5= 0.03

0.1555= 0.193 Pa s

Both of these results are much less than the real value of the viscosity of

chocolate, which has a magnitude of about 2 Pa s at least. For further details,

see Tscheuschner (1993b).

Example 4.6Let us calculate the voluminosity K of the fat-free components of chocolate

according to Eqn (4.172) if the viscosity of the chocolate mass is 2.1 Pa s.

2.1 = 0.031 − (ΦK)1∕3

(0.525K)1∕3 = 6970

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166 Confectionery and chocolate engineering: principles and applications

and

K =( 1

0.525

)(6970

)3

= 1.824

4.8 Rheological properties of gels

4.8.1 Fractal structure of gelsA large variety of intermediate and finished products in the confectionery indus-

try are gels. Their mechanical properties, as determined at small deformations,

vary widely from very soft and deformable to rather stiff, as can be easily experi-

enced by hand. The small-deformation properties are frequently studied, although

their practical importance is limited. The most important reason for studying

them is that they can account for certain aspects of the undisturbed structure of

the gel, if the experiments are done well. In this context, structure is defined as

the spatial distribution of the relevant structural elements (building blocks) of

the network and the interaction forces between them.

The measurement of mechanical properties is especially suitable for investigat-

ing the structure of materials, because they can take account of both the spatial

distribution of the structural elements and the interaction forces between them,

in contrast to most other methods. However, this also makes their interpretation

more complicated.

A ‘small deformation’ is defined as a relative deformation (strain) so small that

applying it does not affect the structure of the material studied.

A characteristic of gels is that they consist of a continuous solid-like network in

a continuous liquid phase over the timescale considered. The latter aspect implies

that certain products can be considered as gels over short times but as liquids

over long times. At intermediate timescales, their reaction to an applied stress

will be partly elastic and partly viscous, that is they behave viscoelastically. So

the dependence on time is an important characteristic of the small-deformation

properties of gels.

A new mathematical tool, fractal geometry, was used in the 1990s for studying

the networks of gel structures (and of fats). Fractal geometry is useful for describ-

ing many of the irregular and fragmented patterns found in nature. The shapes of

these patterns are not lines, planes or three-dimensional objects, and therefore

cannot be described using Euclidean geometry. Fractal geometry is concerned

with the geometric scaling relationships and symmetries associated with fractal

objects, which is the name of a new family of geometrical shapes. The creator of

fractal theory was Mandelbrot (1983).

An important characteristic of a perfect fractal object is that it is self-similar at all

levels of magnification. A fractal system can display statistical self-similarity rather

than exact self-similarity, where the microstructure is similar over a certain range

of magnification (Meakin, 1988).

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The rheology of foods and sweets 167

The principles of fractal geometry can also be used to describe a disordered dis-

tribution of mass, including particles in a colloidal gel and fat crystal networks.

In this case, the patterns are statistically self-similar at different scales of obser-

vation, and the relationship of the radius R to the mass M is given by

M(R) ∼ RD (4.175)

where D is the mass fractal dimension (more frequently referred to simply as

the fractal dimension); see Meakin (1988), Vreeker et al. (1992), Marangoni and

Rousseau (1996) and Narine and Marangoni (1999a).

If Eqn (4.175) were describing a two-dimensional Euclidean object such as a

square, then the value of D would be 2. However, a fractal object may be some-

thing intermediate between a line and a plane or between a plane and a cube.

Therefore, the fractal dimension may be ‘fract(ion)al’: 1<D< 2 or 2<D< 3.

A short summary of the concept of fractals and the determination of various

fractal dimensions is given in Appendix 4 in order to facilitate the understanding

of the applications of this concept in engineering.

After the introduction of the concept of fractals, many studies were carried

out on the structures of polymer and colloidal aggregates. Scaling theory has been

used to explain the elastic properties of protein gels (de Gennes, 1979; Bremer

et al., 1989; Vreeker et al., 1992; Stading et al., 1993). Colloidal aggregates have

been shown to be fractal structures both rheologically and optically (Weitz and

Oliveira, 1984; Brown and Ball, 1985; Sonntag and Russel, 1987; Buscall et al.,

1988; Ball, 1989; Uriev and Ladyzhinsky, 1996).

4.8.2 Scaling behaviour of the elastic properties of colloidalgels

A power-law relationship between the elastic modulus and the solids volume

fraction has been established from work with colloidal aggregates (Brown and

Ball, 1985; Sonntag and Russel, 1987; Buscall et al., 1988; Ball, 1989; Shih et al.,

1990).

The scaling behaviour of the elastic properties of colloidal gels was studied by

Shih et al. (1990), who developed a scaling theory based on treating the structure

of the gel network as a collection of flocs that are fractal objects, closely packed

together throughout the sample. Two regimes, the strong-link and the weak-link

regimes, were identified based on the strength of the links between the flocs

relative to the strength of the links within the flocs themselves. When a network

is composed of very large flocs, which occurs at low particle concentrations (low

solid fat content, SFC), the links between the flocs are stronger than the flocs

themselves.

4.8.2.1 Determination of the elastic constant (shear modulus)Consider a network to which an external force f is applied in the x direction,

causing a deformation. Across a cross-section A perpendicular to x there are N

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168 Confectionery and chocolate engineering: principles and applications

strands or chains per unit area bearing the stress 𝜎, each exerting a reaction force

−(df/dx)Δx, where Δx is the distance over which the relevant structural elements

of the network have moved with respect to each other. This gives

𝜎 = −N

(df

dx

)Δx (4.176)

There is no restriction on the nature of the strands, on the elements that the

strands are constructed from, or on the nature of the interaction forces involved.

If the measurements are done in the so-called linear region, which is normally

the case for small deformation experiments, df/dx is constant.

In general, f can be expressed as −dF/dx, where dF is the change in the Gibbs

energy (free enthalpy) when the elements are moved apart by a distance dx, so

we can write

𝜎 = N

(d2f

dx2

)Δx (4.177)

The local deformation Δx can be related to the macroscopic shear strain 𝛾 by a

characteristic length C determined by the geometric structure of the network:

Δx = 𝛾C (4.178)

In general, C has a tensor character.

As the shear modulus G is given by 𝜎/𝛾,

G = NC

(d2Fdx2

)(4.179)

At constant temperature, we have dF= dH− T dS for the free enthalpy, where H

is the enthalpy and S is the entropy, which results in the equation

G = NC d(dH − T dS)dx2

(4.180)

According to Shih et al. (1990), in the strong-link regime (low SFC), the elastic

constant is related to the solids volume fraction by

G ∼ Φ(3−x)∕(3−D) (4.181)

where x is the so-called backbone fractal dimension, which usually lies between

1 and 1.3 (Shih et al., 1990), and D is the fractal dimension.

When a network is composed of very small flocs formed at a high particle

concentration (high SFC), the links between the flocs are weaker than the flocs

themselves. In this weak-link regime (high SFC), the elastic constant is related

to the solids volume fraction by

G ∼ Φ(3−2)∕(3−D) (4.182)

Equations (4.181) and (4.182) show that in the weak-link regime the elastic

constant of the system increases more slowly with particle concentration than in

the strong-link regime.

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The rheology of foods and sweets 169

4.8.3 Classification of gels with respect to the nature of thestructural elements

According to the discussion by van Vliet (1999), several types of gels can be distin-

guished on the basis of the nature of the structural elements. Such a classification

is irrespective of the energy content of the bonds or of their relaxation times.

4.8.3.1 Gels formed from flexible macromoleculesFlory (1953) derived the classical equation for the shear modulus of flexible

macromolecules,

G = nkT (4.183)

where G is the shear modulus (N/m2), n is the number of elastically effective

chains per unit volume (m−3), k=1.38062×10−23 J/K is the Boltzmann constant,

and T is the temperature (K).

A chain is defined as a part of a macromolecule extending from one cross-link

to the next along the primary molecule. The cross-links represent the fixed points

of the structure in the sense that the chain ends meeting there have to move

together, irrespective of the motion of the cross-link. In terms of Eqn (4.183),

the quantity kT stems from the second derivative of the Gibbs energy, and n

stems from NC. The enthalpic contribution (see Eqn 4.178) may be neglected, as

the contour length L of the chain between cross-links is much longer than the

root-mean-square end-to-end distance ⟨r2⟩1/2 of a free chain of length L (Treloar,

1975).

Equation (4.183) has been shown to hold for many gels composed of synthetic

polymers. For food-grade macromolecules, it holds for gelatin gels under the

conditions that exist in food, and also for heat-set ovalbumin gels in 6 M urea.

Even if Eqn (4.183) holds, however, the relation between the shear modulus

and the concentration of macromolecules is less straightforward than we would

expect from it:

G =(

cMc

)RT (4.184)

where c is the concentration of the gelling substance (w/w), Mc is the average

molecular weight of the chain between two cross-links and R is the gas constant.

Equation (4.184) cannot be used for the determination of molecular weight,

and the probable explanation of this fact is that a proportion of the molecules are

not involved in gel formation and/or that a proportion of the various chains are

elastically ineffective. The proportion that are elastically ineffective will depend

on the history (the cooling regime) and concentration. The storage modulus G′

of gelatin gels (see Eqns 4.140 and 4.141) has been found to be proportional to

the concentration squared for concentrations above 2% (te Nijenhuis, 1981).

In the case of polysaccharide gels, the macromolecular chains are rather stiff.

This means that the requirement L> ⟨r2⟩1/2 does not hold, especially for highly

cross-linked gels.

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170 Confectionery and chocolate engineering: principles and applications

4.8.3.2 Gels Formed from hard particlesOur understanding of the relation between the structure of gels of hard parti-

cles and their small-deformation properties has been greatly enhanced by the

introduction of the idea that clusters with a fractal structure are formed during

aggregation (Bremer et al., 1989, 1990; van Vliet, 1999).

The number of primary particles NP in a cluster with a fractal structure scales

with the radius R:NP

N0

=(

Raeff

)D

(4.185)

where D is the fractal dimension (D< 3), aeff is the radius of the effective build-

ing blocks forming the fractal cluster and N0 is the number of primary particles

forming such a building block.

The size of the clusters scales with R3, and so the volume fraction of particles

Φc in the cluster decreases with increasing radius. At a certain radius Rg, the

average Φc will equal the volume fraction Φ of primary particles in the system;

the clusters will then fill the total volume and a gel will be formed, with

⟨r2⟩1∕2 = aeffΦ1∕(D−3) (4.186)

where Rg is a measure of the average cluster radius at the moment the gel is

formed. In fact, this quantity gives an upper cut-off length, that is the largest

length scale at which the fractal regime exists.

So, given the value of Φ, at least one additional parameter besides D needs

to be known for a full characterization of the fractal clusters forming the gel

network – namely Rg, aeff or N0. Gels built from fractal clusters with the same

value of D but different values of aeff will exhibit different structures at the same

magnification, and hence a different permeability (van Vliet et al., 1997).

4.8.3.3 Gels formed from flexible particlesAfter aggregation of protein particles, such as casein, the particles start to fuse

and the interaction between the original casein micelles becomes just as stiff as

the rest of the casein particles. In such a case, it is inappropriate to speak any

more of an interaction energy between particles. An alternative is to assign a

modulus to the protein chain (van Vliet, 1999).

For a cylindrical chain of aggregated particles of length L and radius a, where

the stiffness of the particles is the same as that of the bonds between them, assum-

ing a linear regime, the Young’s modulus E is given by

E = 𝜎

ΔL∕L=(

f

𝜋a2

)( LΔL

)=(

f

𝜋a2

)( xΔx

)(4.187)

Since

f =(

d2Fdx2

)Δx (4.188)

therefore

E =( 1𝜋a

)(d2Fdx2

)(4.189)

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The rheology of foods and sweets 171

For the shear modulus of the gel, the relations

G = NC𝜋aE (4.190)

where C= a/26 (Bremer and van Vliet, 1991; Bremer et al., 1990), and

G ∼ (𝜋∕26)EΦ2∕(3−D) (4.191)

are obtained.

4.9 Rheological properties of sweets

Machikhin and Machikhin (1987) have given a comprehensive survey of the

rheological properties of various sweets.

4.9.1 Chocolate mass4.9.1.1 Fluid models for describing the flow properties of chocolate massRheological measurements of the properties of chocolate started in the 1950s.

Some notable publications are those of Fincke (1956a), Kleinert (1957), Heiss

and Bartusch (1957a,b), Steiner (1959b), (1962a–d) and Duck (1965). These

researchers clarified some essential points about the measurement of the rhe-

ological properties of various types of chocolate mass (e.g. the importance of the

preparation of the mass for measurement) and the types of flow curves of choco-

late (e.g. the generalized Bingham model). These investigations also clarified the

effects of cocoa butter, temperature, water content and addition of lecithin on

the viscosity and yield stress of molten chocolate.

Kleinert (1954a–c) studied the rheological properties of chocolate couvertures

with a Drage viscometer, and determined that the Bingham model,

𝜏 = 𝜏0 + 𝜂PlD (4.192)

where 𝜏 is the shear stress (Pa s), 𝜏0 is the yield stress (Pa s), 𝜂Pl is the Bingham

plastic viscosity (Pa s) and D is the shear rate (velocity gradient) (s−1), was useful.

Thus, a yield stress could be measured, and the Bingham plastic viscosity was

approximately linear.

Koch (1959) worked with a falling-ball viscometer of the Koch type. The vis-

cosity data measured for chocolate couvertures were in the region of 15–50 Pa s;

the values for couvertures manufactured for hollow figures were in the region

of 25–26 Pa s, and those for chocolate bars were in the region of 25–55 Pa s.

Steiner (1959b) studied the hypothesis of Bingham behaviour for chocolate at

higher shear rates. His data for the yield stress were in the range 9–38 Pa, and the

data for the Bingham plastic viscosity were in the range 1–3.4 Pa s, depending on

the types of viscosimeter used.

Fincke (1956a,b) and Heiss and Bartusch (1956) did not support the con-

cept of the Bingham model for chocolate mass; however, they performed their

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172 Confectionery and chocolate engineering: principles and applications

investigations at low shear rate values. These investigators also reported evi-

dence of thixotropic and sometimes rheopexic behaviour, as a result of making

viscosity measurements first with increasing and then with decreasing rates of

shear. Also, Mohos (1966a,b) observed thixotropy and rheopexy in milk choco-

late (water content, 1.23%; fat content, 38.4%; equipment, falling-ball rheo-

viscometer of Höppler type). Rheopexic behaviour was characteristic of milk

chocolate at higher temperatures (above 60 ∘C).

Fincke (1956a,b), Heiss and Bartusch (1956) and Steiner (1959a,b) deter-

mined that the Casson model (Casson, 1959),

√𝜏 =

√𝜏0CA +

√𝜂CA

√D (4.193a)

where 𝜏 is the shear stress (Pa s), 𝜏0CA is the Casson yield stress (Pa s), 𝜂CA is

the Casson viscosity (Pa s) (independent of D) and D is the shear rate (s−1), can

be used to describe the rheological properties of chocolate mass. It is important

to note that the Casson model is the only one which is based on a physical picture and

not merely an empirical formula as are the other fluid models. For this physical

picture, see Appendix 3.

Later, Heinz (1959) and Heimannn and Fincke (1962a–d) obtained the best fit

of Eqn (4.193a) for milk chocolate when the exponent was equal to 2/3 instead

of 1/2, that is

𝜏2∕3 = 𝜏2∕30 CA + 𝜂2∕3

CA D2∕3 (4.193b)

These investigators had mentioned earlier that the exponent n was sometimes

in the range 1/2≤ n≤1.

The fundamental results of these investigations were summarized in the

classical publication of Fincke (1965). The IOCCC method (the use of which is

presently suspended because it is under checking) uses the Casson equation,

which provides the best fit (standard deviation< 3%) in the shear rate range

D=5–60 s−1 (Tscheuschner and Finke, 1988a). In a relatively broad range of

shear rate (D=0.90–45 s−1), a good fit is obtained for dark chocolate at t=50 ∘Cif n= 0.77 (Tscheuschner, 1993a).

According to the studies of Mohos (1966b, 1967a,b), a general equation

𝜏n = (𝜏0CAn)n + (𝜂CAn)nDn (4.194)

where K0 = (𝜏0CAn)n and K1 = (𝜂CAn)n are constant, can be used for the descrip-

tion of the rheological properties of milk chocolate, where 1/2≤ n≤1 in general.

However, in some cases where the milk proteins have been strongly denatured

owing to the effect of increased temperature (>60 ∘C) during conching or as a

result of being pumped through too hot a tube, the relation n> 1 may be valid.

Mohos (1967a,b) showed that an easy modification of the theoretical frame-

work applied in the Casson model results in the general formula given in Eqn

(4.194). For further details, see Appendix 3. It is to be emphasized, however, that

the exponents n= 2/3 and 1/2≤ n≤1, and so on derive from an effort to obtain

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The rheology of foods and sweets 173

Table 4.5 Flow curve of a plain chocolate evaluated as a Bingham fluid and as a Casson

(n= 1/2) fluid.

Shear stress (Pa) Shear rate (s−1) Shear stress0.5 Shear rate0.5

25.3 3.52 5.029911 1.876166 Intercept 3.029152

27.5 4.47 5.244044 2.114237 Slope 1.043251

30.8 5.7 5.549775 2.387467 Correlation 0.999714

33.9 7.28 5.822371 2.698148

38.1 9.29 6.17252 3.04795

43.4 11.9 6.587868 3.449638

49.9 15.1 7.063993 3.885872

57.7 19.3 7.596052 4.393177

67.6 24.7 8.221922 4.969909

79.7 31.5 8.927486 5.612486

Yield stress 19.62 Pa Casson: 9.18 Pa = Intercept2

Plastic viscosity 1.94 Pa s Casson: 1.09 Pa s = Slope2

Correlation r 0.999138 0.999714

a linear relationship, although the theoretical background may be interpreted in

terms of the fractal nature of the material as well.

In connection with this, the units of 𝜏n and (𝜏0CAn)n are Pa, those of (𝜂CAn)n

are Pa s and those of Dn are s−1. Table 4.5 presents an evaluation of a flow curve

according to two different flow models (the Bingham model and the Casson

model with n= 1/2).

It is to be emphasized that the values of 19.62 Pa and 1.94 Pa s in the table

are the Bingham yield stress and the Bingham (or plastic) viscosity, respectively.

Similarly, the values of 9.18 Pa and 1.09 Pa s are the Casson yield stress and the

Casson viscosity, respectively. These values are conceptually different, since in

one case they relate to a Bingham fluid and in the other case they relate to a

Casson fluid.

The most serious objection against the Casson equation is that the Casson vis-

cosity 𝜂CA and the Casson yield stress 𝜏0CA are not equal to the measured viscosity

and yield stress values, respectively. The difference between 𝜂CA and 𝜂 is under-

standable: because of linearization, 𝜂CA is independent of the shear rate but 𝜂 is

dependent on the shear rate. On the other hand, the yield stress is always a result

of extrapolation, and in the linear plot of the Casson equation, the extrapolation

is easier.

The Tscheuschner equation (Eqn 4.201) is tailored to the special properties of

dark and milk chocolate; therefore, it provides the best fit to the flow curves. For

further details, see Tscheuschner (1993a).

Afoakwa et al. (2009) deal with the relationships between Casson model and

International Confectionery Association recommendations. The two strategies

are compared and correlated in defining rheological properties of molten dark

chocolates prepared using different particle size distributions, fat and lecithin

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174 Confectionery and chocolate engineering: principles and applications

content. Rheological parameters were determined using a shear rate-controlled

rheometer and data examined using correlation, regression and principal com-

ponent analyses to establish their inter-relationships. Correlation and regression

analyses showed high correlation (r=0.89–1.00) and regression coefficients

(R2 = 0.84–1.00). The newer International Confectionery Association technique

gave higher correlation and regression coefficients than the Casson model, but

multivariate principal component analysis showed that the two models were

highly related and either could effectively quantify dark chocolate viscosity

parameters.

Wolf (2011) deals with the specific rheological properties of crumb chocolate

by using the Casson and the Carreau model as well as the Krieger–Dougherty

relation describing the effect of solids volume fractions.

4.9.1.2 Effect of solids content and cocoa butter on the viscosityof chocolate

Steiner (1959b) refers to Harbard (1956), who determined that not all of the

cocoa butter is available as a medium for dispersion of the solid particles. Part

of it is probably absorbed on the surface of the particles present, and will not

influence the viscosity. According to Harbard, a general relation exists over a

wide range of concentrations:

𝜂Pl = 𝜂0

(1 − Φ1 − 𝜈

)−k

(4.195)

where 𝜂Pl is the plastic viscosity of chocolate (Pa s), 𝜂0 is the dynamic viscosity

of cocoa butter when serving as a dispersion medium (Pa s), Φ is the volumetric

proportion of solids (V/V), v is the volumetric proportion of voids in the packed

solids (V/V) determined by centrifugation and k is an exponent (constant). Har-

bard proposed that the value of k could be determined for a single pair of 𝜂Pl

and 𝜂0 if c and v were measured, and thus the corresponding values of 𝜂Pl and 𝜂0

could be calculated for other concentrations.

Although the Habbard formula has not achieved widespread use, its principal

idea is in agreement with that represented by Eqns (4.172)–(4.174), and it pro-

vides a correct picture of the relationship between viscosity and solids content

for chocolate. The Habbard formula is based on the very simple idea expressed

by the equation

bΦ + cF = 1 (4.196)

where b=−1/(1− v)=1/(v− 1) is the volume ratio of solids, c is the volume ratio

of liquids and F is the volume of free liquids (i.e. fats; cocoa butter in the case of

chocolate). The constant b takes into account also the immobilized fat, which is

either absorbed on the particle surfaces or not melted.

From the Habbard formula, a modified form of the Einstein equation can be

derived,

𝜂∞ = 𝜂0(1 + bΦ)k (4.197)

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The rheology of foods and sweets 175

Table 4.6 Variation of plastic viscosity of chocolate as a function of cocoa butter (CB) content,

c and v, assuming that the viscosity of CB is 0.03 Pa s; see the Harbard formula (Eqn 4.195).

CB (%) 𝝓

𝜼Pl (v=0.05, k=6.67)(Pa s)

𝜼Pl (v=0.08, k=6.64)(Pa s)

𝜼Pl (v=0.1, k=6.60)(Pa s)

32 0.57 5.39 5.40 4.88

35 0.53 3.28 2.99 2.72

40 0.46 1.30 1.19 1.08

Bartusch (1974) proposed the Eilers–Maron equation,

𝜂∞ = 𝜂0

[1 − dΦ1 − 𝛽Vd

]2

(4.198)

(where d and 𝛽 are constant), which can also be regarded as a variant of the

Habbard equation.

Example 4.7Let us consider a chocolate mass of plastic viscosity 𝜂Pl =3 Pa s, and assume that

𝜂0 =0.03 Pa s for cocoa butter, that the volumetric proportion of solids Φ for

35 m/m% cocoa butter is 0.525, as in Example 4.5, and that v= 0.05.

From Eqn (4.195), 3=0.03[1− 0.525/(1− 0.05)]−k, and therefore k≈6.64.

Table 4.6 shows the results for 𝜂Pl for various values of cocoa butter (CB) con-

tent and v; the values of Φ were calculated as in Example 4.5.

According to Steiner (1959a,b), the fat (mainly cocoa butter) content, which

may vary between ca. 32 and 40 m/m%, influences the viscosity very effectively

because over this range the apparent viscosity may be reduced by a factor of 10

relative to its original value. In Example 4.7, the viscosities at the ends of this

range are 5.39 Pa s (32% cocoa butter) and 1.29 Pa s (40% cocoa butter), which

means a reduction by a factor of 4.18.

The effect of solids depends not only on the amount but also on the quality

of the solids. In milk chocolate, these solids may be sugar, fat-free dry cocoa

cells and fat-free dried milk, all of which are likely to affect the properties in

various ways. The size distribution of the solids plays an especially great role. A

basic requirement of chocolate quality is that the largest particles must be smaller

than 20 μm. However, if the proportion of very small (<5 μm) particles is too high,

their huge specific surface adsorbs a considerable amount of cocoa butter and,

as a result, the proportion of dispersed phase will be decreased, which causes a

strong increase in viscosity. Evidently, comminution has to be done under strict

control in chocolate manufacture.

Tscheuschner and Finke (1988a) determined that liquid, crystal-free cocoa

butter in the shear rate range from 0 to 500 s−1 and at temperatures between 35

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176 Confectionery and chocolate engineering: principles and applications

and 100 ∘C is a Newtonian fluid. For the temperature function of the viscosity of

cocoa butter, the Frenkel–Eyring equation (Eqn 4.78)

𝜂 = A exp( U

RT

)

holds in the form

𝜂 = 5.7 × 10−7 exp(3533.7

RT

)(Pa s) (4.199)

where R= 8.32 J/kmol.

According to Tscheuschner and Finke (1988b), the rheological properties of

cocoa butter–cocoa solid matter dispersions with a constant particle size distri-

bution depend on the solids volume fraction Φ, the temperature, the moisture

content, the lecithin content and the shear rate. Besides the structure-related

viscosity 𝜂str(D1) see Equations (4.201–4.203), a yield stress 𝜏0 occurs at solids

volume fractions Φ>0.21. The value of the yield stress increases with increasing

Φ. In addition, weak thixotropic flow properties can be observed. However, the

Casson model is not suitable, because at Φ< 0.2 there is no yield; rather, there is a

viscous flow of the structure. Even at higher Φ values, the Casson model is fairly

inaccurate in the shear rate range D< 5 s−1 (Tscheuschner and Finke, 1988a).

Tscheuschner (1993a,b) discussed several suspensions of CB, among them

chocolate. For CB/cocoa solids, CB/sugar and CB/milk powder suspensions, he

recommended

𝜂sp = 𝜂rel − 1 = [𝜂]Φ + AΦn + BΦn (4.200)

where 𝜂rel = 𝜂∞/𝜂CB is the relative viscosity of the suspension, expressed as the

ratio of the viscosity of the suspension (in equilibrium, D→∞) to the viscosity

of clear CB; Φ is the volume concentration of solid spheres in suspension; and A

and B are constants. Equation (4.200) can be regarded as a variant of the Einstein

equation (Eqn 4.157).

Tscheuschner (1989, 1993c) developed a flow model with four parameters for

molten chocolate:

𝜏 = 𝜂∞D + 𝜏0 + 𝜂str(D1)(

DD1

)−n

D (4.201)

or, for the viscosity 𝜂S of chocolate,

𝜂S(D) = 𝜂∞ +𝜏0

D+ 𝜂str(D1)

(DD1

)−n

(4.202)

where 𝜂str(D) is called the structural parameter and depends on D. The units of

D and D1 are s−1.

If D=D1, Eqn (4.202) can be written as

𝜂S(D) = 𝜂∞ +𝜏0

D+ 𝜂str(D1) (4.203)

If the value of D is increased (D→∞), the additive terms 𝜏0/D and 𝜂str(D) dis-

appear (see Eqn 4.202) because the high shear rate destroys the structure of the

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The rheology of foods and sweets 177

suspension and, as a result, Eqn (4.203) simplifies to

𝜂S(D) = 𝜂∞ = constant (4.204)

The viscosity 𝜂∞ refers to the state where D> 200 s−1.

In a study of 19 chocolate masses by Tscheuschner (1993a), the (modified)

Eqns (4.201) and (4.202) provided a better fit than the Casson equation did.

For the relations between the various fluid models (the Newton model, the

Casson model with d=1/2 and n= 2/3, the Heinz model with a general value

of n and the Herschel–Bulkley model) applied to chocolate, see Tscheuschner

(1999).

4.9.1.3 Effect of lecithin on the viscosity of chocolateA substance which radically affects the viscosity of chocolate is lecithin, which

is mostly of soya origin. Most of the reduction occurs with the first 0.2–0.3%,

and there is little further gain beyond additions of 0.5%. Roughly, 0.3% of com-

mercial lecithin is equivalent to a replacement of 4–5% CB. Excessive quantities

of lecithin, however, have been reported as leading to an increase in viscosity

(Liebig, 1953).

Here, it should be mentioned that the control of the yield stress 𝜎0 is important

in the shaping of chocolate products, both in the case of the covering of centres

(see Eqn 4.71) and in the case of shell moulding and the shaping of figures by

use of a spinner. A food additive widely applied for this purpose is polyglycerol

polyricinoleate ((PGPR) E476), which strongly increases the yield stress. A com-

bination of lecithin and PGPR in a ratio of 3 : 1 to 4 : 1 is used, at a maximum

content of 0.5%.

Tscheuschner (1993a, 2008), in connection with the agglomeration phenom-

ena that take place in chocolate during conching, stated that an addition of 0.2%

lecithin somewhat improves the rheological properties because its amphoteric

molecules cover the hydrophilic particle surfaces, leading to a decrease in the

interfacial free energy. But the effect of lecithin alone is not sufficient to hinder

the increase in yield stress at high water content. In this case, a mix of lecithin and

PGPR (in the ratio 7 : 3) gives better results. The effect of PGPR can be explained

by the binding of the PGPR molecules to the heterogeneous surfaces of milk

powder particles rather than to the hydrophilic surfaces of sugar particles. It is to

be stressed that the value of 0.2% for the lecithin content seems to be optimal,

because, when both lower and higher amounts are added, the resulting reduction

in the viscosity of chocolate is weaker.

An excellent summary of the emulsifiers used in chocolate has been given by

Minifie (1999, Chapter 4).

The effect of emulsifiers has a close connection with the water content of the

chocolate. As a general rule, the water content must be below 0.4% – above

this value, the viscosity starts to increase rapidly. The effect of emulsifiers is to

disperse the water content of the chocolate. The undesirable effect of humidity

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178 Confectionery and chocolate engineering: principles and applications

on chocolate manifests itself strongly above 0.4%, which is equivalent to a water

content of the milk powder of about 2.5%. This value of 0.4% is a critical thresh-

old for particle aggregation. It was demonstrated by Tscheuschner (2002) that if

the initial water content of a chocolate suspension is low enough, a long conch-

ing time is not necessary, because it cannot improve the rheological properties.

This perception is fundamental from the point of view of reducing the conching

time and energy consumption. The key point is that it is necessary to decrease

the water content of the milk powder, which can be done, for example, by some

previous preparation of the milk powder.

4.9.1.4 Effect of temperature on the viscosity of chocolateThe relation between the viscosity of melted chocolate and temperature has been

studied by several researchers (Stanley, 1941; Kleinert, 1954d; Fincke and Heinz,

1956) and appears to follow an exponential law (Eqn 4.78). Fincke and Heinz

(1956), using a RotoVisco viscometer, plotted log 𝜂 against 1/T and obtained a

straight line up to 80 or 90 ∘C in the case of plain chocolate. The magnitude of the

effect of temperature was of the order of a 2–3% decrease per 1 ∘C and was sim-

ilar to the effect for CB alone. The temperature coefficient appeared to increase

slightly with shear rate.

For milk chocolate, the logarithmic relationship did not hold above about 60 ∘C,

owing to changes consequent upon heat treatment. According to Heimannn and

Fincke (1962c,d), the critical temperature region starts at about 60 ∘C, where

the Maillard reaction between the milk protein and the sugars in milk chocolate

becomes more and more intense, and this causes a definite increase in both the

viscosity and the yield stress. According to the experiments of Mohos (1982), the

progress of the Maillard reaction, characterized by the hydroxymethylfurfural

(HMF) content of the milk chocolate, is a function of temperature; for further

details, see Section 16.2.1.

4.9.1.5 Pressure dependence of the flow curve of chocolate massMachikhin (1968) investigated the pressure dependence of the flow curves of

chocolate masses at 44 ∘C with a rotoviscometer. According to this study, choco-

late masses were shown to be Bingham fluids. The exponential relationship in

Eqn (4.83) proved valid for the viscosity but less valid for the yield stress. For

more details, see Machikhin and Machikhin (1987, pp. 135–151).

4.9.1.6 Rheological behaviour of pre-crystallized chocolate massDanzl and Ziegleder (2013) studied the rheological properties of pre-crystallized

chocolate masses. They determined that a plate-and-cone geometry seems very

useful since the measurement must be smooth and rapid in order to not influence

the included seed material and destroy the crystalline state. It was shown that

the flow curves and mainly the yield value of such tempered chocolate masses

are influenced by the tempering state.

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The rheology of foods and sweets 179

4.9.2 Truffle massMachikhin et al. (1976) investigated Extra truffle mass (with a fat content of

43.3% and a water content of 7%) with a Rheotest-2 rotational viscometer. In

the manufacturing process, chocolate mass and milk butter (both molten) were

whipped for ca. 30–40 min.

Evaluation of the flow curve according to the Ostwald–de Waele model gave

the results:

𝜏 = (306 − 7.05t)D0.37 (4.205)

and

𝜂 = (306 − 7.05t)D−0.63 (4.206)

where 𝜏 is the shear stress (Pa); 𝜂 is the dynamic viscosity (Pa s); D is the shear

rate (s−1), which ranged from 0.5 to 218.7 s−1; and t is the temperature (∘C),

which ranged from 25 to 34 ∘C. The power law index n is 0.37 and the consistency

index K is equal to 306−7.05t.

4.9.3 Praline massBirfeld (1970) and Birfeld and Machikhin (1970) investigated the viscosity of

various praline masses using rotational viscometers of types RV-8 and RM-1.

The result of the evaluation followed the Ostwald–de Waele model: four pra-

line masses gave the results 𝜂 (kPa s)=1.62D−0.49, 1.44D−0.51, 1.08D−0.41 and

0.79D−0.62, where D is in s−1.

According to Machikhin and Machikhin (1987, Chapter 3), the flow curves

of various praline masses can be described by the Bingham model (Eqn 4.192).

However, in the region D>6–7 s−1, the following formula can be used:

𝜂 = 𝜂Pl exp

(bD

)(4.207)

where b is a constant, and if D→∞, then 𝜂→ 𝜂Pl.

4.9.4 Fondant massNikiforov et al. (1964) found that the viscosity of various fondant masses

can be described by flow curves of the Ostwald–de Waele type. In the region

D=0.4−0.3 s−1,

𝜂 (kPa s) = 8.2D(0.53−1) (4.208)

and in the region D= 0.3–10 s−1,

𝜂 (kPa s) = 5.2D(0.123−1) (4.209)

Nikiforov et al. (1964) investigated the temperature dependence of the viscos-

ity of the fondant masses by evaluating the flow curves in a linear form (ln 𝜂 vs.

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180 Confectionery and chocolate engineering: principles and applications

ln D). The following relations were obtained:

at 16 ∘C∶ 𝜂 = 6.92D−1.073 (4.210)

at 20 ∘C∶ 𝜂 = 4.77D−0.771 (4.211)

at 24 ∘C∶ 𝜂 = 3.65D−0.79 (4.212)

at 28 ∘C∶ 𝜂 = 2.85D−0.814 (4.213)

at 32 ∘C∶ 𝜂 = 1.98D−0.695 (4.214)

The temperature dependence of the viscosity of fondant mass can be described

by the relationship

𝜂 = (12.113 − 0.345 × t)Dn−1 (4.215)

4.9.5 Dessert masses4.9.5.1 Dessert masses containing fondantFlow curves of various dessert masses containing fondant were given by

Koryachkhin (1975), who proposed the following formula according to the

Herschel–Bulkley model:

𝜂 (Pa s) = A + BtD

+ (a + bt)Dn−1 (4.216)

where 𝜂 (Pa s) is the structure viscosity, D (s−1) is the stress rate, A+Bt (Pa) is the

yield stress, a+ bt (Pa sn−1) is the plastic viscosity and t (∘C) is the temperature.

The values of n, A, B, a and b are shown in Table 4.7.

The conditions of validity of Eqn (4.216) are

D = 2 − 140 s−1, t = 28 − 30 ∘C (4.217)

Marshalkin et al. (1970) investigated the structure viscosity of dessert masses

containing fondant. They recommended the following formula:

log 𝜂 = (4.19 − 0.036t)(1 − 0.223 log D) (4.218)

where t (∘C) is the temperature (10–70 ∘C), 𝜂 (Pa s) is the structure viscosity and

D (s−1) is the shear rate. (Here, log means the logarithm to base 10.)

Maksimov (1976) and Maksimov and Machikhin (1976) investigated the rhe-

ological properties of dessert masses containing fondant with a rotoviscometer

Table 4.7 The values of the constants n, A, B, a and b in Eqn (4.216).

n A B a b

0.5 28 525 −875 21 323 −667

0.55 12 900 −400 9 524 −282

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The rheology of foods and sweets 181

of type RV-8 in such a way that the external rotating cylinder was vibrated at

a frequency f (Hz) and the gap between the two cylinders was regarded as the

amplitude of the strain 𝛾. In this arrangement, the shear rate can be calculated as

d𝛾

dt= 2𝜋f 𝛾0 (4.219)

where 𝛾0 is the maximum amplitude (i.e. the gap). The following relationship

was recommended:

𝜂 = ad𝛾

dt(4.220)

where 𝜂 is the viscosity (kPa s), a is a constant that decreases if the temperature is

increased (with values in the range 948–33 500) and b is a constant that increases

if the temperature is increased (with values in the range −0.594 to −1.465).

As Eqns (4.174) and (4.186) show, these masses follow the Ostwald–de Waele

model, that is, a↔K (the consistency coefficient) and b↔n (the index of the

power law or fluid model).

Under the effect of vibration, K decreases, while n increases up to 1. Con-

sequently, the behaviour of these masses approaches that of a Newtonian fluid.

This effect of vibration is very evident in the region of small shear rates, 0–20 s−1.

Because the usual shear rates used in shaping are about 10 s−1, this fact is impor-

tant from a technological viewpoint.

4.9.5.2 Rheological model of dessert fillingsFor modelling the extrusion of dessert fillings, Kot and Gligalo (1969) recom-

mended a complex model consisting of two Hooke elements, a Newton element

and a St Venant (plastic) element (Fig. 4.26). According to Kot and Gligalo’s

tests, the rheological properties of dessert fillings are strongly influenced by the

amount and the size distribution of crystals; for example, if the amount of crys-

tals of maximum size 0.05 mm is less than 50 m/m%, the filling can be regarded

as a Bingham fluid.

4.9.6 Nut brittle (Croquante) massesMaksimov et al. (1973) proposed an Ostwald–de Waele model for nut brittle

masses at various temperatures (Table 4.8):

𝜂 (Pa s) = KDn−1 (4.221)

For further details, see Machikhin and Machikhin (1987, Section 3.1.1).

4.9.7 Whipped massesGoguyeva (1965) measured the viscosity of whipped masses as a function of

the duration of whipping (Table 4.9). A plot of viscosity versus time is approx-

imately linear, but both the initial and the terminal parts of it definitely differ

from linearity.

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182 Confectionery and chocolate engineering: principles and applications

G2

η

τ

τ

G1

P0

Figure 4.26 Fluid model given by Kot and Gligalo (1969) for

extrusion of dessert fillings. Source: Adapted from Kot and

Gligalo (1969).

Table 4.8 The n and K values at various temperatures for Maksimov et al.’s

model.

Temperature (∘C) 90 110 130

n (flow index) 0.46 0.37 0.44

K (consistency coefficient) 1730 1050 350

Table 4.9 Viscosity of whipped masses as

a function of whipping time.

Time (s) Viscosity (Pa s)

180 10.34

210 18.27

240 30

270 42.5

300 50

4.9.8 CaramelBarra (2004) deals with the rheology of caramel in her doctorial theses. The

rheology of caramel was determined as a function of processing temperature

and hydrocolloid additions.

X-ray diffraction showed that although crystalline fat was present, for the most

part the sugars were in the amorphous state. The exception was the lowest water

content caramel (7.9% water w.w.b.) which had been processed to a temperature

of 122 ∘C.

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The rheology of foods and sweets 183

Rotational rheometry gave information on the steady shear viscosity, the

dynamic parameters (storage and loss moduli and related functions) and

the creep compliance and recovery response. Capillary rheometry gave shear

viscosities at high shear rates and an extensional viscosity. It was found that

caramel without added hydrocolloids had behaviour which was close to a

Newtonian liquid characterized by a power-law model. The only exception to

this was the values obtained for the Trouton ratio, which ranged from 10 to 40.

This was considerably higher than the value of 3 for a Newtonian fluid and

may reflect the difficulties in making measurements on these relatively low

viscosity systems in the capillary rheometer. The viscosities obtained from steady

shear, oscillation and creep were combined, and three approaches (an empirical

statistical model, Arrhenius model and Williams–Landel–Ferry (WLF) model)

were used to model the data as a function of measurement temperature and

water content. For simple liquids, deviation from Arrhenius behaviour is well

described by the Vogel–Tammann–Fulcher (VTF) equation.

Incorporation of the hydrocolloids carrageenan and gellan gum into the caramel

made the material non-Newtonian and elastic. For carrageenan incorporation,

in particular, the Trouton ratio increased with carrageenan concentration reaching

a value ∼500 (!) at a strain rate of 100 s−1 for the caramel containing 0.2%

carrageenan. It was demonstrated that incorporation of carrageenan could

be used to prevent cold flow in caramels processed at relatively high water

contents.

Glass transition temperatures (Tg) were measured by differential scanning

calorimetry (DSC) and calculated from the temperature dependence of the shift

factors used to superimpose the oscillatory rheological data. In general, there

was agreement between the two approaches although for some gellan gum

containing samples the rheological Tg was about 10 ∘C higher than the DSC

value. Fragility calculated from the WLF constants for caramel was high as has

been reported for sugars. The Tg for both caramel and sugar water mixtures

calculated using the Couchman–Karasz equation in the water content of interest

(9–15% w.w.b.) was some 30–40 ∘C higher than measured. It is suggested

that this disagreement could be related to the high fragility of the sugar water

systems.

For more details, see Barra (2004).

4.10 Rheological properties of wheat flour doughs

4.10.1 Complex rheological models for describing foodsystems

As Scott Blair (1975) writes, systematic work on the rheology of flour dough was

done by Kosutány and Hankóczy in the first decades of the twentieth century.

Kosutányi (1907) described an apparatus designed by Rejto. Strips of dough, rect-

angular in cross section, were stretched on a series of low-friction metal rollers.

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184 Confectionery and chocolate engineering: principles and applications

Hankóczy (1920) was a pioneer in developing a method for measuring the work

done during the kneading of dough in a mechanical mixer, a method later com-

mercialized by Brabender in Germany and still used today.

In connection with the methods for measuring the rheological properties

of dough, Baird (1983) gave a review of measurements with devices that

provided material properties in engineering/scientific units. In order to obtain

the well-defined flows described earlier that lead to material functions, certain

test geometries must be employed. The material functions defined for shear

flow are most directly obtained with a cone-and-plate rheometer but can also

be determined with a plate–plate rheometer. The cone-and-plate geometry

leads to a uniform shear rate throughout the sample. Hence, from torque and

normal-thrust measurements, 𝜂 and the first normal-stress coefficient can be

obtained as a function of 𝛾 ′ as follows (see Eqn 4.55):

Φ1 = Φ1(𝛾 ′) =𝜎11 − 𝜎22

(𝛾 ′)2=

N1

(𝛾 ′)2(4.222)

In a plate–plate rheometer, 𝛾 ′ varies with the radial position, which requires extra

calculations to obtain 𝜂 and N1 as a function of 𝛾 ′. These test geometries can also

be used to carry out transient shear experiments, although the cone-and-plate

geometry is the preferred geometry.

The dynamic viscosity (𝜂) in a steady shear flow can be obtained at higher shear

rates using a capillary rheometer rather than a rotary rheometer. However, the

shear rate also varies with radial position and is a function of the viscosity.

The wall shear rate can be obtained using a procedure that corrects for the

non-parabolic velocity profile. Unfortunately, there is no established way to

obtain N1 from a capillary rheometer at present. Two companies, Rheometrics

Inc. and Sangamo Ltd, manufacture rotary rheometers suited to carrying out

various shear flow experiments.

The extensional (or elongational) viscosity is obtained most often by extending

the end of a cylindrical specimen exponentially with time, which leads to values

of 𝜀′ independent of the position in the sample, or by extending the end at a

constant rate, which requires a knowledge of the diameter profile to calculate 𝜀′.

By definition,

𝜎33 − 𝜎11 = −𝜂(𝜀′)𝜀′ (4.223)

where 𝜂^(𝜀′) is the extensional viscosity as function of 𝜀′ and 𝜀′ is the exten-

sion rate.

Methods for generating both biaxial extension and planar extension are also

available. An instrument for carrying out various unidirectional elongational

flow experiments is manufactured by Rheometrics. For some special testing

methods, see Section 4.10.2.

Some models for describing the properties of doughs are presented in the

following sections, making use of the results of measurements that provide quan-

tities with engineering significance.

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The rheology of foods and sweets 185

4.10.1.1 Bread doughBread provides an instructive example of the investigation of the rheological

properties of foods containing flour as the principal component. A rheologi-

cal model of the soft part of bread given by Lásztity (1987b) is presented in

Figures 4.27 and 4.28. Figure 4.27 shows the case if the stress P is less than P0

(the yield stress). Figure 4.28 shows the case if P>P0. This model can be charac-

terized by five parameters: G1 and G2 for the Hooke elements, 𝜇1 and 𝜇2 for the

Newton elements and P0 (stress yield) for the St Venant plasticity model.

G1 can be calculated from the elastic deformation, by applying Hooke’s law

(Fig. 4.27):

G1 = P𝜀

(elastic deformation) (4.224)

The following equation applies to the Kelvin model characterized by G2 and 𝜇1:

𝜀 (deformation) =(

PG2

)[1 − exp

(−

G2t

𝜇1

)](4.225)

a

Hooke

Newton

St Venant

b c d e

Elastic

P < P0Deformation

Elastic

Total

t(0) t(1) Time

Retarded

G1

G2 µ1

µ2

P0

Figure 4.27 Model for the soft part of bread (1). Consecutive phases of the deformation

process are indicated by a–e. (a) Initial phase at t= t(0); (b) elastic deformation; (c) retarded

elastic deformation; (d) after t= t(1) (the stress has ceased), recovery of the first phase of

elastic deformation (phase b); (e) recovery of phase c. Source: Lásztity (1987b). Reproduced

with permission from Lásztity.

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186 Confectionery and chocolate engineering: principles and applications

The retarded elastic deformation (see Fig. 4.27 or 4.28) is equal to P/G2, where

P is the stress applied. G2 can be calculated by applying Hooke’s law:

G2 =p

𝜀(retarded elastic deformation) (4.226)

At a given t= 𝜏, the appropriate deformation 𝜀= 𝜀(𝜏) can be read from the curve

(Fig. 4.27), and 𝜇1 can be calculated from Eqns (4.191) and (4.222):

𝜇1 = −G2𝜏

ln[1 − 𝜀(𝜏)G2∕p](4.227)

Deformation

Elastic

Totalelastic

Retarded elastic

Lasting deformation

Timet(1)t(0)

Total

a b c e fd

Figure 4.28 Soft part of bread (2). Consecutive phases of the deformation process are indicated

by a–f. (a–c) As in Fig. 4.27; (d) plastic deformation (represented by a St Venant model); (e)

recovery of phase ‘b’ (elastic deformation); (f) recovery of phase ‘c’ (retarded elastic

deformation). Source: Lásztity (1987b). Reproduced with permission from Lásztity.

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The rheology of foods and sweets 187

Figure 4.29 Glücklich/Shelef model for

wheat dough.

G1

G2

G3

P0,3

P0,2

P0,1

η1

η2

τ

τ

Determination of P0 (the yield stress) and 𝜇2 can be carried out if p is changed

and the flow curve (P vs. d𝜀/dt) is evaluated according to the model

P = P0 + 𝜇2

(d𝜀dt

)(4.228)

P0 is obtained by interpolation of the curve of P to obtain the value at which

d𝜀/dt= 0.

Glücklich and Shelef (1962) recommended a complex model consisting of

eight elements for wheat doughs (Fig. 4.29).

4.10.1.2 Pretzel doughMachikhin (1975) determined the temperature dependence of the viscosity of

sweet pretzel doughs as follows:

𝜂 = 10 exp[(A

t

)B]

(4.229)

where 𝜂 is the viscosity (Pa s), t is the temperature (30–60 ∘C) and A and B are

constants dependent on the shear rate, the water content of the dough and the

overpressure (between 0 and 1.5 MPa). The values of A and B were in the range

0.967–1.062 and 0.106–0.182, respectively, if the water content was 32% and

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188 Confectionery and chocolate engineering: principles and applications

St Venant:τ0

Newtonη

HookeG2

HookeG1

τ

τ Figure 4.30 Shvedov model.

the shear rate was in the range 0.1–0.35 s−1 (at 1.47 MPa), and 1.118–1.061 and

0.198–0.227, respectively, if the water content was 30.4% and the shear rate was

in the range 0.1–1.0 s−1 (again at 1.47 MPa).

Machikhin (1975) recommended the Shvedov model (Fig. 4.30) for charac-

terizing sweet pretzel doughs. This consists of a Newton, a St Venant and two

Hooke elements; consequently, the pretzel mass has a yield stress 𝜏0 (see the

St Venant element). The following differential equation applies to the Shvedov

model (Machikhin, 1975):

D =(

d𝜏dt

)(1

G1

+ 1G2

)+𝜏 − 𝜏0

𝜂(4.230)

where D is the shear rate, 𝜏 is the shear stress, 𝜏0 is the stress yield and G1 and

G2 are the elasticity moduli of the Hooke elements.

For further details, see Machikhin and Machikhin (1987, pp. 121–125).

4.10.2 Special testing methods for the rheological studyof doughs

Szczesniak (1963a) classified texture-measuring instruments into three groups:

• Fundamental tests, in which properties such as Young’s modulus and viscosity

are measured

• Empirical tests that measure properties that are usually poorly defined but that

have been shown by practical experience to be related to textural quality in

some way

• Imitative tests that measure various properties under conditions similar to

those to which the food is subjected during mastication

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The rheology of foods and sweets 189

Bourne (1975) has given a review of texture measurements and instruments

for that purpose.

Food doughs are defined here to be low-moisture mixtures of water and

wheat, corn, oat, semolina or soya flour or mixtures of these flours. Other

ingredients can also be added, such as flavourings and oils. Rheological mea-

surements of food doughs have certainly been carried out for many years in the

food industry.

The various special testing methods for the rheological study of doughs are not

discussed here in detail, but some references are given in the following sections.

4.10.2.1 FarinographTwo of the most widely used physical dough-testing instruments for wheat qual-

ity evaluation studies are the farinograph, designed by Hankóczy (1920), and the

mixograph, designed by Swanson and Working (1933). The technique is to com-

bine flour and water (and other ingredients) and to record the torque required

to mix the resulting dough. This record provides a quantitative measure related

to the rheological properties of the dough.

4.10.2.2 Brabender farinographThe most complete and comprehensive source of information dealing with the

farinograph is the third edition of The Farinograph Handbook by D’Appolonia and

Kunerth (1984). The mixing action is brought about by two sigma-type blades

which rotate at speeds with a ratio of 3 : 2. The type of mixing created by this type

of blade is different from that caused by the pin-type mixer in the mixograph. The

temperature during mixing is controlled by the use of temperature-controlled

water circulating in a jacket surrounding the bowl in which the dough is mixed.

For the evaluation of the results, see Farinograph-E Worldwide Standard for

Testing Flour Quality (1997).

4.10.2.3 Brabender extensographThis is used for measuring the resistance (in Brabender units (B.U.)) of dough

as a function of extensibility (in cm). Measurements made with a Brabender

extensograph can be regarded as supplements to measurements made with a

farinograph. If a plot of 𝜎0 − 𝜎 versus time is prepared, a curve is obtained that is

very similar to that obtained with an extensograph for wheat flours (Buschuk,

1985), which follows the Maxwell model (Eqn 4.84).

4.10.2.4 MixographThe mixograph is a small, high-speed recording dough mixer originally designed

by Swanson and Working (1933) to provide a method of measuring quality,

as far as quality is related to gluten structure. The device measures the rate of

development of the dough, the maximum resistance of the dough to mixing and

the duration of the resistance to mechanical overmixing. The first systematic

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190 Confectionery and chocolate engineering: principles and applications

statistical study relating characteristics measured by mixograph to the results of

baking was conducted by Johnson et al. (1943).

4.10.2.5 AlveographThe alveograph, designed by Chopin (1927), is a rheological technique designed

for the routine testing of wheat flours. A dough prepared from the flour under

standard conditions of water addition and mixing is made into a sheet and

cut into a circular test piece, which, after a period of resting, is subjected to

biaxial extension by inflating it into the shape of a bubble until it ruptures.

The pressure in the bubble is measured with a manometer and recorded on a

chart as a function of time. For further details, see Hlynka and Barth (1955a,b),

Bloksma (1957), Chopin (1962), Scott Blair and Potel (1937) and Rasper and

Hardy (1985).

4.10.2.6 TexturometerMany of the instrumental tests described in the literature relate to the character-

ization of as is baked goods. In the mouth, the products are not only disintegrated

mechanically by mastication but are also mixed with saliva, which softens and

hydrates the structure.

Some special imitative tests applicable to baked goods practically simulate the

process of mastication. A typical example here is the General Foods texturometer,

composed of mechanical jaws, a strain gauge and a recording system (Friedman

et al., 1963). Excellent correlations with sensory ratings have been reported by

Szczesniak (1963a,b). Further references include Brandt et al. (1962) and Tanaka

(1975).

A similar test may be performed using a universal testing machine such as

an Instron tester (Bourne, 1968). The method is known as instrumental texture

profiling analysis (TPA).

4.10.2.7 PenetrometerThe penetrometer is a simple instrument used commonly to assess the strength

of baked goods. A probe or indenter is generally used, and the depth of pene-

tration at a definite time after loading with a constant weight is recorded. The

greater the penetration, the more tender the product. The theory and applica-

tion of puncture testing were described by Bourne (1979). The penetrometer is

also widely used for measuring the textural properties of jellies, whipped sweets,

fondant products, etc.

For further details, see Babb (1965), Funk et al. (1969), Morandini et al. (1972),

Smejkalova (1974) and Choishner et al. (1983).

4.10.3 Studies of the consistency of doughMiller (1985), after many studies with several penetrometers, including an

Instron Universal Tester, developed a method of measuring the consistency of

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The rheology of foods and sweets 191

short doughs using a Stevens LFRA Texture Analyzer. This analysis generated a

standard relationship between the consistency of a dough and the water level of

the recipe which was applicable to all 18 flours tested. This relationship is

W0 =Wt

1 − 0.71 log(C∕234 g)(4.231)

where W0 is the optimum recipe water level (% by flour wt), Wt is the recipe

water level (% by flour wt), C is the consistency (g) and W0 is the optimum recipe

water level (% by flour wt), which produces a dough consistency of 234 g.

Under standardized test conditions, the dough consistency measurements cor-

related well with both the weight of dough samples and the weight of biscuit

pieces. The dough consistency also correlated reasonably well with biscuit thick-

ness. This method has potential applications in problem solving and in laboratory

matching of production doughs.

Nyikolayev (1964, 1976) and Nyikolayev and Mityukova (1976) (1976, 1978)

investigated the tensile strength of doughs made with an aqueous sugar solution

and a yeast suspension using a plastometer of type KP-3. The following rela-

tionship between the tensile strength of the dough and the amount of thinning

solution was given:

𝜏0 = A − Bc (4.232)

where c is the amount of aqueous sugar solution or suspension of yeast added

and A and B are constants.

According to Rebindyer (1958), the following relationship can be applied to

data obtained with a plastometer:

𝜏0 = K(𝛼)Ph2

(4.233)

where 𝜏0 is the tensile strength (Pa), K(𝛼)= (1/𝜋) cos2(𝛼/2) cgt(𝛼/2) is a constant

depending on the angle of the measuring cone, P is the force (N) exerted by the

measuring cone and h is the sinking depth (m) of the measuring cone.

Mazur and Dyatlov (1972) investigated the tensile strength of various doughs

containing fat, sugar and yeast with a plastometer of type KP-3. Based on their

results, the following relationship was recommended:

𝜏0 = a𝜃b (4.234)

where 𝜏0 is the tensile strength (kPa), 𝜃 is the rising time (min), a is a constant,

with values in the range 3.6–4.7× 10−4, and b is a constant, with values in the

range 0.7–1.1. The values of the constants depend on the fat and sugar contents

of the dough.

4.10.3.1 Compressibility of doughsThe compressibility of doughs is an important parameter in the shaping of doughs

by compression.

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192 Confectionery and chocolate engineering: principles and applications

Volarovich and Nyikiforova (1968) investigated the compressibility of biscuit

masses. The decrease in volume was measured. The following relationship could

be applied for biscuit masses:

pV a = b × 10c (4.235)

where p is the pressure (MPa), V is the volume of dough (cm3) at a pressure p

and a, b and c are constants depending on the volume concentration of air in the

dough.

4.10.3.2 Doughs without yeastBlagoveshchenskaya (1975) obtained a relationship for the viscosity of doughs

without yeast:

𝜂 = c + eaWa (4.236)

where 𝜂 is the viscosity (Pa s), W is the water content (%) and a, b, c and e are

constants.

If the temperature dependence of the viscosity of such doughs is investigated

at a given shear rate, a minimum value of the viscosity is found, and the temper-

ature at which this minimum value occurs becomes higher as the water content

of the dough is made lower.

4.10.3.3 Tadzhik girdle cakesLibkin et al. (1978) investigated the flow curve of Tadzhik girdle cakes, and the

following relationship was determined:

𝜂 = aDn

(4.237)

where 𝜂 is the viscosity at 20 ∘C (Pa s) and D is the shear rate (s−1). The dimen-

sion of the constant a depends on the value of n; for example, if n= 0.668, then

a= 5426 Pa s(1−0.668). The Tadzhik girdle cakes followed the Ostwald–de Waele

model.

For the temperature dependence of the viscosity of Tadzhik girdle cakes, the

following relationship gave a good approximation:

𝜂 = a + bt + ct2 (4.238)

where 𝜂 is the viscosity (Pa s), t is the temperature (20–34 ∘C) and a, b and c are

constants depending on the experimental conditions and the shear rate.

4.10.3.4 Biscuit doughsMachikhin and Machikhin (1987) recommended the following relationship for

the viscosity versus shear rate curve (measured with an RM-1 rotoviscometer)

of biscuit doughs:

𝜂 = 1(a + bD)

(4.239)

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The rheology of foods and sweets 193

where 𝜂 is the viscosity (Pa s), D is the shear rate (s−1), a is a constant [(Pa s)−1],

with values between 0.018 and 0.08, and b is a constant (Pa−1), with values

between 0.062 and 0.636. Different viscosity values were obtained when the

components of the recipe (fat, flour, yeast and aqueous solutions of sugar and

salt) were changed. For further details, see Machikhin and Machikhin (1987,

Chapter 3).

Manohar and Rao (1997) studied the effect of mixing time and additives on the

rheological characteristics of dough and on the quality of the resulting biscuits.

They found that an increased mixing time influenced the rheological character-

istics by increasing the compliance, elastic recovery, cohesiveness, adhesiveness

and stickiness and by reducing the extrusion time, the apparent biaxial exten-

sional viscosity and the consistency hardness. Doughs mixed for 180 s gave bis-

cuits of superior quality compared with those made from a dough mixed for

either 90 or 300 s. The incorporation of cysteine or dithioerythritol, particularly

in doughs from medium strong wheat flour, resulted in biscuits with greater

spread and crispness.

For further details concerning the dough rheology see Appendix A.3.3.5.

4.11 Relationship between food oral processingand rheology

The anatomy and physiology of the oral processing of foods is complicated (Lucas

et al., 2002).A major problem compared with other processes is the lack of visu-

alization of what goes on, but as great as technical problems to solve this are, it is

the dearth of simple physiological models that seems to stand out as a dire need.

Food oral processing can be separated to two partial processes, that is, masti-

cation and swallowing.

Mastication is usually, but not always, a comminution process. Mastication

involves two analytically separable processes (Epstein, 1947): the chance of

a particle being contacted by the teeth (termed the selection function) and the

degree of size reduction produced by the teeth when a selected particle breaks

(called the breakage function). These are usually defined in terms of breakage

steps. A chewing cycle forms a natural step in mastication.

The selection function depends, for any given mouthful of a particular food, on

food particle size, as well as on the propensity of food particles to clump together

to form a bolus as they get mixed with saliva. Tooth size is critical to the selection

function (van der Glas et al., 1992).

In contrast, the breakage function is the measurement of the distribution of frag-

ments of broken particles formed per chew, referred to the size of the parent

particle.

Studying the mastication step needs studying the solidity and plasticity of foods

(e.g. Young modulus).

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194 Confectionery and chocolate engineering: principles and applications

4.11.1 SwallowingFood particle size reduction is only one of the functions of the mouth, which

has, at some point, to be cleared of food by swallowing. Efficient clearance has

been under great selective pressure in mammalian evolution, but is not easy to

understand.

Although there is a large number of experiments that suggest that swallowing

is not simply determined by a food particle size threshold, it seems very likely that

there is some critical particle size for swallowing, probably in the low millime-

tre range (Lillford, 1991), which may depend on the mechanical properties of

the food. Hutchings and Lillford (1988) made an important conceptual advance

in understanding swallowing by defining a lubrication threshold in addition to a

size threshold. In their view, both thresholds have to be satisfied before swallow-

ing can commence. Swallowing is influenced by adhesive, viscous and cohesive

forces of foods. Lucas et al. (2002) provide a review on different models or food

oral processing.

Gaikwad (2012) studied the oral processing of dark and milk chocolate, in

detail: the chocolate bolus formation, the chocolate eating strategies, the physical

properties and microstructure of ready-to-swallow dark and milk chocolate, the

analysis of moisture (saliva)-uptake by bolus during mastication, mechanical and

rheological characterization of chocolate boluses and so on. Some statements of

Gaikwad (2012, p. 101) are as follows:

The observed differences in mastication strategies between chocolates and the

sensory results for all attributes in question could well be correlated to the phys-

ical properties of the chocolates studied.

Differences in chewing parameters (total number of chews and number of

chews until first swallow) between chocolates may be predominantly related

to the differences in the physical character of the fat phase in turn relating to

differences in hardness and melting behaviour.

The dark chocolate with relatively higher SFC at room temperature was harder

compared with the milk chocolate; consequently, it required greater number of

chewing cycles to comminute its initial serving as well as the subsequent size

reduced particles during the masticatory sequence.

Higher values is melting properties (Tonset, Tend, Tpeak and ΔHmelt) resulting

from its continuous phase character may also be contributed through delayed

onset of melting, higher energy requirements for melting and lower melting rates

for dark chocolate, resulting in higher chewing parameters.

Further reading

Ancey, C. (2005) Introduction to Fluid Rheology, Notebook, École polytechnique fédérale de Lau-

sanne.

Barnes, H.A. (2000) A Handbook of Elementary Rheology, University of Wales.

Brouwers, H.J.H. (2010) Viscosity of a concentrated suspension of rigid monosized particles.

Physical Review E, 81 051402, 1–11, 029903, 1–2.

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The rheology of foods and sweets 195

Cakebread, S.H. (1971) Physical properties of confectionery ingredients – viscosity of carbohy-

drate solutions. Confectionery Production, 37 (11), 662–665.

Cakebread, S.H. (1971) Physical properties of confectionery ingredients – viscosity of high boil-

ings. Mixtures of high solids content of high temperatures. Confectionery Production, 37 (12),

705–709.

Cicuta, P. and Donald, A.M. (2007) Microrheology: a review of the method and applications.

Soft Matter, 3, 1449–1455.

CISA (2011) ALMA MATER Publishing House, “VASILE ALECSANDRI”. University of Bacau,

Bacau, Romania, April 28–30.

Emri, I. (2005) Rheology of solid polymers. Rheology Reviews, 1, 49–100 (http://www.bsr.org

.uk).

Eszterle, M. (1990) Viscosity and molecular structure of pure sucrose solutions. Zuckerindustrie,

115 (4), 263–267.

Figura, L.O. and Teixeira, A.A. (2007) Food Physics: Physical Properties, Measurement and Appli-

cations, Springer.

Huang, J. (1999) Extensional viscosity of dilute polymer solutions. MSc theses. University of

Toronto.

Khan, S.A. and Larson, R.G. (1987) Comparison of simple constitutive equations for polymer

melts in shear and biaxial and uniaxial extensions. Journal of Rheology, 31 (3), 207–234.

Kress-Rogers, E. and Brimelow, C.J.B. (2001) Instrumentation and Sensors for the Food Industry,

CRC Press, Boca Raton, FL.

Lambert-Meretei, A. (2012) Method for measuring the textural properties of bread. PhD Thesis.

Hungarian, Corvinus University of Budapest, Faculty of Food Engineering.

Launey, B. and Bure, J. (1974) Stress relaxation in wheat flour dough following a finite period

of shearing. 1. Qualitative study. Cereal Chemistry, 51 (2), 151.

Lewis, M.J. (1996) Physical Properties of Foods and Food Processing Systems, Woodhead Publishing,

Cambridge.

MacKintosh, F.C. and Schmidt, C.F. (1999) Microrheology. Current Opinion in Colloid & Interface

Science, 4, 300–307.

Manley, D.J.R. (1981) Dough mixing and its effect on biscuit forming. Cake and Biscuit Alliance

Technologists’ Conference.

Marangoni, A.G. and Narine, S.S. (2004) Fat Crystal Networks, Marcel Dekker, New York.

Mason, T.G. (1999) New fundamental concepts in emulsion rheology. Current Opinion in Colloid

and Interface Science, 4, 231–238.

Mewis, J. and Spaull, A.J.B. (1976) Rheology of concentrated dispersions. Advances in Colloid

and Interface Science, 6, 173–200.

Miller, A.R. (1984) Rotary Moulded Short-Dough Biscuits, Part V: The Use of Penetrometers in

Measuring the Consistency of Short Doughs. FMBRA Report 120.

Naccache, M.F., de Souza Mendes, P.R., Frey, S., Calado, V., Thompson, R. (2013) Proceedings

of the VIth Brazilian Conference on Rheology, Rio de Janeiro, pp. 1–149.

Narine, S.S. and Marangoni, A.G. (2002) Physical Properties of Lipids, Marcel Dekker, New York.

Pavlik, M. (2009) The dependence of suspension viscosity on particle size, shear rate and solvent

viscosity. PhD theses, DePaul University, Chicago.

Peixuan, V. (2011) Development of acoustic wave devices to characterize viscosity and its non-

linearity. PhD Thesis. Auburn University, Alabama, USA.

Pollen, N.R. (2002) Instrumental and sensory characterization for a texture profile analysis of

fluid foods. PhD theses. North Carolina State University, Raleigh.

Rao, M.A. (2014) Rheology of Fluid, Semisolid, and Solid Foods, Food Engineering Series, Springer

Science+Business Media, New York. doi: 10.1007/978-1-4614-9230-6_2

Sai Manohar, R. and Haridas Rao, P. (1977) Use of a penetrometer for measuring rheological

characteristics of biscuit dough. Cereal Chemistry, 69 (6), 619–623.

Scholey, J., et al. (1975) Physical Properties of Bakery Jams. BFMIRA Report 217.

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196 Confectionery and chocolate engineering: principles and applications

Scholey, J. and Vane-Wright, R. (1973) Physical Properties of Bakery Jams: An Investigation

into Methods of Measurement. BFMIRA Technology Circular 540.

Schramm, G. (2000) A Practical Approach to Rheology and Rheometry, 2nd edn, Gebruder HAAKE

GmbH, Karlsruhe, Germany.

Shen Kuan Ng, T. (2007) Linear to nonlinear rheology of bread dough and is constituents. PhD theses.

Massachusetts Institute of Technology, USA.

Sriram, I. and Fursf, E.M. (2009) Small amplitude active oscillatory microrheology of a colloidal

suspension. Journal of Rheology, 53 (2), 357–381.

Steele, I.W. (1977) The search for consistency in biscuit doughs. Baking Industry Journal, 9 (3),

21.

Thacker, D. and Miller, A.R. (1979) Process Variables in the Manufacture of Rotary Moulded Lincoln

Biscuits. Cake and Biscuit Alliance Technologists’ Conference.

Townsend, A.K. and Wilson, H.J. (2016) The fluid dynamics of the chocolate fountain. European

Journal of Physics, 37, 015803(23pp). doi: 10.1088/0143-0807/37/1/015803

VDI-GVC (2006) VDI-Wärmeatlas, Springer, Berlin.

Verhoef, M.R.J., van den Brule, B.H.A.A. and Hulsen, M.A. (1999) On the modelling off a

PIB/PB Boger fluid in extensional flow. Journal of Non-Newtonian Fluid Mechanics, 80, 155–182.

Verkroost, J.A. (1979) Some Effects on Recipe Variations on Physical Properties of Baker Jams.

BFMIRA Report 297.

Vermand, J. (2010) Rheology and Structure of Complex Fluids, Lecture. Department of Chem-

ical Engineering, KU Leuven, www.eu-softcomp.net/FILES/IFFFS_REO-1.pdf, pp. 1–130.

Vizireanu, C., Ionescu, A. Istrati, D. and Dima, F. (2011) Rheological behavior of pastry creams.

Paper presented at the International Conference of Applied Sciences, Chemistry and Chem-

ical Engineering.

Wade, P. (1965) Investigation of the Mixing Process for Hard Sweet Biscuit Doughs, Part I, Com-

parison of Large and Small Scale Doughs. BBIRA Report 76.

Wade, P. and Davis, R.I. (1964) Energy Requirement for the Mixing of Biscuit Doughs under

Industrial Conditions. BBIRA Report 71.

Walters, K. and Webster, M.F. (2001) The distinctive CFD (computational fluid dynamics) chal-

lenges of computational rheology, Europ. Congress on Comput. Methods in Appl. Sciences

and Engin., ECCOMAS Computational Fluid Dynamics Conference, Swansea, Wales, UK,

ECCOMAS.

Young, N.W.G. and Muhrbeck, P. (1997) Comparison of shear and extensional viscosity charac-

teristics of starch pastes. Annual Transactions of the Nordic Rheology Society, 5, 1–4.

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CHAPTER 5

Introduction to food colloids

5.1 The colloidal state

5.1.1 Colloids in the confectionery industryThe materials used in the chocolate, confectionery and biscuit industries are

very diverse from the point of view of their structural complexity. Among them

there are both chemical compounds consisting of small molecules (water, baking

salts, monosaccharides, etc.) and substances consisting of giant macromolecules

(starch, cellulose derivatives, proteins of vegetable and animal origin, etc.);

however, between these structural extremities, many more materials can be

found. Disregarding the substances consisting of small molecules (M< c. 500 Da),

all other substances used or produced by these industries behave like colloids,

and this statement holds even for a concentrated solution of sucrose! During

comminution, substances that are originally of cellular structure are dispersed

into particles with a large surface area. These particles have peculiar properties

that are characteristic of the group of materials called colloids. Therefore a study

of food colloids is essential for understanding the engineering aspects of food

production.

5.1.2 The colloidal regionDuring comminution, smaller and smaller particles are generated. At the begin-

ning of the process, the surface of these particles does not play an important role

in the bulk properties of the substance, because the proportion of the mass on the

surface is small. However, as the degree of comminution increases, this propor-

tion becomes increasingly dominant in the bulk properties. There is a size region

between 500 and 1 μm in which interfacial phenomena determine the bulk prop-

erties of substances. This is the colloidal region, a characteristic of which is that

the material parameters change continuously between particles even though the

local coordinates of the particles are discontinuous (Fig. 5.1). Figure 5.2 shows

the position of the colloidal region and how to generate colloids in practice.

The principal difference between the deformation and dispersion methods is

that one dimension of the colloids generated by deformation is macroscopic;

for example, the length of a silk fibre can be large enough to be considered

macroscopic even though its diameter (two dimensions) is tiny. The colloids

Confectionery and Chocolate Engineering: Principles and Applications, Second Edition. Ferenc Á. Mohos.© 2017 John Wiley & Sons Ltd. Published 2017 by John Wiley & Sons Ltd.

197

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198 Confectionery and chocolate engineering: principles and applications

Interface

Substance BSubstance A

Figure 5.1 In the colloidal region, the material parameters do not change discontinuously

(dotted line), but continuously (continuous line).

Submicroscopic

disperse

systemsColloids

(microscopic

disperse

systems)

500 μm

Deformation Dispersion

Corpuscles

sheets

fibres

Lamination

(e.g. soap layer on

water surface)

Pulling fibres

(e.g. pulling of a fibre

of jelly, or silk pulled

by a silkworm)

Generated by

1 μm

Coarse

disperse

systems

Figure 5.2 The colloidal region: generation of colloids by deformation and dispersion.

generated by dispersion (i.e. comminution) have particles of colloidal size in all

three dimensions.

In connection with this characteristic size region, colloidal solutions have par-

ticular optical properties which make possible the determination of the size and

the molecular weight of the colloidal particles. In the colloidal size region, two

subregions can be distinguished according to the size d of the dissolved colloidal

molecules:

• The Rayleigh region, d< 1/𝜆, where 𝜆 is the wavelength of visible light

• The Debye region, 1/𝜆< d<𝜆

These regions are different with respect to the absorption and dispersion of

light. Many colloidal solutions show optical anisotropy as well.

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Introduction to food colloids 199

Dispersion medium

Dis

pe

rse

d p

ha

se

Gaseous

Aerosol

or

colloidal fog

Colliodal

gas

dispersion

Aerosol

or

colloidal

smoke

Gaseous

Fluid

Emulsion

Suspension

Fluid

Solid

Solid

gas dispersion

(solid foam

if coarse)

Xerosol

(fluid

inclusions

if coarse)

Xerosol

or

aerosol

Solid

Figure 5.3 The various types of colloidal systems, considered as combinations of states.

Although the optical properties of colloidal solutions are important in food

chemistry and engineering, this topic does not play an essential role from our

viewpoint.

5.1.3 The various types of colloidal systemsFigure 5.3 shows the possible combinations of states that can give colloidal sys-

tems; of these, emulsions and suspensions are of particular interest.

5.2 Formation of colloids

The colloidal region may be approached either:

• From large sizes, that is, by deformation or dispersion, or

• From molecular sizes: molecules→microphases→macromolecules→micelles

→disperse and cohesive systems

5.2.1 MicrophasesWhen the concentration of a molecule exceeds its solubility, the solution

becomes saturated, and a new phase of agglomerates is then formed from the

molecules, which has a surface with a physical meaning. The consequences of

phase formation are that

• The surface has an interfacial energy.

• Neighbouring molecules will adhere to this new surface.

• Adhering molecules on the surface can react with each other.

The size region where this surface emerges can be regarded as the minimum

value of the colloidal range of size and is about 1 nm (10−9 m). The upper

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200 Confectionery and chocolate engineering: principles and applications

boundary of this region is about 1 μm (10−6 m), which is the characteristic size

of the so-called microphases. The structure of microphases can be crystalline or

amorphous, solid or liquid – even similar to that of macrophases.

5.2.2 MacromoleculesAnother method of formation of particles of large mass is the coupling of small

molecules to create macromolecules by means of covalent bonds. The charac-

teristic parts of a macromolecule are the primer molecules (or monomers) and

the segments; the latter are well-differentiated parts of the chain of the macro-

molecule. The emergence of segments means new qualitative behaviour. The

range of size of macromolecules that can be formed by this method is about

104–107 Da. Giant macromolecules formed by the effect of covalent bonds, which

are of infinite mass in the chemical sense, cannot be regarded as colloids, because

they do not have the ability to perform thermal motion.

5.2.3 MicellesMicelles are associations of molecules. Their typical size range is about

102–103 Da. The molecules that form micelles have a polar and a non-polar

part – such molecules are called amphipathic. Micelles containing 50–100

molecules can be formed only in more concentrated solutions, and they are

in equilibrium with the free molecules and of uniform globular form. Micelles

of laminar structure or of very large size can be formed in very concentrated

solutions, and their size is inhomogeneous.

5.2.4 Disperse (or non-cohesive) and cohesive systemsIf there are no attractive forces between the colloidal particles or these forces

are too weak to overcome the energy of thermal motion, then the particles are

independent of each other, and the system formed by them is fluid:

0 ≤ Ucoh ≤ kT (5.1)

where Ucoh is the attractive energy, kT is the energy of thermal motion, k is the

Boltzmann constant and T is the absolute temperature.

This type of system is called disperse or non-cohesive. Such systems can be

regarded as stable systems from the point of view of thermodynamics, which in

fact is a consequence of the relationship expressed in Eqn (5.1).

The classes of disperse systems are:

• Macromolecular colloidal solutions, for example, dissolved proteins

• Colloidal solutions of association, for example, detergents

• Colloid dispersions or sols, for example, sugar particles finely dispersed in fat

• Coarse dispersions, for example, sugar particles coarsely dispersed in fat

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Introduction to food colloids 201

For cohesive systems,

kT < Ucoh. (5.2)

Two types of cohesive systems can be differentiated according to the strength

of the attractive forces between the particles:

1 If the attractive forces are relatively weak, the system is a gel or agglomerate (or

heap). Its characteristic feature is a stable shape, although the system becomes

fluid under the effect of even a weak force. If the system is thinned (Ucoh is

decreased) or warmed (kT is increased), then the aforementioned relationship

may change to

kT > Ucoh (5.3)

and the system transforms into a disperse (incoherent) system. For this rea-

son, such systems are called reversible cohesive systems.

The classes that these systems are usually divided into are:

∘ Polymer gels, for example, gelatin gel

∘ Micelle gels, for example, soaps

∘ Colloidal aggregates (referred to as gels if they are a mixture of a liquid

medium and solid particles), for example, finely crystallized fats

∘ Coarse aggregates, for example, monodisaccharides coarsely crystallized

from aqueous solution with starch syrup (fondant)

2 If the attractive forces are of chemical nature, the system does not contain indi-

vidual particles anymore, and both the medium and the particles in it form

unbroken, continuous networks. Both phases become deformed to a great

extent; therefore such systems were called deformed systems by Buzágh (1937).

The important representatives of these systems are:

∘ Chemical gels, for example, pectin gels

∘ Solid–gas xerogels, for example, activated charcoal

∘ Solid–liquid xerogels, for example, porous catalysts in a liquid medium

Some typical values of interaction energies are:

∘ Chemical bonds: 80–800 kJ/mol

∘ Hydrogen bonds: 8–40 kJ/mol

∘ Dispersion bonds: 1–8 kJ/mol

The relatively strong hydrogen bonds are characteristic of pectin jellies, which

are chemical gels. If the molecular polarity is decreased, the interaction energy

decreases in parallel:

• Polar molecule/polar molecule: For example, for water (M=18), the inter-

nal molar heat of evaporation is 44 kJ/mol, so the cohesive-energy density is

44/18 kJ/g=2.444 kJ/g.

• Non-polar molecule/non-polar molecule: For example, for pentane (M= 72),

the internal molar heat of evaporation is 25 kJ/mol, so the cohesive-energy

density is 25/72 kJ/g= 0.3472 kJ/g.

• Polar molecule/non-polar molecule: The values of the cohesive-energy density

are between those above.

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202 Confectionery and chocolate engineering: principles and applications

5.2.5 Energy conditions for colloid formationThe formation of a colloid is governed by the change of (Gibbs) free enthalpy:

ΔG = ΔW − TΔS, (5.4)

taking into consideration the fact that ΔS is always positive, and

ΔW = Wm−m + Wp−p − 2Wp−m (5.5)

where ΔG is the change of free enthalpy, ΔW is the change of interaction energy,

Wm–m is the interaction energy between molecules of the medium, Wm–p is the

interaction energy between a molecule of the medium and a molecule of the

particles, Wp–p is the interaction energy between molecules of the particles, T is

the absolute temperature and ΔS is the change of entropy. The condition for the

formation of a colloid is

ΔG < 0. (5.6)

Evidently, an increase in temperature helps in the formation of colloids.

Moreover, if

ΔW ≤ 0, (5.7)

then the formation of a colloid will certainly occur spontaneously. This means

that

Wm−m + Wp−p ≤ 2Wp−m. (5.8)

If ΔW≫ 0, then the formation of a colloid is impossible.

Solutions of macromolecules and colloidal solutions of association may be formed

if ΔG< 0, so these are stable. Colloidal dispersions cannot be formed spontaneously,

because of the high value of the interfacial energy of the particles – if, neverthe-

less, they are formed, they are unstable. In the case of microphases, the attractive

forces between the particles are strong. However, if a protective layer at the inter-

face between the phases hinders the aggregation of particles, the separation of the

particles can be maintained for some time. After a shorter or longer delay, how-

ever, such a system becomes heterogeneous, directly or indirectly via a cohesive

system, because this transformation is accompanied by a decrease of interfacial

energy.

When the attractive energy Ucoh between the particles overcomes the kinetic

energy derived from thermal motion (see Eqn 5.2), the energy barrier can no

longer hinder collisions between particles, and a network, that is, a cohesive

system, will be formed.

5.3 Properties of macromolecular colloids

5.3.1 Structural typesThe properties of macromolecular colloids are determined by the monomers

and the segments. A segment consisting of monomer molecules is capable of

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Introduction to food colloids 203

microscopic Brownian movement but does not participate in the macroscopic

Brownian movement of the whole polymer.

The structural types of macromolecules may be classified as follows:

• Macromolecules built up from monomers by covalent bonds:

– Homopolymers: The structural element is a single type of monomer (e.g.

amylose, amylopectin and cellulose).

– Copolymers: These are made up from structural elements that are more than

one type of monomer (e.g. substituted compounds of a monomer, such as

methylated/amylated glucose, and alginic acid).

• Macromolecules (called polyelectrolytes) containing dissociating groups; typical

representatives are proteins containing carboxyl, hydroxyl, methyl and amyl

groups. The coil volume of these macromolecules is influenced by pH as well

and is minimum at the isoelectric point (iep).

The skeleton of a macromolecule may be of the following types:

• Linear, for example, amylose, agarose, alginic acid, carrageenans and cellulose

• Branched, for example, amylopectin

• Globular, for example, casein

• Network, for example, gelatin

The flexibility of a chain is dependent on:

• Chemical structure (bond angles and rotation)

• Solvation

The structure of a dissolved linear polymer is loose and coil-like and is perme-

ated by the solvent. The volume of the coil is larger in a better solvent since the

solvation is higher.

The average chain-terminal distance h is a characteristic quantity for linear macro-

molecular colloids. If it is supposed that there is no interaction between the seg-

ments, the shortest average chain-terminal distance (h0) is obtained in a 𝜃-solvent.

This is the worst solvent which still dissolves the polymer. Solvation means loos-

ening of the coil, a measure of which is the expansion factor 𝛼, for which the

following is valid:

h2 = 𝛼2h20. (5.9)

The conditions for solution of a polymer are given by the following equations:

Wm−m + Wp−p = 2Wp−m (athermic process) (5.10)

Wm−m + Wp−p < 2Wp−m (exothermic process) (5.11)

Wm−m + Wp−p < 2Wp−m (endothermic process) (5.12)

Many polymer solutions are thermodynamically stable systems.

Another important parameter which characterizes the interaction between a

polymer and a solvent is the interaction parameter 𝜒 :

For good solvents, 𝛼 >1 and 0<𝜒 < 0.5.

For a theta solvent, 𝛼 = 1 and 𝜒 = 0.5.

For unsuitable solvents, 𝛼 <1 and 𝜒 > 0.5.

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204 Confectionery and chocolate engineering: principles and applications

The interaction parameter can be determined by measuring the specific

osmotic pressure 𝜋/c of the polymer solution as a function of polymer

concentration:

𝜋∕c = RT( 1

M+ Ac + Bc2 + · · ·

)(5.13)

where M is the molar mass of the polymer (the intercept of the curve of 𝜋/c vs.

c is RT/M), R is the universal gas constant, T is the absolute temperature and A

is calculated from the slope of the linear section of the curve, which is equal to

RTA. In addition, we can write

A = k(0.5 − 𝜒). (5.14)

From Eqn (5.14), 𝜒 can be calculated. The value of k (not to be confused with

the Boltzmann constant k) is dependent on the type of solvent.

The expansion factor can be determined from the Mark–Houwink equation

(see Eqn 4.163) and a modification of this equation by Flory and Fox. The interac-

tion parameter can be determined from the Stockmayer–Fixman equation. These

equations are related to the intrinsic viscosity of the solution. For further details,

see Sun (2004).

5.3.2 Interactions between dissolved macromoleculesWhen the concentration of a polymer solution is increased, the segments may

permeate through neighbouring segments, and the movement of neighbouring

molecules will be more and more hindered. The viscosity is increased, and the

stretching of the coils becomes more and more elastic. The elastic and viscosity

properties of the concentrated solution become characteristic of such concen-

trated solutions.

The effect of a precipitant on dilute polymer solutions can be expressed by

saying that the attractive forces between segments become stronger and, as a

result, the coils shrink and globules are formed. Finally, as a result of the effect

of attraction, the globules are united into flocs, or coacervates.

However, the effect of a precipitant on concentrated polymer solutions is dif-

ferent: the attractive forces between segments that are permeating each other

stimulate the formation of a network of segments. As a result, a cohesive system,

that is, a polymer gel, is formed.

In protein solutions, the interactions are strongest at the iep, at which isolabile

proteins are precipitated from a sufficiently concentrated solution, and a protein

gel is formed.

5.3.3 Structural changes in solid polymersWhen a polymer is cooled, the linear molecules settle into bundles, micelles are

formed from the bundles, and, finally, crystallites are formed from the micelles.

Amorphous regions remain among the crystallites; the crystallites produce solid-

ity, and the amorphous fraction provided flexibility to the structure.

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Introduction to food colloids 205

Under the effect of a solvent, a solid polymer becomes swollen (in the case of

foods, the only solvent of interest is water). The swelling of the macromolecules

in a chemical network is limited. The swelling of the macromolecules in a phys-

ical network is limited if the solvent is worse than a θ-solvent; if the solvent

is better than a θ-solvent, the swelling is unlimited, and the polymer becomes

dissolved.

5.3.3.1 Velocity of swellingThe velocity of wetting is the amount of solvent absorbed per unit time, which

can be described by (Gábor 1987, p. 35)

m(t) = m∞ − (m∞ − m0) exp(−kt) (5.15)

or

lnm∞ − m0

m∞ − m(t)= kt (5.16)

where m(t) is the mass of the polymer plus the swelling solvent (e.g. water) (kg),

m∞ is the value of m(t) if the time t is large (t→∞), m0 is the initial value of m(t)

(at t= 0) and k is the rate constant for swelling (with dimensions of 1/time).

In the case of unlimited swelling, the value of m∞ is not exactly defined. The

value of k is dependent on the surface of the swelling macromolecule and the

temperature of the solvent.

Example 5.1Stringy agar is soaked in cold water (its water content can easily be measured

during the swelling). The first column in Table 5.1 shows the time points at

which the water content was measured, and the second column shows the

measured values. We assume that m∞ = 36 m/m%, thus (m∞ −m0)= (36−20)

m/m%=16 m/m%.

Syneresis can be understood as the reverse process, during which – a conse-

quence of shrinkage of the gelling agent – a gel loses water according to the

equation

m(t) = m∞ + (m0 − m∞) exp(−kt) (5.17)

Table 5.1 Calculation of rate constant for the swelling of stringy agar

according to Eqn (5.16).a

Time (h) W (m/m%) 36−W 16/(36−W) ln Slope

0 20 16 1 0 0.293244

1 25 11 1.454545 0.374693

2 28 8 2 0.693147

3 30 6 2.666667 0.980829

4 31 5 3.2 1.163151

aW = water content.

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206 Confectionery and chocolate engineering: principles and applications

where k is the rate constant for syneresis and m∞ refers to a very dry state. For

further details on syneresis, see Sections 11.2.6 and 11.4.5.

5.3.3.2 Capillary rise and flow dynamicsThe driving force for liquid penetration into a capillary is given by the Laplace

equation:

Δp =2𝛾LV cos 𝜃

r(5.18)

where Δp is the driving force (sucking effect); 𝛾LV is the liquid/vapour tension

(>0); 𝜃 is the so-called apparent contact angle, which determines the curvature

of the meniscus; and r is the radius of the capillary.

In order to interpret the results of capillary penetration experiments, theo-

retical models are required. The simplest is the well-known Washburn equation

(Washburn, 1921). Washburn showed that the velocity v= dh/dt of the liquid–air

meniscus along the tube drops very quickly to such a value that the conditions of

laminar flow assumed in the Hagen–Poiseuille equation are established, so that

dvdt

= r2𝜋 dhdt

=r4𝜋Δp

8𝜂h,

that is,dhdt

=r2Δp

8𝜂h(5.19)

where h is the height of the liquid front, t is the time of penetration and 𝜂 is the

dynamic viscosity of the liquid.

If the value of Δp is substituted from Eqn (5.18) into Eqn (5.19), the following

differential equation is obtained:

dhdt

=r𝛾LV cos 𝜃

4𝜂h. (5.20)

After integration (from h=0 to h and from t= 0 to t),

h2 =tr𝛾LV cos 𝜃

2𝜂. (5.21)

In many cases, it has been found experimentally that the Washburn law

(Eqn 5.21) is dimensionally applicable for liquids penetrating a porous medium,

that is, h∼ t1/2. However, this type of Washburn law is valid only for the

short-time regime. In the long-time limit, the penetration slows down and shows

an exponential relaxation towards the equilibrium height, h∞:

h(t) = h∞

[1 − exp

(−𝜌gr2t

8𝜂h∞

)](5.22)

and

h∞ =2𝛾LV cos 𝜃

𝜌gr(5.23)

where 𝜌 is the density of the liquid, g is the gravitational acceleration and h∞ is

defined by the balance of capillary and hydrostatic pressures.

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Introduction to food colloids 207

For details of the wettability of porous solids, see Li and Neumann (1996) and

Grundke (2002).

Example 5.2Water penetrates into a capillary of radius r= 0.1 mm=10−4 m. The viscosity of

water is 𝜂 = 10−3 Pa s, the interfacial tension of water is 𝛾LV = 73×10−3 N/m, and

the apparent contact angle is zero, that is, cos 𝜃 =1.

According to Eqn (5.21),

h2 =tr𝛾LV cos 𝜃

2𝜂=

t × 10−4m × 73 × 10−3 (N∕m) × 1

2 × 10−3 Pa s

= t × 10−4 ×(73

2

)m2∕s.

If t= 1 s, the distance of penetration is h =√(73∕2) = 6.04 …× 10−2m =

6.04 … cm.

The penetration height at equilibrium (see Eqn 5.23) is

h∞ =2𝛾LV cos 𝜃

𝜌gr

=2 × 73 × 10−3 (N∕m) × 1

103 (kg∕m3) × 9.81 (m∕s2) × 10−4 m

= 14.88 … cm.

5.3.3.3 Swelling pressureDuring the solvation of macromolecules, molecules of the solvent penetrate into

the inside of the macromolecules. If the energy of solvation exceeds the energy

associated with the binding forces in a network of macromolecules, the binding

points of the network become loose, and dissolution of the macromolecules will

start. This process may be accelerated by a rise in temperature.

The swelling pressure is the pressure difference between the gel phase and the

pure solvent. It can be calculated from the equation

𝜋sw =RT ln as

Vs

(5.24)

where R is the universal gas constant, T is the temperature, aS is the activity of

the solvent in the gel phase and VS is the partial molar volume of the solvent in

the gel phase. The accelerating effect of a temperature rise can be read directly

from Eqn (5.24).

The volume of a macromolecule is increased as a result of solvation; however,

the increase is not equal to the volume of solvent added, because inter-

molecular changes take place during the process, for example, contraction,

amorphous/crystalline state transitions and similar structural changes.

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208 Confectionery and chocolate engineering: principles and applications

Fluid

Elastic

Temperature

Tgl TflTm

Glassy

Str

ain

Figure 5.4 The effect of strain on an amorphous polymer as the temperature is increased.

5.3.3.4 Effect of heat on amorphous polymersFigure 5.4 shows the effect of a constant strain (tension) on amorphous polymers

as the temperature is increased. At Tgl, the polymer ceases to have a glassy con-

sistency, and it then behaves elastically. With a further increase in temperature,

the polymer melts at Tm, and above Tfl it behaves like a fluid, that is, in the range

Tgl < Tm <Tfl. This behaviour is characteristic of fats.

This phenomenon can be observed when a sugar mass is being shaped into

drops, although the temperature sequence is reversed. When the sugar mass

is fluid at ca. 120 to 100 ∘C, flavouring and colouring can be done; then, it is

shaped into a sugar rope, which is elastic at ca. 40 to 35 ∘C; and, finally, the

glassy consistency of the drops is achieved on cooling (at about 16 ∘C).

5.4 Properties of colloids of association

5.4.1 Types of colloids of associationOrganic substances which contain both polar and non-polar groups are capable of

forming associations. For associations of large size, a sufficiently large solubility,

a suitable temperature, a large molecular mass and a special molecular structure

(that of an amphipathic compound consisting of 30–100 atoms) are needed.

If the polar and non-polar groups are well separated spatially, a so-called criti-

cal micelle-forming concentration cM can be determined, and if the concentration

c of a colloidal solution is higher than cM, then globular micelles of almost homoge-

neous size are formed. However, in highly concentrated solutions (c≫ cM), large

micelles with a sheet structure are formed, and, finally, the aggregation of these

large micelles produces a micelle gel.

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Introduction to food colloids 209

If the colloid molecules contain larger numbers of polar and non-polar groups

(e.g. the majority of non-ionic surfactants are of this kind), the micelles become

less regular in shape, and also the value of cM is less sharp in this case. If the

concentration in an aqueous system is increased, a weak network of non-polar

bonds is formed, which is highly viscous.

Amphipathic compounds have an important property: they can be adsorbed

at interfaces with a large polarity difference (e.g. air–water and oil–water inter-

faces), and, as a result, the polarity of the interface is modified, the wetting ability

is influenced, and colloids and coarse dispersions may be stabilized.

The compounds with a molecular mass of about 300–3000 Da which form

micelles contain both polar and non-polar groups, and the balance of these

groups is an important characteristic of such compounds: the hydrophile–

lipophile balance (HLB) number has been defined to characterize their

micelle-forming behaviour. For details, see Section 5.8.8.

Colloidal solutions containing small micelles are in equilibrium in the thermo-

dynamic sense. For a reaction of the type

T ⇄ nT ⇄ (T)n,

the following equation is valid in equilibrium:

K =[(T)n][T]n

=c(q∕n)

[c(1 − q)]n(5.25)

where T is the symbol for a surfactant (amphipathic) molecule, the square brack-

ets [ ] denote a molar concentration, q is the molecular ratio of the surfactant in

a micelle, n is the number of molecules of the surfactant in the micelle, c is the

molar concentration and K is the equilibrium constant.

The thermodynamic force for micelle formation is mainly the interaction

between the water molecules and the surrounding non-polar groups (denoted

by A) of the amphipathic molecules. The formation of a colloidal solution is

determined by the Gibbs free enthalpy change ΔG=ΔW−TΔS, where ΔW is

the enthalpy change by virtue of the interactions (H2O–H2O, A–H2O and A–A)

between the water molecules and the non-polar groups. The distribution of

colloidal particles in a solvent is always accompanied by an increase in entropy,

that is, ΔS> 0. Consequently, the sign and value of ΔW determine the sign of

ΔG, since

2A + 2H2O ⇄ 2A − H2O,

that is,

ΔW = −2WA−H2O + WH2O−H2O + WA−A (5.26)

where WA−H2O is the interaction energy between non-polar groups and water

molecules, WH2O−H2O is the interaction energy between water molecules and

WA–A is the interaction energy between non-polar groups. If ΔW≤0, the forma-

tion of a colloidal solution (→) occurs spontaneously; if ΔW≫0, the formation

of a colloidal solution is hindered, although micelle formation (←) is possible.

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210 Confectionery and chocolate engineering: principles and applications

A compact monomolecular interfacial layer is formed by amphipathic com-

pounds at a relatively low critical micelle-forming concentration cM, and there-

fore these substances are called surface-active compounds.

It can be seen that an increase in temperature decreases ΔG (i.e. provides easier

solubilization) until the increase of ΔW, which also depends on the temperature,

compensates this effect.

5.4.2 Parameters influencing the structure of micelles and thevalue of CM

In water the non-polar groups and in a non-polar solvent the polar groups are

associated:

Micelles of regular structure (globular or sheet-like) are formed in ionic surfactants.

Large, sheet-like micelles are formed in concentrated solutions (c≫ cM).

Chain-like micelles may be formed in organic solvents from ionic surfactants and

in water from non-ionic surfactants.

In aqueous solutions, the value of cM increases as the non-polar part of the

amphipathic molecule becomes larger; for example, for paraffin derivatives (Cn−),

if n increases, then cM decreases. Concentrated surfactant solutions with a net-

work structure are viscous sols, and in the case of a network made up of large

micelles, the solution forms a gel, that is, it becomes solid.

Amphipathic substances decrease the interfacial tension of water because

the exterior side of the interfacial layer is formed by the non-polar groups.

This decrease of interfacial tension continues up to the point where c= cM is

approached.

The specific molar electrical conductivity Λ decreases steeply at c= cM since a certain

proportion of the molecules in a micelle do not dissociate.

Some non-polar substances that are insoluble in water become soluble

in surfactant solutions if c> cM because these substances become enriched

in the non-polar parts of the micelles or because mixed micelles form. This

phenomenon is called solubilization.

5.5 Properties of interfaces

5.5.1 Boundary layer and surface energyThe properties of colloids and of coarse dispersions made up of microphases are

determined by the structure of the boundary layer between the two phases. The

thickness of the boundary layer is usually about 1–2 nm, and the parameters

change over this distance, rather than discontinuously. However, when the liquid

also contains dissolved substances, these substances may press on the molecules

of solvent from the interface and adsorb at it. This phenomenon is called adsorp-

tion. The thickness of the boundary layer can be increased to ca. 100 nm in the

case of adsorbed macromolecules.

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Introduction to food colloids 211

The atoms or molecules on the free surface of a phase are not bonded in the

direction of the free side. The forces resulting from this lack of bonding are man-

ifested in surface and interfacial tension and in surface and interfacial surplus

energy. (In the case of a gas–liquid boundary, we speak of surface surplus energy,

and in the case of a liquid–liquid boundary layer, interface surplus energy.)

The energy of a free surface is equal to the work needed to create a unit area of surface

in a reversible way.

In the case of chemically pure substances, the interfacial tension and the inter-

facial surplus energy are numerically equal and may be measured in units of

J/m2.

5.5.2 Formation of boundary layer: adsorptionWhen two immiscible phases come into contact, their atoms or molecules bond

partially to the field of the other phase. Two cases can be distinguished:

1 Two phases of chemically pure substances come into contact. The original surfaces

disappear, and a new boundary layer is formed. As a result, the interfacial

energy is always less than the sum of the energies of the original surfaces.

The usual interfacial phenomena are adhesion, wetting and an exothermic

thermal effect.

2 Two phases of solutions come into contact. This is a more complicated case. The

chemical composition of the boundary layer usually differs from the composi-

tions of the two phases that constitute it because the concentration conditions

in the boundary layer are determined by the requirement that the decrease in

the (Gibbs) free enthalpy should be a maximum. For example, if the dissolved

substance is an amphipathic compound, its concentration in the boundary

layer will be higher than that in the solution because its polar groups will be

oriented towards the water and its non-polar groups will be oriented towards

the non-polar phase. As a result, the amphipathic compound will be enriched

in the boundary layer.

The concentrations of components in the boundary layer cannot be directly

measured in general, and therefore the usual way is to determine the decrease

in the concentration in the interior of the solution after adsorption and then to

calculate the interfacial surplus (n𝜎 , in units of mol).

The Gibbs interfacial concentration is defined by

Γ𝜎 = n𝜎

AS

(mol∕m2) (5.27)

where AS is the surface area of the boundary layer (m2). If the surface area of the

boundary layer is unknown, the interfacial surplus can be related to the amount

mS of one of the phases (e.g. the mass of the adsorbent). In this case, this param-

eter is called the specific adsorbed amount:

m𝜎 = n𝜎

mS

(mol∕kg). (5.28)

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212 Confectionery and chocolate engineering: principles and applications

The adsorption isotherm is defined as the plot of Γ𝜎 versus c or Γ𝜎 versus p at

constant temperature, where c is the (decreased) concentration of an adsorbed

substance inside the solution after adsorption and p is the (decreased) partial

tension of an adsorbed gas after adsorption. (In these isotherms, m𝜎 can also be

used, if necessary, instead of Γ𝜎 .)

The thermodynamic force for adsorption can be rather strong when the

boundary is established by a contact of the type polar ↔ (polar+non-polar)

↔ non-polar groups, where ↔ means contact and (polar+ non-polar) relates to

the amphipathic substance, which, so to speak, joins together the polar and

non-polar phases, which are otherwise immiscible.

Ions of ordinary electrolytes may be adsorbed on a polar surface if the atoms

or polar groups of the surface are chemically similar to those ions. In this case

the adsorbed ions are located near to the surface, and their counter-ions a little

further away. An electric double layer is formed in this way.

5.5.3 Dependence of interfacial energy on surface morphologyIt is easy to demonstrate that liquid drops are thermodynamically unstable.

It is well known that the vapour pressure of a curved liquid surface differs

from that of a planar surface. The relationship between these pressures can be

determined from the capillary elevation or depression.

If the vapour pressure above a planar liquid surface is p0 and is pr in a closed

capillary, where the surface is curved, then, according to the barometric formula

(which is a consequence of the Boltzmann distribution),

pr = p0 exp

(−Mgh

RT

)(5.29)

where M is the molar mass of the liquid, g is the gravitational acceleration

(9.81 m/s2), h is the capillary elevation (positive) or depression (negative), R is

the universal gas constant and T is the temperature (in K).

However, an expression for h can be obtained from the equilibrium of the

weight of the liquid column in the capillary and the interfacial force acting on

the wall of the capillary:

(interfacial force)2𝜋r𝛾 = r2𝜋hg𝜌(weight of liquid), (5.30)

that is,

h = 2𝛾

rg𝜌(5.31)

where r is the radius of the capillary, 𝛾 is the interfacial tension of the liquid (this

is always positive!) and 𝜌 is the density of the liquid. If the surface of the liquid

is concave or convex, r is positive or negative, respectively.

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Introduction to food colloids 213

Taking this expression for h into account, the relative change of vapour

pressure can be obtained from the barometric formula as follows (using

ex ≈1+ x+ · · ·, if x→0):

pr = p0 exp(−2𝛾M∕r𝜌RT) ≈ p0(1 − 2𝛾M∕r𝜌RT) (5.32)

Δp∕p0 = (pr − p0)∕p0 = −2𝛾M∕r𝜌RT. (5.33)

Since the surface of a drop is always convex, that is, r is negative, the vapour

pressure of a drop of liquid is always higher than that of the pure liquid. Conse-

quently, diffusion of vapour occurs from smaller drops to larger ones and from

the larger drops to the planar surface of the pure liquid. (The continuous liquid

can be regarded as being in a stable state from the point of view of thermody-

namics.)

This picture is valid for pure liquids only, and if two (or more) liquids are

dispersed in each other, diffusion of this kind between them can be decreased or

inhibited – this is the aim of the techniques of emulsification.

A similar relationship can be developed for the solubility of small crystals, and

explains why nuclei are necessary before crystals can form, even from a super-

saturated solution. It explains why larger crystals grow at the expense of smaller ones, a

fact that is made use of in the chemical industry and is known as Ostwald ripening;

see Section 10.6.1. Consequently, the surface of a solid is always heterogeneous

from the point of view of energy: on the peaks and edges, the free energies of

atoms or molecules are higher than on a planar surface.

5.5.4 Phenomena when phases are in contactThe surface energy of chemically pure substances in contact with their own

vapour is proportional to the strength of the bonds between their atoms or

molecules. This fact is demonstrated in Table 5.2.

The surface energy of polar, chemically pure liquids is roughly proportional to

their polarity. The surface energy of amphipathic substances is less than expected

because the non-polar groups in them are oriented towards the vapour phase.

The surface tension of non-polar homologous substances is roughly proportional

Table 5.2 Surface energy compared with interaction energy (approximate values).

Substance Type of bond Surface energy (mJ/m2) Interaction energy (kJ/mol)

n-Hexane Dispersion 18 1–8

Water Hydrogen 73 8–40

Mercury Molecular 480 80–800

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214 Confectionery and chocolate engineering: principles and applications

to their molar mass because the dispersive forces are stronger if the molecule is

larger.

When a solid and a liquid substance (condensed phases) plus their vapour are

in contact, the total surface energy is less than the sum of the surface energies of

the separate phases. The energy liberated is called the adhesion energy Wa:

Wa = −𝛾SV − 𝛾LV + 𝛾SL (5.34)

where 𝛾SV is the interfacial tension of the solid, related to the solid–vapour inter-

face; 𝛾LV is the interfacial tension of the liquid, related to the liquid–vapour

interface; and 𝛾SL is the interfacial tension of the solid–liquid interface.

When the temperature is increased, the interfacial tension always decreases;

this observation has led to some important perceptions. According to Ramsay,

𝛾 = const.(T ′cr − T) (5.35)

where 𝛾 is the interfacial tension of the liquid; T ′cr is a characteristic temperature

value, usually less than the critical temperature of the liquid by 4–6 K; and T is

the temperature.

If a drop of liquid is placed on the surface of a solid, the drop will spread to

an extent that depends on the relevant surface energies: all three phases (solid,

liquid and gas) attempt to decrease their surface area because of their surface

energy. The extent of spreading can be described by Young’s equation (illustrated

in Fig. 5.5):

cos 𝜃 = 𝛾SV − 𝛾SL

𝛾LV(5.36)

where 𝜃 is the contact angle, which is defined as the angle formed at the junction

of the three phases. Solid particles are preferentially wetted by the liquid phase

if cos 𝜃 is positive (𝜃 < 90∘), that is, 𝛾SV > 𝛾SL. The balance of surface tensions,

Liquid

surface

SLθ

γLV

γSV

γLV cos θ

γ

Vapour phase

Solid surface

Figure 5.5 Illustration of Young’s equation. 𝛾SV = solid–vapour interfacial energy,

𝛾SL = solid–liquid interfacial energy and 𝛾LV = liquid–vapour interfacial energy.

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Introduction to food colloids 215

considered as vectors, is obtained as follows:

𝛾SV = 𝛾SL + 𝛾LV cos 𝜃. (5.37)

In the case of solid particles absorbed at an oil–water interface, Young’s

equation may be written in the form

cos 𝜃 = 𝛾PO − 𝛾PW

𝛾OW(5.38)

where O denotes oil, P denotes the solid particles and W denotes water. Solid

particles are preferentially wetted by an aqueous phase if cos 𝜃 is positive (𝜃 < 90∘),that is, 𝛾SV > 𝛾SL (see Eqn 5.36).

5.5.4.1 Mercury porosimetryA contrasting example is provided by mercury, which has a very high surface ten-

sion (480 mN/m) (see Table 5.2) and does not wet solids (𝜃 =140∘). This specific

property of mercury is used for the determination of pore distributions because

mercury can fill the volume of pores without any gaps owing to its extremely

high surface tension. Mercury intrusion porosimetry requires the sample to be placed

in a special filling device that allows the sample to be evacuated, followed by the

introduction of liquid mercury. The size of the envelope of the mercury is then

measured as a function of increasing applied pressure. The basis of evaluation is

the Laplace equation (Eqn 5.18), where Δp is the pressure difference acting on a

fluid of surface tension 𝛾LV if the contact angle is 𝜃. If Δp is positive, the surface

tension pulls the fluid up from a dish into a capillary – this is the case for fluids

(e.g. water) that wet the solid. This is called capillary rise or positive capillarity. It

should be mentioned that the interfacial tension of a surface is always positive!

Since in the case of mercury cos 140∘ =−0.7660, Δp is negative, that is, a cap-

illary depression (negative capillarity) will result. When the pores of a material

are filled with mercury, a measurement of this counter-pressure can be used to

determine the size of the pores.

In mercury porosimetry, the sample is first evacuated and then surrounded

with mercury, and, finally, pressure is applied to force mercury into the void

spaces while the amount of mercury intruded is monitored. Data for the intruded

volume of mercury versus applied pressure are obtained, and the pressures are

converted to pore sizes using Eqn (5.18). The greater the applied pressure, the

smaller the pores entered by the mercury. This method is typically used over the

range of pore sizes from 300 to 0.0035 μm. The difference between water and

mercury is well manifested by the fact that water is easily adsorbed by filling

the pores independently of their size, that is, such a method is suitable for mea-

suring the total volume of pores. However, mercury is suitable for measuring the

distribution of pore sizes according to Eqn (5.18).

Because of increased concern over the use of mercury, several non-mercury

intrusion techniques have been developed. Pabst and Gregorová (2007) deal with

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216 Confectionery and chocolate engineering: principles and applications

the principles of mercury intrusion and Mayer–Stowe theory. For further details,

see, for example, Brouwer et al. (2002) for applications to investigations of cocoa,

and for chocolate products, see Loisel et al. (1997).

Example 5.3Let us use Eqn (5.18) to calculate the pressure p of mercury that has to be applied

if the radius r of the pores is 5, 10 or 15 μm:

p(5 μm) = 2𝛾 cos 𝜃

r= 2 × 480 × 10−3 (N∕m) × 0.766

5 × 10−6 m≈ 147 × 103 Pa

p(10 μm) =(147

2

)× 103 Pa

p(15 μm) =(147

3

)× 103 Pa.

5.5.4.2 Location of particles on a water–oil interfaceAccording to Dickinson (1992, p. 33), for casein micelles (protein parti-

cles) in homogenized milk, reasonable values for the interfacial tensions are

𝛾PO =10 mN/m, 𝛾PW = 0 mN/m and 𝛾OW = 20 mN/m. (1 dyn/cm= 1 mN/m=1 mJ/m2.) Substituting these values into Eqn (5.38) gives a contact angle of the

order of 60∘, which means that the casein micelles are located predominantly

on the outside of the milk fat globules.

The smaller the contact angle, the more effective the wetting is and the larger

the spreading of drops is. For total spreading,

𝜃 = 0and cos 𝜃 = 1. (5.39)

This means that the vector component 𝛾OW cos 𝜃 = 𝛾OW causes a drop to spread

entirely over a surface. The spreading coefficient S is defined as

S = 𝛾SV − 𝛾SL − 𝛾LV. (5.40)

For total spreading, from Eqns (5.40) and (5.37), we obtain

S = 𝛾SV − 𝛾SL − 𝛾LV = (𝛾SL + 𝛾LV cos 𝜃) − 𝛾SL − 𝛾LV = 𝛾LV(cos 𝜃 − 1) ≤ 0. (5.41)

5.5.5 Adsorption on the free surface of a liquidOn the free surface of a liquid, the interfacial tension is dependent on the concen-

tration of dissolved substances, and the change of the interfacial tension relative

to that of the solvent is caused by adsorption of the dissolved substance on the

boundary layer between the liquid and the vapour. Let us investigate the change

of the (Gibbs) free enthalpy. The free enthalpy g (J/mol) is the sum of the chem-

ical potentials of the components and the surface energy:

g = 𝜇1n1 + 𝜇2n2 + 𝛾F (5.42)

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Introduction to food colloids 217

or, as a total differential,

dg = 𝜇1dn1 + 𝜇2dn2 + d𝜇1n1 + d𝜇2n2 + 𝛾dF + d𝛾F (5.43)

where 𝜇1n1 is the chemical potential×number of moles of the solvent (J), 𝜇2n2

is the chemical potential×number of dissolved moles of the dissolved substance

(J) and 𝛾 (J/m2) is the interfacial tension of a free surface of area F (m2).

Since

dg = −sdT + vdp + d(𝜇1n1 + 𝜇2n2) (5.44)

is the isobaric (p= constant) reversible work, where s is the entropy (J/K), then if

T and p are constant, the isobaric reversible work which establishes a new surface

of area dF is equal to 𝛾 dF, and as a result,

dg = 𝜇1dn1 + 𝜇2dn2 + 𝛾dF. (5.45)

Considering Eqn (5.43), the following equation holds for part of the total dif-

ferential dg:

d𝜇1n1 + d𝜇2n2 + d𝛾F = 0 (5.46)

(the Gibbs–Duhem equation). This is because n1 and n2 do not depend on 𝜇1

and 𝜇2, respectively, and F does not depend on 𝛾. The Gibbs–Duhem equation

is valid also for the interior of the homogeneous phase (where molar quantities

are denoted by ‘∘’):d𝜇1n∘1 + d𝜇2n∘2 = 0. (5.47)

The chemical potential 𝜇1 of the solvent can be eliminated from Eqn (5.46):[

n2 − n1

(n∘2n∘1

)]d𝜇2 + F d𝛾 = 0. (5.48)

Note that the expression in the square brackets [ ] in Eqn (5.48) is equal to the

surplus of the dissolved substance on the surface of area F, that is,[n2 − n1(n∘2∕n∘1)

]

F≡ Γ2 (the Gibbs interfacial concentration) (5.49)

or, in another form,−dy

d𝜇2

= Γ2 = −( a2

RT

)(d𝛾

da2

)(5.50)

where a2 is the chemical activity of the dissolved substance.

Shishkowsky derived a relationship for amphipathic (capillary-active) sub-

stances:

Δ𝛾 = 𝛾∘ − 𝛾 = A ln(1 + Bc) (5.51)

where 𝛾∘ is the interfacial tension of the pure solvent, 𝛾 is the interfacial tension

of the solution, A and B are constants and c is the concentration of the dissolved

substance. After differentiation of Eqn (5.51) with respect to c,

−d𝛾

dc= Γ2 = A

RT

[ Bc1 + Bc

]. (5.52)

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218 Confectionery and chocolate engineering: principles and applications

This type of equation was studied for the first time by Langmuir, although in

that case it was related to kinetic topics, and it is called the Langmuir isotherm.

If c→0 (initial section of the isotherm), the slope of the isotherm is AB/RT. If

c→∞ (the region of high concentration),

Γ∞ = ART

. (5.53)

It should be mentioned that in the case of capillary-active substances, Γ∞ can-

not be reached for several reasons. In order to understand this discrepancy, we

must take into account the fact that instead of the concentration c, the chemical

activity a determines the behaviour of the system.

For further details on the various sorption isotherms, see Section 17.1.5.

The constant B can be regarded as a measure of capillarity, for which an empir-

ical rule was given by Traube in the case of homologous series:

Bn+1

Bn

≈ 3.4 (5.54)

which shows that capillarity becomes stronger as the molecular mass increases.

If an amphipathic substance of concentration c that is the nth member of a

homologous series produces a decrease Δ𝛾 in the interfacial tension, then the

(n+ 1)th member of this series produces the same decrease with a solution of

concentration c/3 [(1/3)×3.4)≈ 1]. It can be easily seen, from Eqn (5.52), that{ A

RT

[ Bc1 + Bc

]}

n+1≈{ A

RT

[ Bc1 + Bc

]}

n

Bn+1cn+1

1 + Bn+1cn+1

≈Bncn

1 + Bncn

Bn+1

Bn

≈ 3.4 ≈cn

cn+1

→ cn+1 ≈cn

3.

Water-soluble macromolecular substances are mostly of amphipathic struc-

ture; consequently, the more non-polar the surface of a solid or fluid is, the better

they can be adsorbed from aqueous solution.

It is characteristic of polymers that only some fractions of their monomers are

coupled to the surface; the other monomers remain in the solution in the form

of coils. If the amount of adsorbed polymer is increased, the length of these coils

becomes larger.

Langmuir showed that fatty acids, alcohols and esters with long carbon chains

form a monomolecular layer (or film) on the surface of water and that this film

strongly decreases the surface tension of the water. To decrease the surface ten-

sion from 73× 10−3 to 50× 10−3 N/m, the thickness of this monomolecular layer

must be about 20 (20×10−10 m). This thickness is practically equal to the length

of a paraffin chain (for n=16–18) if the chain is maximally stretched. This means

that the polar part of the chain is oriented towards the water and the non-polar

part is oriented towards the vapour phase.

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Introduction to food colloids 219

The decrease in the surface tension of water caused by a small amount of

oil may result in moderation of the bubbling of aqueous solutions or calming

of the surging of the sea around a ship – the latter phenomenon was first

described by Benjamin Franklin. Bubbling may be very disadvantageous when

one is warming or evaporating carbohydrate solutions, and a small amount

of oil or fat is widely used also in the confectionery industry as a bubbling

inhibitor.

5.6 Electrical properties of interfaces

5.6.1 The electric double layer and electrokinetic phenomenaIf two layers are in contact or move relative to each other, there exists an electric

potential difference between them. This potential difference appears as an electric

double layer at the interface. The reason for this potential difference may be that

the electric charges of the layers are not equal or that there is relative movement

between them. The latter induces electrokinetic phenomena.

The charges at interfaces may be derived from specially adsorbed ions,

adsorbed ionic surfactants, adsorbed polyelectrolytes or interfacial dissociation.

The size and sign (positive or negative) of the interfacial charge are dependent

on pH if the charge is derived from adsorbed polyelectrolytes or the surface is an

inorganic substance. It should be emphasized, however, that the electric charges

of protein molecules derive from dissociation of their acidic or basic groups and

not from the electric double layer. At the iep, the positive and negative charges

compensate each other. In the case of a surplus of positive charges (a cation

surplus in the solution), pH> iep; in the opposite case, pH< iep. Therefore, the

movement of charges is determined by their mobility, which depends on the net

charge difference.

The various electrokinetic phenomena are as follows:

Electrophoresis: Small suspended or colloidal particles move under the effect of an

electric field to a positive or negative electrode.

Electro-osmosis: The movement of a fluid through capillaries or pores in a solid

under the effect of an electric field.

Streaming potentials (the reverse of electro-osmosis): These are induced when a

fluid is forced through capillaries or pores in a solids.

Sedimentation potentials (or electrophoretic potentials) (the reverse of elec-

trophoresis): Settling particles are charged by the effect of their zeta potential,

and their movement creates a potential difference.

The phenomenon of electrophoresis is very important in colloids because their

stability is definitely dependent on their zeta potential. The effect of electrolytes

on the stability of colloids is exerted mainly via a change in the surface charge

of the colloidal particles at the iep; see, for example, the discussion of gelatin in

Section 11.13.5.

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220 Confectionery and chocolate engineering: principles and applications

5.6.2 Structure of the electric double layerThe presence of an electric double layer is demonstrated by the fact that there

is always a certain amount of liquid, adsorbed on the solid surface, that remains

fixed to the particles when particles move in a liquid or when a liquid moves

relative to particles. The various conditions that can occur in the electric double

layer are illustrated in Figure 5.6.

In concentrated electrolytes, the entire double layer moves together with the parti-

cles. In this case the double layer is similar to a planar capacitor (a Helmholtz-like

double layer), and the potential 𝜀 is a linear function of position x (Fig. 5.6(a)).

Moreover, there is no electrokinetic potential difference between the particles

and the solution because both parts of the electric double layer move together.

However, in dilute electrolytes, the double layer penetrates deeply into the inte-

rior of the solution (Fig. 5.6(b)), and its structure consists of two parts – a planar

capacitor and a diffuse part – which are separated by the splitting plane. The

electrode potential 𝜀 versus position x is an exponential function in this case,

if 𝜀0 <25 mV:

𝜀 = 𝜀0 exp(−kx) (5.55)

where k is a parameter related to the characteristic thickness of the ion atmo-

sphere and the strength of the ions and x is the distance from the solid surface. If

x= 0, then 𝜀= 𝜀0. If x= 1/k, then 𝜀= 𝜀0/e, that is, 1/k is the fictive or characteristic

thickness of the electric double layer (in Fig. 5.6(b), 1/k= d is the thickness of the

splitting plane); 1/k is the position where the density of electron charge has its

maximum. In equilibrium, the splitting plane separates the electrode potential 𝜀

into two parts:

𝜀 = 𝜓 + 𝜁 (5.56)

where 𝜓 is the potential difference in the layer adsorbed at the surface of the

solid particle (𝜓0 = 𝜀0 is the surface potential) and 𝜁 is the electrokinetic or zeta

potential derived from the relative movement of the solid and liquid phases.

Potential

(a)

Helmholtz-like

electric double layer

Diffuse

electric double layer

(b) (c)

d

ψ

ψ

ε ε εd d

xxx

Potential Potential

ζ

ζ

Figure 5.6 Electric double layer: (a) in concentrated electrolyte; (b) in dilute electrolyte; (c)

when one ion adsorbs strongly.

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Introduction to food colloids 221

If one of the adsorbing ions adsorbs strongly at the solid surface, then the case

shown in Figure 5.6(c) is also possible, that is, 𝜀<𝜓 .

The more dilute the solution, the larger the diffuse part of the electric double

layer. If the ion concentration is increased, the value of the zeta potential can

decrease to zero. If the dispersion forces are very strong, an increase in the ion

concentration can cause the zeta potential to decrease below zero, and then, from

a negative value (trans-charging in the case of ions of three or more valencies), it

starts to increase back to zero as in Figure 5.6(c).

The diffuse part of the electric double layer can be described by the

Debye–Hückel theory, if we suppose that the Helmholtz-like part of the electric

double layer is absent. The usual value of the zeta potential is less than 0.1 V;

its sign (positive or negative) is dependent on the qualitative nature of the

solid and liquid and also on the concentration of the liquid. Electrolytes change

the zeta potential in both size and sign in a complicated way. Amphipathic

substances may greatly influence the zeta potential if they are strongly adsorbed

by changing the structure of the electric double layer.

5.7 Theory of colloidal stability: the DLVO theory

The theory of the stability of sols, that is, the Derjaguin–Landau–Verwey–

Overbeek (DLVO) theory, gives the potential describing the interaction between

two globular particles as the sum of a repulsive potential VR and an attractive

potential VA. In simple cases, the form of these potentials is

VR =

(𝜀a𝜓2

0

2

)ln(1 + ekH) (5.57)

if 𝜓0 < 25 mV (small surface potential) and ka> 10 (medium to thick double

layer), where 𝜓0 is the permittivity of the medium, a is the radius of the par-

ticles, 𝜓0 is the surface potential, k is a parameter (see Eqn 5.55) and H is the

distance between the two globular particles, and

VA =A12a

12H(5.58)

if H≪ a, where A12 is the complex Hamaker constant.

The repulsive effect may be derived from the steric potential of adsorbed amphi-

pathic substances (macromolecules or surfactants) or from coils that protrude

into the interior of the solution to a distance dp. In this case the repulsive poten-

tial contains two additional parts:

• If H< 2dp, then the osmotic pressure is increased as a result of penetration of the

coils of the macromolecules into each other; this is the mixing part VR(M).

• If H< dp, the repulsive effect is strengthened as a result of compression of the

polymer layer; this is the volume restriction part VR(V).

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222 Confectionery and chocolate engineering: principles and applications

Consequently, in the general case, the entire (repulsive+ attractive) potential

(VR+A) is given by

VR = VR(E) + VR(M) + VR(V) (5.59)

and

VR+A = VR(E) + VR(M) + VR(V) − VA (5.60)

where VR(E) is the repulsive potential of the electric double layer (Fig. 5.7).

Figure 5.7 shows the attractive (VA), repulsive (VR) and resultant (VR+A)

potentials according to the DLVO theory.

The condition for flocculation is

Δg = Δh − TΔs > 0 (5.61)

where Δg is the change of free (Gibbs) enthalpy, Δh is the change of enthalpy, T

is the temperature and Δs is the change of entropy of the system.

During the approach of particles to each other, as the coils penetrate into each

other, the entropy decreases continuously (Δs<0) because the solution becomes

more concentrated. However, this decrease becomes more important when vol-

ume restriction starts, since volume restriction causes an additional decrease of

entropy: as a result, the free movement of the chains becomes more and more

limited. This means a decrease in the configurational entropy as well.

As the coils penetrate into each other, the segment–segment interaction

becomes stronger and the segment–solution interaction becomes weaker. The

balance of these interactions determines the sign of the enthalpy change Δh.

Potential

barrier (VM)

Primary

minimum (VM)

Att

ractio

n

Po

ten

tia

l V

Re

pu

lsio

n

Secondary

minimum

VRVR+A

HM

VA

H

Figure 5.7 Attractive (VA), repulsive (VR) and resultant (VR+A) potentials according to the

DLVO theory.

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Introduction to food colloids 223

Among the attractive forces, the dispersive (van der Waals) forces are the most

important; these are the sum of all the forces between the atoms of the particles.

Therefore the distance over which they are effective is the largest. Very near to

the particle (i.e. when H is very small), the attractive force exceeds the repulsion

(see the primary minimum Vm in Fig. 5.7). In contrast, the distance over which

the repulsive effects act is relatively small, and its terminal point is at the sec-

ondary minimum in Figure 5.7. The depth of the secondary minimum is about

kT (the energy of thermal movement).

Between the two minima, there is a potential barrier VM, at which the repulsive

effect is the strongest. If a particle can get over the potential barrier (i.e. the

particles get nearer to each other), the attractive effect starts to intensify and,

according to the DLVO theory, will result in the direct contact of particles. If

VM > 10kT, the system is stable, since only some particles have sufficient thermal

energy to get over the potential barrier. So no flocculation takes place. However,

if the effective distance of the repulsive effect is small, there is no potential barrier

(VM = 0), and every collision between particles will result in flocculation.

However, the situation is in fact more complicated than this because of sec-

ondary processes if VM <10kT. If an electrolyte is added to a sol stabilized by

an electric double layer in increasing amounts, flocculation (or coagulation as it

is called in the case of electrolytes) will start, the rate of which increases until

the potential barrier VM equals zero. In the case of a thick double layer (H>H′′)

(Fig. 5.8), V(H′′)+VM is not too large, and the particles can get back, for example,

because of the effect of thermal energy, into a state in which exclusively the

attractive forces affect them if the electrolyte is subsequently extracted from the

system. Consequently, the process

Sol → flocculation → (repeptization) → sol

is reversible.

Potential

barrier (VM)

VR+A

Primary

minimum (VM)

HMHʹ Hʺ

Figure 5.8 Potential conditions for flocculation according to

the DLVO theory.

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224 Confectionery and chocolate engineering: principles and applications

Figure 5.8 shows the potential conditions for flocculation according to the

DLVO theory. However, if H=H′ <H′′, that is, the particles approach too near

to each other V(H′)+VM is too large, and repeptization is impossible. If the elec-

trolyte concentration is very high, the polymer goes into the theta state and then

will be precipitated. But this process is essentially distinct from flocculation.

The approach of particles to each other may be caused by cooling, ultrafiltra-

tion and other means, not only by flocculation.

The most readily apparent merit of the DLVO theory is the explanation of the

destabilizing action of neutral salts. If the concentration is increased, the poten-

tial drops faster with distance. At very short distances, the attractive potential

is always dominant. At medium distances, where the maximum is found, the

reduction of the repulsive potential may be considerable. In this way, the com-

pression of the double layer may cause the energy barrier to disappear. The

mechanism gives an explanation of the fact that the addition of a salt which does

not adsorb nevertheless causes flocculation. Divalent ions are about 50 times as

efficient as monovalent ones in destabilizing a suspension. This is known as the

Schulze–Hardy rule.

However, emulsions generally contain two liquids and the electric double layer

extends into both phases. This fact makes the treatment of emulsions more com-

plicated. While the DLVO theory can be applied to describe the conditions beyond

the potential barrier, that is, where H>HM and VM =V(HM), the investigation of

repeptization relates to the region where H<HM.

5.8 Stability and changes of colloids and coarsedispersions

5.8.1 Stability of emulsionsFood emulsions cover an extremely wide area in practice. One finds semi-solid

varieties such as margarine, butter, many confectionery fillings and creams and

liquid varieties such as milk, sauces, dressings and various beverages. In addi-

tion, the concept of food emulsions also covers an array of products that con-

tain both solids (suspensions) and gases in addition to two liquid phases (e.g.

ice cream).

Dispersions are systems that contain microphases dispersed in a medium. Their

position is between homogeneous and heterogeneous systems (Fig. 5.9). In con-

trast to dissolved macromolecules, these microphases have a surface in a physical

sense, and therefore they have a surface energy as well; consequently, they are

thermodynamically unstable. The stability of food emulsions is a field which offers a

large spectrum of scientifically interesting phenomena that are only incompletely

understood.

The three most common dispersed phases in food colloids are liquid water

(or an aqueous solution), liquid oil (or partly crystalline fat) and gaseous air

(or carbon dioxide). It is natural, therefore, to think of many food colloids as

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Introduction to food colloids 225

Dispersion

(sol)

Heterogeneous

systems

Heap

(gel)

Peptization

Homogeneous

systems

Dispersion

+ stabilizationFlocculation

Solution,

evaporation

Solution,

evaporation

Crystallization,

coalescence

Crystallization,

coalescence

Condensation

+ stabilization

Dispergation

+ aggregation

Condensation

+ aggregation

Figure 5.9 Stability of colloids and coarse dispersions, and transformations between them.

being primarily emulsions or foams rather than colloidal dispersions. Neverthe-

less, despite the foremost importance of emulsions and foams, there are two good

reasons why colloidal dispersions should also be interesting.

There is a pragmatic reason for studying particulate dispersions. It concerns

the behaviour of casein micelles, the ubiquitous dispersed particles found in milk

and in most other dairy colloids. Interactions between casein micelles in different

states of dispersion determine the colloidal stability of milk, as well as the forma-

tion, structure and rheology of dairy products such as cheese and yogurt. Milk

derivatives also play an important role in various aspects of the confectionery

industry.

As will be seen later, a rigid dividing line cannot be drawn between emulsions

and suspensions.

As mentioned earlier, see Section 5.5.3, emulsions are unstable systems. This is

easily understood, since Eqns (5.29) and (5.33), as a consequence of the Boltz-

mann distribution, refer also to emulsions: p means solubility in this case. That

is, the smaller particles tend to become associated into larger particles; see the

discussion of Ostwald ripening in Section 5.9.5. Therefore, the technical aim of

achieving stable emulsions has, scientifically, to be limited to control of the kinet-

ics of the processes that lead to the breakdown of emulsions. The technologist

has two main tools available for this purpose: (1) the use of mechanical devices

to disperse the system and (2) the addition of stabilizing chemical additives or

natural compounds (low-molecular-weight emulsifiers and polymers) to keep it

dispersed.

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226 Confectionery and chocolate engineering: principles and applications

5.8.2 Two-phase emulsionsIn a two-phase emulsion, one liquid is dispersed in another in the form of large

droplets (≥0.3 μm). The emulsion is called an oil-in-water (O/W) emulsion if

the continuous phase is water; the opposite arrangement is called a water-in-oil

(W/O) emulsion. In some cases the dispersed droplets themselves are emulsions;

for example, the dispersed phase (L1) may now be the continuous phase for

droplets of the original continuous phase (L2). An emulsion of this kind is called

a multiple emulsion and is denoted by W/O/W or O/W/O depending on the nature

of the continuous phase. For further details, see John (1970, 1972), Bauckhage

(1973), Mersmann and Grossmann (1980), Koglin et al. (1981), Pörtner and

Werner (1989) and Pedrocchi and Widmer (1989).

5.8.3 Three-phase emulsionsMost of the emulsions encountered in food systems are more complicated than

the systems of two liquids described earlier. It is not feasible to describe all the

variations of solid, gel, liquid and gas dispersions found in food emulsions. We

shall mention only three examples here, each illustrating a property that cannot

be achieved in a two-phase emulsion. In the first, the presence of a third liquid

facilitates emulsification to form emulsions with small droplets; in the second,

small solid particles stabilize an emulsion; and in the third, an emulsifier forms

a liquid crystal, incorporating part of the aqueous and oil phases. For further

details, see Kriechbaumer and Marr (1983) and Friberg and El-Nokay (1983).

5.8.4 Two liquid phases plus a solid phaseThe mechanism of stabilization by solid particles is of importance in food

emulsions, considering the fact that the most common food emulsifiers, the

monoglycerides (MGs), show crystallization during their use, forming particles

at the interface.

It is a well-known fact (King and Mukerjee 1938, Schulman and Leja, 1954)

that the wetting conditions of the two liquids on the solid particles are the key

factor in the stabilization mechanism. The particles will stabilize the emulsion if

they are located at the interface between the two liquids (see Fig. 5.7), where

they serve as a mechanical barrier to prevent coalescence of the droplets. If they

are electrically charged in a continuous aqueous phase, the stabilization against

flocculation will also be enhanced by the electric double layer. However, the focus

in this section is on the mechanical action against coalescence.

The protection against coalescence is based on the wetting energy needed to

expel the particles from the interface into the dispersed droplets. This energy

depends on the contact angles between the liquids and the solid. It is obvious

from Figure 5.10 that a particle with a contact angle of 90∘ will give the most

stable emulsion.

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Introduction to food colloids 227

Oil phase

γ < 90°

Solid particle

γ = 90°

γ > 90°

Figure 5.10 Water droplet on an interface between a solid particle and an oil phase. 𝛾 = contact

angle. .Source: Larson and Friberg (1990, Fig. 18, p. 29). With kind permission from Elsevier

Ltd., the Netherlands

The energy that is necessary to force a sphere into the most strongly wetting

phase is

ΔE = 𝜋r2𝛾O∕W(1 − cos 𝜃)2 (5.62)

where ΔE is the energy required to expel a spherical particle of radius r from the

interface into a phase with which its contact angle is 𝜃 and 𝛾O/W is the interfacial

tension between the oil and water phases. A contact angle of 75∘ gives only half

of the energy compared with a sphere with a contact angle of 90∘, and the energy

is almost zero at 30∘:

cos 90∘ = 0 → (1 − cos 90∘)2 = 1.

cos 75∘ ≈ 0.26 → 0.742 ≈ 0.55.

cos 30∘ ≈ 0.87 → 0.132 ≈ 0.0169.

These values clearly demonstrate that the contact angle must be close to

90∘. An angle greater than 90∘ (cos 𝜃 < 0) will give an even higher energy in

Eqn (5.62). Unfortunately, a contact angle greater than 90∘ has been shown

to give less stability in practice; the solid particles are now squeezed into the

continuous phase during flocculation.

The wetting energies involved in Eqn (5.62) are sufficient to stabilize an

emulsion. Preliminary calculations showed the wetting energy to be signifi-

cantly greater than the van der Waals attraction potential at optimal distances

between the droplet surfaces. However, the wetting energy is strongly reduced

with increasing distance and serves, in a way, to prevent flocculation of the

droplets. Hence, this form of stabilization is most useful for systems with

high-internal-ratio emulsions. A detailed procedure to optimize the contact

angle was described by Friberg et al. (1990).

In this procedure, the solid particles must be small (≤0.1 μm) and are assumed

to be heavier than the aqueous phase, which in turn is assumed to be heavier

than the oil. Optimal results are obtained by bringing the oil, with all added

components, into contact with the aqueous phase, which also contains all its

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228 Confectionery and chocolate engineering: principles and applications

components, to obtain equilibrium before the experiment. The separated oil

phase is placed in a vessel, and a drop of the aqueous phase is placed on a

powder consisting of the solid particles. The shape of the drop decides the next

steps taken. Three different cases may emerge, as shown in Figure 5.10:

• A contact angle 𝜃 of 90∘ between the aqueous phase and the solid material

means that the solid particles are optimally useful for stabilizing the emulsion,

and no further action is needed.

• If 𝜃 <90∘, the interfacial free energy between the oil and the solid material is

too high. In this case, an oil-soluble surface-active agent must be added, which

should bind strongly to the solid surface.

• If 𝜃 > 90∘, a surfactant is added to the aqueous phase, and the same adjustments

as in the second case are made.

5.8.5 Emulsifying properties of food proteinsThe tests used for the evaluation of proteins as emulsifiers are more or less empir-

ical. The most popular is the measurement of the emulsifying capacity (EC), where

the maximum amount of fat emulsified by a protein dispersion just prior to the

inversion point is determined. The EC method was originally developed by Swift

et al. (1961), and it has been used widely, though modified in certain respects.

Comparisons between results from different laboratories are difficult to make

because this type of investigation is very much influenced by the conditions of

measurement.

The emulsifying activity index (EAI), as developed by Pearce and Kinsella (1978),

is a rough estimate of the particle size of the emulsion, based on the interfacial

area (calculated via turbidity) per unit of protein.

Dagorn-Scaviner et al. (1987) have compared the EC and EAI methods by

studying the emulsifying properties of some food proteins (bovine serum albu-

min (BSA) and casein, among others). The ranking order of the proteins, BSA

being the best, was the same, irrespective of the method used. However, a proper

characterization of the emulsifying power of a protein requires as full a descrip-

tion as possible of the protein-stabilized emulsion formed.

5.8.6 Emulsion droplet size data and the kineticsof emulsification

The size distribution of the droplets is a most important parameter for character-

izing any emulsion. Two emulsions may have the same average droplet diameter

yet exhibit quite dissimilar behaviour because of differences in the distribution of

diameters. Stability and resistance to creaming, rheology, chemical reactivity and

physiological efficiency are but a few of the phenomena influenced by both rel-

ative size and size distribution. Thus the evaluation of an emulsion for size can

involve measurements of its droplet number, length (diameter), area, volume

and mass (Tornberg et al., 1990).

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Introduction to food colloids 229

5.8.6.1 Distribution functions and oil droplet size distributionThe distribution functions most often used to characterize the size distribution

of emulsion droplets are the normal and log-normal distributions, the modified

log-normal probability distribution, the Espenscheid and Kerker distributions,

the Matijevic distribution (another modification of the logarithmic function),

the gamma and Weibull distributions and the Nukiyama–Tanasawa distribution

(which is bimodal and is used in the case of atomization of a liquid). For details,

see Bürkholz (1973), Kurzhals and Reuter (1973) and Orr (1983).

Emulsification is a dynamic process involving the disruption and recombi-

nation or coalescence (called recoalescence) of fat globules. Coalescence is the

joining of small droplets together into larger ones. Thus, the final droplet size

distribution will be governed by the detailed conditions of the balance between

disruption and coalescence during emulsification.

Inertial and viscous forces can deform and disrupt globules. Viscous forces gen-

erate velocity differences, and inertial forces give rise to pressure gradients within

the liquids. To achieve disruption of globules, they have to be deformed to such

an extent as to oppose the Laplace pressure within the globule:

Δp = 2𝛾

r(5.63)

where 𝛾 is the interfacial tension and r is the radius of the globule (see Eqn 5.18).

Therefore, pressure or velocity gradients of the order of 2𝛾/r2 (applied over a dis-

tance r) have to be formed. These high velocity and pressure gradients needed

are produced by intense agitation, but unfortunately most of the energy of this

agitation is dissipated as heat.

Some kind of average of the oil droplet size distribution is given by a droplet

size determination, but one needs to be aware of the type of average being calcu-

lated. The nth moment of the frequency distribution of the globule diameter can

be used as an auxiliary parameter:

Sn =∑

i

nidni . (5.64)

For example, S0 is the total number of droplets per unit volume. The number

average diameter d10 is given by S1/S0, and the volume/surface average diam-

eter d32 is equal to S3/S2, called the Sauter mean diameter. The latter average

diameter is related to the specific surface area A of the emulsion by the formula

A=6Φ/d32, where Φ is the volume fraction of the dispersed phase. According to

Eqn (5.64),

S0 =∑

ni = total number of droplets per unit volume.

S1 =∑

ndi and S1∕S0 = d10 = number average diameter.

S2 =∑

nid2i , S3 =

∑nid

3i and the Sauter mean diameter is d32 = S3∕S2.

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230 Confectionery and chocolate engineering: principles and applications

If it is assumed that the shape of the particles is spherical (and that d is the

diameter), then

V (volume) = d3𝜋

6, S(surface area) = d2𝜋, i.e.

SV

= 6d

.

If the volume concentration of the dispersed phase in the emulsion is Φ, where

0≤Φ≤ 1, then ( SV

)

phase= A = 6Φ

d32

. (5.65)

For further details, see Tornberg et al. (1990).

The moments of a distribution are the coefficients of the Taylor series of the

generating function of the distribution (Alexits and Fenyo, 1955; Gnedenko,

1988).

5.8.6.2 Kinetics of emulsificationUsing an intuitive approach, several researchers have proposed that the time

for d32 to reach its equilibrium value d32(∞) could be described by analogy to

reaction kinetics:

dZ∕dU = −aZb (5.66a)

where Z= d32(t)/d32(∞)− 1, U=Nt, N is the impeller speed (in revolutions per

second), t is the time and d32(t) is the Sauter mean diameter at the time t.

The terms a and b are analogous to a reaction rate constant and reaction order,

respectively. Equation (5.66a) can be written as

dZ∕dt = −cZb (5.66b)

where c= aN is a constant. An implicit assumption is that the entire droplet size

distribution evolves similarly. For b= 1, d32(t) decays exponentially. Hong and

Lee (1985) found that this was the case for stirred-tank systems undergoing

simultaneous breakage and coalescence (0.05<Φ<0.2). For details, see Treiber

and Kiefer (1976), Koglin et al. (1981), Heusch (1983), Armbruster et al. (1991)

and Leng and Calabrese (2003).

For studies of the kinetics of dispersion, see Zielinski et al. (1974), Becker et al.

(1981), Herndl and Mershmann (1982), Kneuele (1983), Ebert (1983), Volt and

Mersmann (1985), Zehner (1986), Latzen and Molerus (1987), Kraume and

Zehner (1988), Kipke (1992) and Gyenis (1992).

5.8.7 Bancroft’s rule for the type of emulsionBancroft’s rule tells us that the type of emulsion is dictated by the emulsifier and

that the emulsifier should be soluble in the continuous phase. This empirical

observation can be rationalized by considering the interfacial tension at the

oil–surfactant and water–surfactant interfaces. There are some exceptions to

Bancroft’s rule, but it is a very useful rule of thumb for most systems.

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Introduction to food colloids 231

If one translates Bancroft’s rule to the HLB language (see Section 5.8.8), it

means that:

For O/W emulsions, one should use emulsifying agents that are more soluble in

water than in oil (high-HLB surfactants).

For W/O emulsions, one should use emulsifying agents that are more soluble in

oil than in water (low-HLB surfactants).

The facts that lecithin (HLB≈ 4, i.e. a low value) is soluble in cocoa butter

and that it has a very strong viscosity-lowering effect are in accordance with

Bancroft’s rule, since cocoa butter is the continuous phase in chocolate.

5.8.8 HLB value and stabilization of emulsionsThe main factor in the stabilizing action of surfactants is their tendency to adsorb

at the interface instead of being dissolved in one of the liquid phases, that is, their

properties must be balanced between hydrophilic and lipophilic characteristics.

The methods for selecting a surfactant are of two principal kinds. In the first,

the surfactant per se is characterized by a value for the balance in question, andeach W/O combination will have its specific value for the optimal surfactant. The

second kind of method considers the combination of the surfactant with the oil

and the water, and the whole system is characterized by a number.

The best-known system of the first kind is based on the HLB number,

introduced by Griffin (1949). This number is based on the relative percentage

of hydrophilic to hydrophobic groups in the surfactant molecule. The origi-

nal method for determining the HLB number requires a long and laborious

experimental procedure (Griffin, 1954).

However, for certain types of non-ionic surfactant, namely, polyoxyethylene

derivatives of fatty alcohols R(CH2CH2O)xOH and polyhydric alcohol fatty acid

esters, the HLB number may be calculated using the following expression:

HLB = 20(

1 − SA

)(5.67)

where S is the saponification number of the ester and A is the acid number of

the acid. But for many fatty acid esters (e.g. lanolin and beeswax), it is difficultto determine S accurately. In this case, Griffin gave the following expression:

HLB = E + P5

(5.68)

where E is the weight percentage of the oxyethylene content and P is the weight

percentage of the polyhydric alcohol content. In surfactants where only ethy-

lene oxide is used as the hydrophilic portion, the HLB number is simply 5. For

a summary of the HLB number ranges required for various systems, see Atlas

Chemical Industries (1963).

Davies (1959) divided the structure of emulsifiers into component groups,

each of which can be assigned a number (positive or negative) that contributes to

the total HLB number. The HLB number can then be calculated using the relation

HLB = 7 + E(hydrophilic group number) − F(lipophilic group number) .

(5.69)

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232 Confectionery and chocolate engineering: principles and applications

HLB numbers are approximately additive; for example, a combination of sev-

eral surfactants will act as one surfactant that has the weighted average (by mass)

of the HLB numbers. If, for example, the optimal HLB value is 12, this can

be implemented by using a mixture of a solubilizer (HLB= 18, concentration

c1 = 0.4 m/m) and an emulsifier (HLB= 8, concentration c2 = 0.6 m/m):

HLB (mixture) = 0.4 × 18 + 0.6 × 8 = 12.

To produce emulsions of high stability, mixtures of surfactants are used that

consist of surfactants of low and high HLB value because the optimal HLB value

is dependent on the material properties of the phases to be emulsified. If a sur-

factant soluble in both water and oil is used, a thick adsorption layer can be

established. Complex emulsions can also be produced in this way; for example,

water droplets of size 1–2 μm can be emulsified in oil droplets of size 10–12 μm

which, in turn, are dispersed in water.

HLB numbers are usually assigned to emulsifying agents without taking into

consideration the properties of other components in the emulsion. Marszall and

Van Valkenburg (1982) argued that the HLB value is based on only the molecu-

lar structure of the emulsifier and does not take into consideration all the factors

that affect the performance of an emulsifier, such as the type of oil, the temper-

ature and the additives in the oil and water phases. With these facts in mind,

Marszall and Van Valkenburg (1982) argued for the term effective HLB value. This

is a performance value that takes the aforementioned factors into account.

Shinoda and Arai (1964) introduced the concept of the HLB temperature, or

phase inversion temperature (PIT), which is a characteristic property of an emul-

sion with a surfactant present. The PIT of an emulsion is the temperature at which

the hydrophilic and lipophilic properties of a non-ionic surfactant are balanced.

At higher temperatures, emulsions are of W/O type but change to an O/W type

at lower temperatures.

A correlation exists between the HLB number and the HLB temperature

(Shinoda and Sagitani, 1978), and one can determine the HLB number from

the HLB temperature of a surfactant using a calibration curve (Shinoda and

Friberg, 1986). The simplest method to determine the PIT of an emulsion is by

direct visual observation (Shinoda and Arai, 1964). A more sensitive method

is to follow the conductivity of the emulsion as a function of temperature.

Parkinson and Sherman (1977) suggested the use of the measured PIT value

as a rapid method for evaluating emulsion stability. The HLB number and

HLB temperature provide a tool for designing energy-efficient methods of

emulsification. For more detail, see Ludwig (1969) and Friberg et al. (1990).

5.8.9 Emulsifiers used in the confectionery industryLecithin (E 322). This is the most frequently used emulsifier and is a natural mix-

ture of phosphatidylcholine (PC), phosphatidylethanolamine and other phos-

pholipids. The standard lecithin (mainly of soybean origin) is a hydrophobic

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Introduction to food colloids 233

mixture dominated by the properties of phosphatidylethanolamine (effective

HLB about 4). It is typically used in margarines and spreads as a hydrophobic

emulsifier and in chocolates as a viscosity regulator; it is also used as a wetting

additive in powders.

PC-enhanced lecithin (E 322). The PC concentration is increased by selective extrac-

tion of the non-PC components of the lecithin. It is more hydrophilic than the

native mixture and is used in applications where more hydrophilic properties

are required. The product has less taste and a purer character than the original

material.

Hydrolysed lecithin (E 322). This is also more hydrophilic than standard lecithin. It

is dispersible in water and is used in applications where the continuous phase

is water, such as mayonnaise and dressings.

Distilled MGs (E 471). These are about 90% MGs, with a fatty acid composition

depending on the fat base, and are slightly on the lipophilic side (HLB about

5). They are used, for example, in the margarine industry as a lipophilic emul-

sifier, in the baking industry as an additive to retard the staling of bread and

in whipped toppings.

MGs/diglycerides (DGs) (E 471). These are typically 40% MGs and 60% DGs. They

are more lipophilic than distilled MGs (HLB less than 5) and are used as emul-

sion destabilizers in the ice cream industry.

Modified MGs (E 472). (Lactylated, acetylated, etc.) These are used in baked prod-

ucts, whipped toppings and frozen desserts and cakes.

Polyglycerol esters (E 475). These are hydrophobic emulsifiers (HLB typically less

than 4) and are used in the chocolate industry in combination with lecithin

as viscosity regulators. Polyglycerol polyricinoleate (PGPR) is a derivative

of ricinic (castor) oil. Lecithin has a radical decreasing effect on the viscosity

of chocolate mass; however, PGPR decreases the shear yield (also called the

yield stress, 𝜏0) of chocolate mass. The usual combination is 0.25–0.3 m/m%

lecithin+ ca. 0.1 m/m% PGPR (calculated relative to 100% chocolate).

Sorbitan esters (E 491). Sorbitan stearate (solid) and sorbitan oleate (liquid). These

are lipophilic emulsifiers (HLB about 4) and are used in emulsions in a wide

range of products.

Polysorbates (E 433). Polysorbate 80 (oleate, liquid) is a hydrophilic emulsifier

(HLB typically about 12–16) used in frozen desserts and dressings.

5.9 Emulsion instability

5.9.1 Mechanisms of destabilizationFour main mechanisms of emulsion destabilization can be identified:

1 Creaming, which is separation caused by the upward motion of emulsion

droplets that have a lower density than the surrounding medium.

2 Flocculation, which is the aggregation of droplets. Flocculation takes place

when the kinetic energy during collisions brings droplets over the repulsive

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234 Confectionery and chocolate engineering: principles and applications

force barrier and into a region where attractive forces operate and cause the

droplets to attach to each other.

3 Coalescence, which means that two droplets, when they collide, lose their iden-

tity and form a single larger one.

4 Ostwald ripening, which is caused by diffusional transport from small droplets

to larger ones. The reason for this process is that the chemical potential of the

liquid in the droplets decreases as the droplet radius increases. This is analo-

gous to the radius dependence of the vapour pressure above water droplets

and above water condensed in capillaries.

The concentration of droplets in an emulsion and the droplet size are key

parameters in determining the timescale of the instability process. Basically, coa-

lescence is dominant at high concentrations (above 10–50%), flocculation at low

concentrations and for small droplets (below 5% and 1 μm in size), and creaming

at low concentrations and for large droplets (below 10–50% and above 2–5 μm

in size). At intermediate concentrations and sizes, each instability mechanism

has to be considered in more detail to identify which one predominates. This

information is important because different instability mechanisms are influenced

differently by emulsion parameters such as concentration, particle size, type of

emulsifier and viscosity.

The first stages in the destabilization of an emulsion are flocculation and

sedimentation (or creaming), where two droplets adhere to each other after

they have collided. First, the number of droplets is reduced, and, second, the

enlarged mass of the droplets makes sedimentation faster. These two processes

are instrumental in destabilization and depend on each other. The quantitative

relationships are well established.

Flocculation and creaming are followed by coalescence, in which two adhering

droplets become one larger droplet. Ostwald ripening is a relatively long-lasting

process.

5.9.2 FlocculationThe induction of flocculation by polymers is a well-known process. A suspen-

sion that is stable over time may suddenly start sedimentation when a small

concentration of a polymer is added to the solution. In the case where the inter-

actions responsible for this process are confined to polymer–surface interactions,

the validity of the bridging theory of La Mer and Healy (1963) has been demon-

strated in extensive investigations by Fleer et al. (1972). The mechanism con-

sists of adsorption, on the uncovered surface of a second particle, of a polar

group of a polymer that is already attached to an initial particle. A polymer is

adsorbed at an interface so as to form trains (the molecules on the liquid surface

are joined up like the carriages of a train), loops (as if the carriages are jammed)

and tails (a string of carriages stands on its end). The results of Fleer et al. (1972)

show convincingly that flocculation will take place when the loops or tails reachthe uncovered surface of a particle on which the polymer groups are strongly

adsorbed.

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Introduction to food colloids 235

The stabilization and flocculation of a suspension by polymers are, however,

dependent not only on the interactions between polymer groups and the sur-

faces of the particles but also on polymer–polymer and polymer–solvent interactions.

When two particles approach each other, interpenetration of segments from dif-

ferent polymer molecules occurs, and compression also takes place if the distance

between the particles is sufficiently small. Thus, the approach of the particles

alters the free energy of the system, and the choice between flocculation and sta-

bilization is indicated by the sign of the change of the total (Gibbs) free enthalpy:

ΔGtot = ΔGpi −( H

12

)(ad

)(5.70)

where Gtot is the change of the total free enthalpy, Gpi is the change in free

enthalpy due to the interaction of polymers, H is the Hamaker constant, a is the

radius of a spherical particle, d is the distance between the surfaces of the parti-

cles and the last term is the van der Waals interaction. Repulsive forces due to

the electric double layer are neglected here. Since the distance is comparatively

large, the first term in Eqn (5.70) is dominant, and the following discussion is

limited to this term.

The change in free enthalpy is divided into an enthalpic and an entropic term:

ΔGpi = ΔH − TΔS. (5.71)

The enthalpic term H might be said to reflect the change of the molecular

interaction from a mainly polymer–solvent one to a more pronounced polymer–

polymer one on interpenetration. The entropic term TΔS describes the change

in the order of the system when solvent molecules are replaced by polymer seg-

ments in the interaction zone. Also, compression of the chains leads to a reduc-

tion in the magnitude of the entropic term. A decrease in temperature causes a

reduction in the size of the entropic term, and destabilization might occur.

A good solvent for the polymer will bring about stabilization, since the

interpenetration of the polymer chains will give rise to an increase in the free

enthalpy, and ΔGpi (and also ΔGtot) will be positive.

Changing the solvent by addition of a non-solvent may lead to the creation of

conditions where the polymer will not react to the presence of the solvent but

will instead behave as if in a vacuum. When these conditions are obtained, the

suspension will flocculate, but, by addition of a good solvent, the suspension can

be spontaneously redispersed.

5.9.2.1 Flocculation kineticsIf no distance-dependent forces act on the droplets, the number of collisions and

the flocculation depend on the diffusion of droplets only. This is called Brown-

ian flocculation. The flocculation rate is described by the number of the original

particles which disappear per unit time and volume, given by the Smoluchowski

equation:dndt

= −16𝜋Dan2 = −(8

3

) kTn2

𝜂(5.72)

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236 Confectionery and chocolate engineering: principles and applications

where dn/dt is the flocculation rate (s m3)−1, a is the droplet radius (m), D is

the diffusion coefficient for one droplet (m2/s), n is the number of particles per

unit volume (m−3), k= 1.38062×10−23 J/K is the Boltzmann constant, T is the

absolute temperature (K) and 𝜂 is the viscosity of the continuous medium (Pa s).

The second equation in Eqn (5.72) is obtained from the first one by using the

Einstein equation:

D = kTf

(5.73)

and Stokes’ law for friction in a fluid:

f = 6𝜋𝜂a → D = kT6𝜋𝜂a

(5.74)

where f (kg/s) is the friction coefficient for a droplet.

The rate of destabilization is easier to understand in terms of the half-life (the

time required for the number of droplets to be reduced to one half of its original

value):

t1∕2 = 3𝜂

8kTn. (5.75)

5.9.2.2 Stability from viscosity increaseAn increase in the viscosity of the continuous phase adds to the kinetic stability,

and this is a fact that is intuitively evident. However, the effect is smaller than

intuition might lead us to believe, and, without a concurrent energy barrier, vis-

cosity as such has only a small effect on stabilization.

Creaming and flocculation induce emulsion instability at a rate that depends

on the droplet size. When the diameter of the particles is reduced by a factor

of 2, the particle concentration (number of droplets per unit volume) increases

by a factor of 23. Therefore, for a fixed volume concentration, the flocculation

rate increases rapidly with decreasing particle size. The Smoluchowski equation

assumes that hydrodynamic interactions are unimportant and that the system

is dilute (concentrations below 1%). However, in practice, hydrodynamic inter-

actions are of importance in collision events. Furthermore, in technologically

important systems, the concentration is often considerably larger than 1%,

which means that the flocculation rate is lower than that predicted by the

Smoluchowski formula. The reason is that particles shield each other (compare

the discussion of hindered settling in Section 5.9.3.1).

Concerning shear-induced flocculation, see Zeichner and Schowalter (1979), and

for gravity-induced flocculation, see Reddy et al. (1981) and Bergenstahl and Claes-

son (1990).

5.9.3 Sedimentation (creaming)A droplet moves in a gravitational field. Its movement is slowed by the frictional

force from the surrounding medium. For small droplets, Brownian movement

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Introduction to food colloids 237

(diffusion) is also important. The first two forces and Brownian movement (grav-

itation− friction±diffusion)) determine the sedimentation rate and sedimentation

equilibrium.

5.9.3.1 Sedimentation rateThe settling rate v, given by Stokes’ law (see Eqn 5.74), is the predominant cause

of emulsion instability when the size of the droplets is above around 2–5 μm:

Gravitation

(4a3𝜋

3

)gΔ𝜌 = vf = v6𝜋𝜂a(friction) (5.76)

v =2a2gΔ𝜌

9𝜂(5.77a)

where a is the particle radius (m), Δ𝜌 is the density difference (kg/m3), g= 9.81

(m/s2) is the gravitational acceleration and 𝜂 is the viscosity of the continuous

phase (Pa s).

Equation (5.76) means that, initially, gravitation accelerates the particle and

then its velocity reaches v (see Eqn 5.77a). From this moment, gravitation and

friction compensate each other, and the particle maintains its velocity according

to Newton’s first law since the effect of diffusion can be neglected.

Greenwald, cited by Gábor (1987, p. 134), gave a relation for the settling rate

w in a bulk liquid, the particle size distribution of which is characterized by a

general value ri:

w =∑[

2(ri)2gΔ𝜌9𝜂

]∑[4(ri)3𝜋

3

] ( 1V

)=∑[

8𝜋(ri)2gΔ𝜌27𝜂V

](5.77b)

where V is the volume of liquid. Evidently, Eqn (5.77b) is a variant of Stokes’

law (Eqn 5.76).

Stokes’ law holds under dilute conditions Φ<2%. In concentrated systems, a

smaller settling rate is observed experimentally than that calculated from Stokes’

law. Stokes’ law can be applied to the settling of solid particles in suspensions

as well.

For more concentrated dispersions, Buscall et al. (1982) suggested

v(effective) = v(Stokes) ×(

1 − Φp

)5p

(5.78)

where Φ is the volume fraction of the dispersed phase and p is an empirical

variable, approximately equal to the final volume of the dispersed phase in the

sediment or cream layer. The reason for the decrease in velocity is that the emul-

sion droplets get in each other’s way and hinder each other’s movement. This

phenomenon, which is common in practice, is called hindered settling. This is, for

instance, the reason why cream is a stable emulsion, whereas unhomogenized

milk (which is a less concentrated emulsion) is unstable towards creaming.

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238 Confectionery and chocolate engineering: principles and applications

5.9.3.2 Sedimentation equilibriumSedimentation equilibrium can be illustrated by the number of droplets per unit

volume at two levels in a container after equilibrium has been reached.

The Boltzmann distribution gives directly the ratio

ln

(n1

n2

)= −

gΔhΔ𝜌V

kT(5.79)

where nl and n2 are the numbers of droplets per unit volume at two levels,

g= 9.81 m/s2 is the gravitational acceleration, Δh (m) is the difference in height

between the two levels, Δ𝜌 (kg/m3) is the density difference between the dis-

persed liquid and the continuous liquid, V (m3) is the volume of one droplet, k

(J/K) is the Boltzmann constant and T (K) is the temperature. The numerator

of the right-hand side is the difference of potential energy in the gravitational

field, which is related to the distribution as a function of height. This is really the

barometric formula (Eqn 5.29).

Example 5.4Equation (5.77a) is the basis of Andreasen’s pipette method of particle size anal-

ysis by sedimentation; see Andreasen (1935), Koglin (1972) and Thomas (2006).

With the substitution a= d/2, where d is the particle size, the equation

d2 = 18𝜂v

gΔ𝜌(5.77c)

provides the appropriate relation; the measured parameters are h and t (the

height and the time of sedimentation, respectively), and v= h/t.

Cocoa powder is settling in water at 20 ∘C; its particle size is 50 μm. What is

the distance by which it sediments after a settling time of 10 s? (The viscosity of

water is 0.001 Pa s.)

The density of cocoa powder is 1232 (kg/m3), that is, Δ𝜌≈ 232 (kg/m3). From

Eqn (5.77c),

25 × 10−10 = 18 × 10−3 × v9.81 × 232

v = 315.88μm∕s → h ≈ 3.158mm(per10s).

If h and t are known, d can be calculated.

5.9.3.3 Structure of aggregates, gels and sedimentsThe stability behaviour of concentrated dispersions is much less well understood

than that of dilute systems. The complex interplay of Brownian motion, colloidal

forces and hydrodynamic interactions means that the theory of aggregation is

far more complicated than for dilute sols, where a description in terms of pair

interactions is generally adequate.

Aggregates produced by the irreversible coagulation of colloidal particles are

not closely packed. They have an open disordered structure and are examples of

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Introduction to food colloids 239

fractals. It is the sticking together of the particles (and clusters of particles) under

the influence of Brownian motion which bestows upon the structure its fractal

character, and, indeed, the irregular trajectory of a Brownian particle is itself a

fractal object. See Appendix 4 for a discussion of fractals.

While the sticking together of individual particles one at a time is a reasonable

model for deposition or sedimentation in dilute systems, the aggregates formed in

the later stages of Brownian coagulation in the absence of an external field occur

by cluster–cluster aggregation and not by particle–cluster aggregation. Very large

simulated structures formed by diffusion-limited cluster–cluster aggregation in

two or three dimensions are found to be self-similar, that is, at length scales

appreciably larger than the particle radius a, the structure is scale invariant.

The fractal dimension D is defined by

Ra∼ N1∕D

p (Np → ∞) (5.80)

where R is the radius of gyration of an aggregate composed of Np particles. In

three dimensions (d= 3), the fractal dimension for diffusion-limited coagulation

is 1.78±0.01.

Denser aggregates are formed if particles are able to alter their relative posi-

tions immediately after collision. This is expressed by a sticking probability PS,

which is less than unity. In the limit PS → 0, we reach the situation known as

reaction-limited cluster–cluster aggregation. This also leads to self-similar structures,

but with a larger fractal dimension D≈ 2.05 in the limit of very large clusters

(Np →∞) at very low total particle volume fractions (Φ→0).

At finite particle volume fractions, the end result of the coagulation process is

a sediment (or cream) or a particle gel. That is, the large aggregates either settle

under gravity to form a low-density porous sediment or join together to fill all

the available space with a particle gel network. The size of the aggregates making

up the network depends strongly on the particle concentration. The number Nc

of particles in a close-packed aggregate of radius R is given by

Nc =(R

a

)3

, (5.81)

and so, from Eqn (5.80), we have

Φf =Np

Nc

=(R

a

)1∕(D−3). (5.82)

The condition for gelation is that the average volume fraction Φf of the fractal

aggregate is equal to the overall volume fraction Φ:

Φf = Φ. (5.83)

The critical aggregate radius Rc at which a gel is formed is therefore

Rc = aΦ(D−3). (5.84)

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240 Confectionery and chocolate engineering: principles and applications

The strong dependence of Rc on the volume fraction Φ leads to a strong depen-

dence on Φ of the properties of the particle gel, both mechanical (e.g. rigidity)

and structural (e.g. porosity).

In a low-density sediment or particle gel formed from irreversibly aggregated

spherical colloidal particles, three different spatial scales of structure may be iden-

tified (Dickinson, 1992):

• Short-range order from packing and excluded-volume effects

• Medium-range disorder associated with the fractal characteristics of the

diffusion-controlled aggregation process

• Long-range uniformity in the case of a material that is macroscopically homo-

geneous

Food particle gels may be produced by the aggregation of casein micelles (in

cheese and yogurt) or fat crystals (in margarine). The fractal dimensions of

casein particle gels produced by renneting or acidification tend to lie in the range

2.2<D< 2.4 depending on the experimental conditions. However, the network

structure of casein particle gels is more complicated than that of idealized models

because of the polydispersity and heterogeneity of the aggregating particles and

also because of macromolecular rearrangements within the network, which

continue to occur after gelation. The relationship between the structure and the

rheology of casein particle gels depends in a complicated way on the conditions

of aggregation of the colloidal particles.

It is clear that the concepts of fractal geometry are a useful tool for unravelling

this important aspect of the processing of food colloids.

5.9.3.4 Polymer gels and particle gelsNevertheless, even though casein gels are composed of polymers, their properties

are quite different from those of true polymer gels such as gelatin or alginate. In

contrast to a polymer gel, whose elasticity is mainly of entropic origin, the rheol-

ogy of a particle gel is related to energetic (enthalpic) aspects such as the bending

energies of network connections and the breaking energies of linkages (Dickin-

son, 1992).

The three main physical factors affecting the rheology of a particle gel are:

• The volume fraction of particles

• The deformability of the particles and their linkages

• The fractal dimension of the network

5.9.3.5 Interparticle interactionsThe interparticle interactions are determined mainly by the properties of the sur-

faces of the droplets in the emulsion, which in food emulsions are coated with

various surface-active molecules, in most cases of biological origin:

Surface forces. The surface forces are all of the static forces that act between parti-

cles and depend on the separation of the particles. These forces are influenced

by the properties of both the particles and the separating medium. The term

surface forces is used because the chemical composition of the outermost layer of

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Introduction to food colloids 241

the particles influences the range and magnitude of the forces much more than

does the bulk composition. The types of forces most commonly observed are

van der Waals, electrostatic double-layer, hydration, hydrophobic and steric

forces. Only van der Waals and double-layer forces are taken into account in

the DLVO theory of colloidal stability.

Electrostatic double-layer forces. Typical food emulsions coated with proteins or

hydrocolloids have small surface charge densities, corresponding to low zeta

potentials, normally between −1 and −20 mV. In long-shelf-life emulsions,

such as mayonnaise, the electrolyte concentration is also rather high, which

reduces the range of the electrostatic repulsion. Consequently, in many

food emulsions, double-layer forces are not very important, and the DLVO

theory can rarely explain emulsion stability or solve stability problems in food

systems.

Van der Waals forces. These are repulsive when the dielectric function of the

medium is between those of two interacting particles; for example, repulsive

van der Waals forces act between an air bubble and an oil droplet in aqueous

solutions according to Hough and Whire (1980). The magnitude and sign

of the van der Waals force are determined by the dielectric properties of

the particles and of the surrounding medium, and it is in principle easy to

calculate the non-retarded van der Waals force from dielectric data; see Hough

and Whire (1980). However, in practice it is often the case that the dielectric

properties of the media are unknown.

5.9.4 CoalescenceHow rapidly two droplets coalesce depends on the stability of the thin film sep-

arating them. When the dispersed phase is a liquid, coalescence follows rapidly

once the separating film ruptures.

Numerous studies have dealt with the coalescence of a single droplet with a

planar interface created by a settled, coalesced layer. These studies involve mea-

surement of the time that elapses from the arrival of a droplet at the interface

to coalescence. Many factors influence the waiting time, or film drainage time,

including the age of the interface. The times can be correlated using film drainage

theory. The simplest model for film drainage assumes that the conditions affect-

ing the drainage rate are time invariant. By analogy to squeezing flow between

parallel discs (the lubrication approximation), the rate at which the film thins is

given bydhdt

= −k1h3 (5.85)

where h (m) is the thickness of the film, k1 (s m2)−1 is a constant and t is the

time (s). The interface is assumed to be mobile but motionless. The initial sepa-

ration distance is h0, and h is the separation distance after time t. The constant k1

accounts for all the factors that determine the drainage time. After integration of

Eqn (5.85),1h2

− 1

h20

= k1t. (5.86)

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242 Confectionery and chocolate engineering: principles and applications

Estimation of the initial film thickness h0 is not critical, since the initial thin-

ning is fast. After a short time, h−2 ≫h0−2, allowing evaluation of the drainage

rate constant k1 from precise measurements of film thickness versus time. Esti-

mates of the film thickness at rupture from 25 to 500 Å have been reported.

Studies involving mass transfer from droplets show that in the presence of mass

transfer, coalescence times are much shorter.

In the case of a collision between two droplets with equal diameters d, the

leading edges of the two deformable droplets become flattened on collision.

This deformation creates a parallel, disc-like geometry. Therefore, the dynamics

of film drainage can be represented as a squeezing flow between two discs of

radius R (m), separated by distance h (m), that approach each other owing

to a force F (N). The excess pressure in the film must be of the order of the

Young–Laplace pressure. These suppositions lead to the following drainage rate

(compare Eqn 5.85):dhdt

= −32𝜋𝜎2h3

3𝜂d2F(5.87)

where 𝜂 is the viscosity (Pa s) of the continuous phase and 𝜎 is the interfacial

tension (N/m).

Equation (5.87) shows that the film drainage rate is inversely proportional to

the approach force, again demonstrating that coalescence is promoted by gentle

collisions. Integration of Eqn (5.87) with the initial condition h= h0 at t=0 and

the final condition h=hc at t= 𝜏 leads to

𝜏 =(

3𝜂d2F

64𝜋𝜎2

)(1

h2c

− 1

h20

)(5.88)

where 𝜏 is the time (s) required for film rupture and hc (m) is the critical thickness

required for film rupture. The initial distance h0 is usually much greater than hc,

so that1

h2c

− 1

h20

≈ 1

h2c

. (5.89)

Coalescence occurs only if the contact time tc is greater than 𝜏. For further

detail, see Leng and Calabrese (2003).

5.9.5 Ostwald ripening in emulsionsOstwald ripening is caused by diffusional transport from small droplets to larger

ones. The reason for this process is that the chemical potential of the liquid

in a droplet decreases as the droplet radius increases. This is analogous to the

radius dependence of the vapour pressure above water droplets and above water

condensed in capillaries (see Eqn 5.29). A similar observation can be made in

connection with the solubility of crystals: particles that are smaller than a critical

particle radius will disappear owing to their higher solubility, and larger particles

will grow owing to their lower solubility. The Ostwald–Thomson equation gives

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Introduction to food colloids 243

the solubility of crystals of different sizes (Gábor, 1987, p. 95):

RT ln

(Lr

L∞

)=

2𝛾SLM

r(dS − dL)(5.90)

where R is the universal gas constant (8.31434 J/mol K), T is the temperature

(K), Lr is the solubility of a crystal of radius r m, L∞ is the solubility of a crystal

of infinite radius (i.e. that of a planar surface), 𝛾SL is the solid–liquid interfacial

tension (N/m), M is the molar mass of the crystalline substance (kg/kmol), dS

is the density of the crystalline substance (kg/m3) and dL is the density of the

solution (kg/m3). The Ostwald–Thomson equation can be derived directly from

the Boltzmann distribution, which is valid for equilibrium (see also Eqn 5.79 for

sedimentation):

ln

(N1

N2

)= − U

kT(5.91)

where N1 and N2 are the numbers of particles per unit volume at positions 1 and

2, respectively, and U is the potential-energy difference between these positions.

A model for Ostwald ripening in emulsions has been developed by Yarran-

ton and Masliyah (1997); see also Matz (1984), Pawlowski et al. (1986) and

Sections 10.6.1 and 16.4.

5.10 Phase inversion

The conversion of an O/W emulsion into a W/O emulsion or vice versa is called

emulsion phase inversion (or simply inversion). In food systems, the process of

emulsion phase inversion does not usually occur spontaneously: large amounts

of mechanical energy are frequently required. This is because inversion is not a

single physical process like creaming, coalescence or flocculation, but is a com-

posite phenomenon, possibly involving all three of these primary processes, as

well as involving one or more complex intermediate colloidal states (foams, mul-

tiple emulsions, bicontinuous structures, etc.).

The most important parameter in the description of emulsion phase inversion

is the volume fraction Φ of the dispersed phase. Experimentally, as Φ increases at

constant emulsifier concentration, there is a systematic increase in the viscosity

of the emulsion until, at a certain critical volume fraction Φc, there is a sudden

drop in viscosity corresponding to a sudden change in volume fraction from a

high value Φc to a low value 1−Φc at the inversion point. Another easily mea-

surable quantity showing a sharp change at the inversion point is the electrical

conductivity: high for O/W systems but low for W/O systems. Assuming that

oil or water droplets in emulsions can be regarded as non-deformable spheres,

Ostwald suggested that Φc should be taken as 0.74, corresponding to the max-

imum ordered packing fraction for identical hard spheres. Both emulsion types

are possible for 1−Φc ≤Φc ≤Φ, but only one type exists outside this range. In

practice, some emulsions do invert near Φ≈ 0.74, but many others do not. This

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244 Confectionery and chocolate engineering: principles and applications

is due, in part, to the polydispersity and deformability of real emulsion droplets.

In addition, Φc depends substantially on the chemical nature of the emulsifier,

a factor ignored completely in the geometrical approach of Ostwald. Irrespective

of O/W ratio, an emulsifier with a low HLB number will be unlikely to stabilize

an O/W emulsion, and one with a high HLB number will not readily stabilize a

W/O emulsion.

If filling a large container with small equal-sized spheres, experiment shows

that dropping spheres in randomly will achieved a density of around 65%. A

higher density can be achieved by carefully arranging the spheres in cubic close

or hexagonal close packing just the way you see oranges stacked in a shop. Each

of these arrangements has an average density of

𝜋∕(3√

2) = 0.740480489 … .

Kepler’s conjecture says that this is the best that can be done – no other arrange-

ment of spheres has a higher average density. During four centuries, the Kepler

conjecture was one of the unsolved problems of mathematics until Hales (2005)

published a complete proof of it finally. Ostwald’s geometric approach is likely

based on this well-known conjecture (presently proved theorem) of Kepler.

The universal features of emulsion phase inversion in a system consisting of

oil+water+ emulsifier are neatly described by a mathematical approach called

catastrophe theory. The four reasons why emulsion phase inversion may be

regarded mathematically as a catastrophic event are as follows:

1 Emulsion morphologies are bimodal; that is for a large range of volume frac-

tions, they can exist indefinitely in one of two stable states (O/W or W/O),

but not as something in between. (Note, in this respect, that these latter states

are thermodynamically unstable; no minima of the Gibbs free enthalpy g cor-

respond to them.)

2 In accordance with the abrupt change in morphology, inversion involves a

sudden jump in physical properties such as viscosity and electrical conductivity.

3 The system exhibits hysteresis, that is, the morphology depends on the exper-

imental path or the previous history of the emulsion.

4 Two emulsions prepared only slightly differently from the same amounts of

oil+water+ emulsifier may show divergent behaviour.

In the mathematical theory of phase inversion (Dickinson, 1981, 1992,

pp. 100–115), the Gibbs free enthalpy g is expressed as a fourth-degree poly-

nomial of a variable s, and the three roots of the equation dg/ds=0, where the

derivative dg/ds is a third-degree polynomial, provide the characteristic quan-

tities of the states O/W and W/O and the transition. Such a form of the Gibbs

free enthalpy as a function of fourth order is, however, a pure mathematical

construct with no underlying physical justification apart from its success in

describing the observed phenomenon (Dickinson, 1992).

See Section 2.1.4 for details of a phase inversion experiment by Mohos (1982).

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Introduction to food colloids 245

5.11 Foams

5.11.1 Transient and metastable (permanent) foamsA foam is a coarse dispersion of gas bubbles in a liquid (or, sometimes, solid)

continuous phase (usually water). It is a colloidal state in the sense that the thin

films separating adjacent gas cells in a foam are typically of colloidal dimensions.

Two easily recognizable structures in foam systems can be described. A

kugelschaum, or sphere foam, is produced in freshly prepared systems and consists

of small, roughly spherical bubbles separated by thick films of viscous liquid.

The foam may be considered as a temporary dilute dispersion of bubbles in the

liquid. But on ageing the structure gradually changes, and the bubbles transform

into polyhedral gas cells with thin, flat walls.

A few terms are useful for distinguishing qualitatively between different kinds

of liquid foams. In structural terms, a bubbly foam (e.g. ice cream), in which the

amount of gas incorporated is low enough for the bubbles to retain their roughly

spherical shape, is substantially different from a polyhedral foam (e.g. beer foam),

in which the gas-to-liquid ratio is so large that the bubbles are pressed against

one another in a honeycomb-type structure. In kinetic terms, it is convenient to

distinguish between an unstable transient foam (e.g. champagne bubbles), whose

lifetime is measured in seconds or minutes, and a metastable permanent foam (e.g.

meringue), whose lifetime is measured in days. In the confectionery industry, it

is an essential requirement to produce permanent foams.

Pure water does not foam. Gas bubbles introduced beneath the liquid surface

burst as fast as the liquid can drain away from them. The stability of a transient

foam may be estimated by noting the persistence time of the bubbles.

In the context of foods, the most important gas used to make bubbles, apart

from air, is carbon dioxide. This gas has the advantage of being non-toxic and

natural, being produced in situ during breadmaking, biscuit/cake production (by

yeast or baking powder) and beer fermentation (by yeast). Nitrogen gas, how-

ever, gives a more stable head than carbon dioxide because it diffuses more

slowly from small bubbles to large ones owing to its lower solubility in water

(see Example 5.5).

Permanent food foams are stabilized by macromolecules or by particles. As

the gas dissolves into the aqueous phase from a bubble, the surface area of the

bubble decreases, and since there is negligible desorption of adsorbed macro-

molecules or particles, there is a decrease in surface tension, which stabilizes the

Laplace pressure difference across the film, and so the bubble shrinks no fur-

ther. The adsorbed macromolecules most commonly used to stabilize food foams

are egg-white proteins and milk proteins. Many dairy colloids, such as whipped

cream and ice cream, are emulsions as well as foams; they are primarily stabilized

not by adsorbed protein films but by a matrix of partially aggregated fat globules

at the air–water interface. The major food ingredients apart from fat that have a

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246 Confectionery and chocolate engineering: principles and applications

significant effect on the structure and stability of food foams are starch and egg

yolk (in baked products) and sugar (in confectionery).

Foams and emulsions have much in common in terms of their colloidal stabil-

ity, but there are several important differences from the physical point of view.

Gas bubbles are about 103 times as large as emulsion droplets, mainly because

gases are much more soluble in water than oil is in water or water is in oil. The

surface tension of a gas bubble is several times the interfacial tension of an emul-

sion droplet. A bubbly foam has a strong tendency to cream because, in addition

to the large bubble size, the density difference between the phases is more than

10 times than in an emulsion. In addition, gas bubbles are about 105 times as

compressible as emulsion droplets, and they are more easily deformed because

of their large size.

The combination of fast creaming and the deformability of bubbles rapidly

converts a bubbly foam into a polyhedral foam, unless the aqueous phase is

a high-viscosity liquid or a gel-like solid. In addition, liquid foams are much

more susceptible than emulsions to disturbing influences, for example, evap-

oration, dust, draughts, temperature gradients, vibration and the addition of

foam-breaking chemicals. This is mainly because of the much larger dimensions

of the liquid films in foams than of those in emulsions. On top of it all, the dis-

proportionation of bubbles in foams is much faster than the Ostwald ripening of

emulsion droplets. The overall effect of all these physical factors is that small bub-

bles are hard to make and tend to disappear rapidly, and a foam with large bubbles

is susceptible to fast drainage and rupture. Stability is best achieved with insoluble

adsorbed layers of coagulated protein (e.g. egg white in meringue) or immobile

particles (e.g. fat globules in whipped cream) or by converting the liquid foam

into a solid foam (as in the baking of a cake).

Conversion of a bubbly foam into a creamed layer happens in a matter of

minutes if the liquid has a viscosity of the order of that of water. Creaming may

be prevented by the addition of a hydrocolloid that gives a yield stress in excess

of ca. 10 Pa. This stress is so low as not to be perceptible during normal handling.

This means that bubbles can be kept in suspension under quiescent conditions by

a weak gel network in a liquid medium that behaves like a low-viscosity aqueous

solution under normal conditions of pouring, mixing and drinking.

5.11.2 Expansion ratio and dispersityThe expansion ratio n is expressed by the equation

n =VF

VL

=VG + VL

VL

= 1 +VG

VL

(5.92)

where VF is the volume of the foam, VL is the volume of the liquid content of

the foam and VG is the volume of the gas content of the foam. The foam density

𝜌F can also be used to characterize the expansion ratio of a foam:

𝜌F =(mG + mL)

VF

=𝜌GVG + 𝜌LVL

VF

(5.93a)

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Introduction to food colloids 247

where mG is the mass of gas in the foam, mL is the mass of liquid in the foam

and 𝜌L is the density of liquid in the foam. Since the foams of interest are usually

aqueous solutions, 𝜌G/𝜌L = 𝜌AIR/𝜌WATER ≈ 1/1000, and therefore Eqn (5.93a) can

be simplified to

𝜌F =𝜌GVG + 𝜌LVL

VF

≈𝜌LVL

VF

=𝜌L

n→ n ≈

𝜌L

𝜌F

. (5.93b)

In confectionery practice, the values of 𝜌F are in the range 0.25–0.8 and

those of 𝜌L are in the range 1.1–1.2 (aqueous solutions of carbohydrates);

consequently, from Eqn (5.93a), the values of n vary over a range of about

1.5–5.

The dispersity of gas emulsions and polyhedral foams is a very important param-

eter, which determines many of their properties and the processes occurring in

them (diffusion transfer, drainage, etc.) and therefore their technological char-

acteristics and areas of application. The procedure usually followed in order to

obtain detailed information about the bubble size distribution involves group-

ing bubbles into fractions by size and counting the number of bubbles Ni and

determining the radius of the bubbles Ri in each fraction. Thus, it is possible to

evaluate:

• The bubble radius RV, averaged by volume:

R3V =

( 34𝜋

)v =

∑R3

i Ni∑

Ni

(5.94)

where v is the average bubble volume

• The bubble radius RA, averaged by area:

R2A = A

4𝜋=

∑R2

i∑Ni

(5.95)

where A is the average surface area

• The bubble radius RL, averaged by length:

RL =

∑RiNi

∑Ni

. (5.96)

The results of dispersion analysis make it possible to calculate also the specific

surface area:

𝜀G =3∑

R2i Ni

∑R3

i Ni

(5.97)

and the average radius by volume and surface area:

RAV =

∑R3

i Ni∑

R2i Ni

. (5.98)

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248 Confectionery and chocolate engineering: principles and applications

The distribution function is represented graphically both as integral and as dif-

ferential distribution curves. All of the universal distribution functions (gamma,

Gaussian, Maxwell, Pearson, Boltzmann, binomial, Poisson, etc.) are used for

the evaluation of the size distribution of foams. For details, see Exerowa and

Kruglyakov (1998, pp. 25–30).

5.11.3 Disproportionation5.11.3.1 The Plateau borderThe diffusion of gas from small bubbles into large bubbles is referred to as dispro-

portionation. In the absence of a stabilizing film of polymer molecules or particles,

disproportionation occurs remarkably quickly. Overall, it is probably the most

important type of instability in foams.

The driving force for disproportionation is the Laplace pressure difference of a

curved bubble surface, which results in a higher pressure in a small bubble than

in a large one [see Fig. 5.11, which depicts a Plateau border (Section 5.11.5)]:

Δp = 𝛾

(1r1

+ 1r2

)(5.99)

where 𝛾 is the surface tension and r1 and r2 are the radii of the two bubbles of

different size.

As the solubility of gases increases with pressure (Henry’s law), more gas dis-

solves near the small bubble than near the large one, and so the latter grows at

the expense of the former. Assuming that gas transport takes place by diffusion

(obeying Fick’s law) through the continuous phase (Dickinson, 1992, p. 126),

dVdt

= Adrdt

∼ −A(P1 − P2) = −A𝛾(1

r− 1

R

)∼ −A𝛾

r,

that is,drdt

∼ −𝛾r→ r dr ∼ −𝛾 dt (5.100)

where ∼ means proportional to, V=Ar is the volume of the bubble, A is the surface

area of the bubble, P1 − P2 is the Laplace pressure difference and 𝛾 is the surface

P1

P1

P1

P2 = P0 + γ/R

P1 = P0 + γ/r

P1

R

r

Figure 5.11 A Plateau border.

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Introduction to food colloids 249

Food foams

Parabola

(theoretical)

Infection Time t

Bubble

radiu

s r

Figure 5.12 Shrinkage of bubbles.

tension. After integration of Eqn (5.100), the change in radius r of a small bubble

with respect to time t is given by

r2 = r20 −

(4RTDG∕LS∞𝛾

p𝜆

)t (5.101)

where r0 is the bubble radius at t=0, DG/L is the diffusion coefficient of the gas

in the liquid, S∞ is the solubility of the gas at a planar interface (r→∞), p is the

pressure and 𝜆 is the distance over which gas diffuses from the small bubble to

one with an infinite radius of curvature. A plot of r versus t for Eqn (5.101) is a

parabola (Fig. 5.12).

Example 5.5Prins (1987) published the following data relating to the parameters in

Eqn (5.101):

r0 = 125 × 10−6 m

𝛾 = 39 × 10−3 N∕m

𝜆 = 10−5 m

Dg∕l(C) = 1.77 × 10−9 m2∕s (diffusion coefficient of CO2 in the liquid)

Dg∕l(N) = 1.99 × 10−9 m2∕s (diffusion coefficient of N2 in the liquid)

S∞(C) = 3.9 × 10−4mol∕Nm (solubility of CO2 at a planar interface if r → ∞)

S∞(N) = 6.9 × 10−6 mol∕Nm (solubility of N2 at a planar interface if r → ∞)

P = 105 N∕m2

𝜆 = 10−5 m

Let us calculate (at T= 293 K) the time t needed for r→0 (see Eqn 5.101).

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250 Confectionery and chocolate engineering: principles and applications

For carbon dioxide,

1252 × 10−12 =4 × 8.31(Nm∕molK) × 293K × 39 × 10−3N∕m × 1.77 × 10−9(m2∕s)

× 3.9 × 10−4mol∕Nm × t[105(N∕m2) × 10−5m].

For nitrogen,

1252 × 10−12 =4 × 8.31(Nm∕molK) × 293K × 39 × 10−3N∕m × 1.99 × 10−9(m2∕s)

× 6.9 × 10−6mol∕Nm × t[105(N∕m2) × 10−5m].

After some calculations,

t(carbon dioxide) = 4.11 × 10−11 s [1.77 × 10−9 × 3.9 × 10−4] = 59.5 s

t(nitrogen) = 4.11 × 10−11 s [1.99 × 10−9 × 6.9 × 10−6] = 2993 s.

Obviously, in Example 5.5 the difference between the times that are neces-

sary for the disappearance of the bubbles is derived mainly from the difference

between the solubilities S∞(C) and S∞(N) of the gases. In food foams, how-

ever, with surface-active species present at the air–water interface, the situa-

tion is more complicated because the surface tension of a shrinking bubble is

less than the equilibrium value. Therefore, the surface tension decreases during

shrinkage, and the disproportionation process may stop completely, that is, r may

stop decreasing. In this case a different type of curve for r= r(t) is obtained; see

Figure 5.12, which has an inflection point P.

5.11.3.2 Surface dilational viscosity and surface dilational modulusThe change in the surface tension 𝛾 with decreasing bubble size can be expressed

in terms of the surface dilational viscosity 𝜂d, defined by

𝜂d = Δ𝛾d ln A∕dt

(5.102)

where Δ𝛾 (N/m) is the increase (or decrease) in surface tension compared with

the equilibrium value and d ln A/dt (s−1) is the relative rate at which the area is

changing; d ln A is dimensionless. The surface dilational viscosity 𝜂d measures the

ability of a liquid surface to resist an external disturbance, such as an increase in

surface area A or a shrinking stress exerted on the surface by a streaming liquid.

The related surface dilational modulus (or Gibbs coefficient) 𝜀d is defined by

𝜀d = d𝛾

d ln A. (5.103)

Taking account of 𝜂d when r is large makes little difference, but it can have a

considerable slowing-down effect when r is small. If A= r2, then d ln A=2 d ln r.

Consequently, if r is large, 𝜂d is small, and if r is small, 𝜂d is large, that is, the

slowing-down effect of 𝜂d is strong.

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Introduction to food colloids 251

When the dilational surface rheology of the bubble surface has a purely elastic

component, the disproportionation process stops completely. The stability con-

dition is

𝜀d = d𝛾

d ln A=(1

2

)(d𝛾

d ln r

)≥𝛾

2(5.104)

where 𝜀d is the surface dilational modulus and 𝛾 is the surface tension in equi-

librium. For small-molecule surfactants, 𝜀d is effectively zero on the timescale

of bubble shrinkage because the surfactant dissolves into the bulk phase as r

becomes smaller to restore the equilibrium adsorption condition.

5.11.3.3 Gibbs adsorption equationMaterials that adsorb strongly at an interface, and therefore cause a substantial

lowering of the surface tension at low concentrations, are called surfactants. For

a surfactant solution, it is usually a very good approximation to take Γ2 as the

absolute surface concentration in the Gibbs adsorption equation

Γ2 = −( 1

RT

) d𝛾

d ln(x2f2)(5.105)

where x2 and f2 are the concentration and the activity coefficient (unity for an

ideal solution), respectively, of the solute.

Because a small-molecule surfactant dissolves into the bulk phase as r becomes

small, the absolute surface concentration Γ2 of it becomes zero at the interface.

This means that foams made with surfactants that form a simple monolayer are

unstable with respect to bubble collapse by disproportionation.

However, the situation is different with an adsorbed protein film at the inter-

face, especially when the protein is susceptible to surface coagulation, as is the

case with the egg-white protein ovalbumin. There is no desorption over the

timescale for bubble shrinkage, and as r decreases, d becomes large enough to

satisfy Eqn (5.104): hence the foam is stable towards disproportionation. The

condition for stability is also satisfied if the bubble surface becomes packed with

hydrophilic solid particles (as in the case of the fat globules in whipped dairy

foams) or if a small-molecule surfactant is present in sufficient concentration to

form an elastic liquid-crystalline gel phase around the bubbles.

For details of the manufacture of foams, see Henzler (1980), Beyer von Mor-

genstern and Mersmann (1982), Stein (1987a,b, 1988) and Brauer et al. (1989).

5.11.4 Foam stability: coefficient of stability and lifetimehistogram

All foams are thermodynamically unstable owing to their high interfacial free energy,

which decreases on rupture or drainage.

A detailed description of test methods for foam stability, together with litera-

ture references, has been given by Pugh (2002). Various methods are employed

to estimate and compare foam stability with respect to destruction of a foam col-

umn. Most often, these methods can be reduced to determination of the lifetime

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252 Confectionery and chocolate engineering: principles and applications

of a foam column (or part of it) up to its complete disappearance. In connection

with the stability of flotation foams (froths), the concept of a coefficient of stability

B has been developed:

B = tVF

(5.106)

where t is the time for foam destruction and VF is the volume of the foam.

When a foam decays in a gravitational field, the capillary pressure in its upper

parts is reduced owing to the diminishing height of the foam column. Hence, the

times of decay of the various local layers are different, and the total lifetime of

the whole foam column is an integral that takes account of the effect of the local

pressure and the total height H0 of the foam column:

t =∫

H0

0

dtdH

dt. (5.107)

The function t versus H is often obtained in the form of a histogram of the

distribution of the lifetimes of local foam layers of, for example, 2 cm thickness.

To compare the stability of foams made using various surfactants or with differ-

ent surfactant concentrations, it is advisable to measure the foam lifetime at con-

stant pressure, tP, in the Plateau borders. The quantity tP is a much better-defined

indicator of foam stability since the pressure in the borders throughout the height

of the foam column remains constant during its destruction. This parameter is

also much more sensitive to the kind of surfactant, the electrolyte concentration

and the presence of other additives than the lifetime of the foam in a gravitational

field.

Drainage strongly affects foam collapse. The higher the drainage rate, the more

rapidly the equilibrium state is reached and, therefore, stability can be reduced.

That is why a correlation is often observed between the rate of drainage and foam

stability: the slower the rate of drainage, the longer the foam lifetime is.

5.11.5 Stability of polyhedral foamsIn a polyhedral foam, the liquid films (lamellae) between the bubbles are thin

and flat. In order to satisfy the condition of mechanical equilibrium, the films

meet each other at an angle of 120∘. The meeting point is called a Plateau border.

Owing to the curvature of the interface, the pressure in a Plateau border is lower

than that in a bubble by an amount:

Δp = 𝛾

r1

(5.108)

where r1 is the radius of curvature of the Plateau border surface. Equation (5.108)

takes into account the fact that in polyhedral foams the lamellae are thin and the

other radius (r2) of curvature of the Plateau border surface has become practically

infinite, that is, 1/r2 ≈ 0; see Eqn (5.99).

As in the case of coalescence in emulsions, the stability of a polyhedral foam

depends on two distinct processes: film drainage and film rupture.

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Introduction to food colloids 253

5.11.6 Thinning of foam films and foam drainage5.11.6.1 ThinningThe lifetime Δt of a thinning foam film can be estimated from the relation

Δt =∫

hCR

h0

dhw

(5.109)

where h0 is the initial thickness of the film, hCR is the critical thickness at which

the film ruptures and w= dh/dt is the rate of thinning. Under certain conditions,

the hydrodynamics of films in foams is very well described by the lubrication theory

of Reynolds (the Stefan–Reynolds relation):

− dhdt

=2h3Δp

3𝜂r2(5.110)

where h is the thickness between two solid circular plates of radius r, as a func-

tion of the time t; Δp is the pressure drop between the capillary pressure of the

meniscus p𝜎 and the disjoining pressure of the film; and 𝜂 is the dynamic viscosity

of the solution. Equation (5.110) leads to

d(h−2)dt

=4Δp

3𝜂r2. (5.111)

Manev et al. (1974) showed the following relationship to be useful:

h = h0 exp(−kt) (5.112)

where k (s−1) is a constant, experimentally determined.

5.11.6.2 Foam drainage: foam syneresisAt the moment of formation, the liquid content of a foam is usually considerably

larger than that in hydrostatic equilibrium. For this reason, liquid starts draining

out of a foam even during generation of the foam. The excess liquid in the films

drains into the Plateau borders and then flows down through them from the

upper to the lower layers of the foam following the direction of gravity until the

gradient of the capillary pressure balances the gravitational force (dp𝜎/dL= 𝜌g,

where L is a coordinate in the direction opposite to gravity). Simultaneously

with drainage from the films into the borders, the liquid begins to flow out from

the foam when the pressure in the lower layers exceeds the external pressure.

By analogy with gel syneresis, the outflow of liquid from a foam was called foam

syneresis by Arbuzov and Grebenshchikov (1937).

The main driving force for drainage is gravity, which acts directly on the liquid

in a non-horizontal film and indirectly through suction acting on the Plateau

borders. The rate of drainage is determined not only by the hydrodynamic char-

acteristics of the foam (the shape and size of the borders, the viscosity of the

liquid phase, the pressure gradient, the mobility of the liquid–gas interface, etc.)

but also by the rate of internal collapse of the foam (both films and borders)

and the breakdown of the foam column. The outflow of liquid from the foam

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254 Confectionery and chocolate engineering: principles and applications

represents the last stage of a process that includes film thinning and rupture and

outflow through the borders and films.

5.11.6.3 Film rupture: the role of particular materials and mechanicaldisruption

Film rupture is a stochastic process. In practice, the most important mechanism

of film rupture is that involving particular materials in the film. If a hydrophobic

particle is large enough to touch both surfaces, the Laplace pressure in the film

adjacent to the particle may become positive. This will lead to flow of liquid away

from the extraneous particle, eventually resulting in the liquid breaking contact

with the particle (i.e. film rupture).

Another type of contaminant particle is one that spreads its contents over the

air–water interface. This spreading causes adjacent liquid in the film to move in

the same direction. This movement of liquid induces local thinning of the film,

which enhances the probability of rupture. This type of mechanism is believed

to be responsible for the destabilizing effect of fatty particles in aqueous foams.

Examples of this phenomenon are the poor foaming behaviour of whole milk

as compared with skimmed milk and the detrimental effect of a small amount

of egg yolk on the foaming of egg white.

In addition to contamination by particles, other forms of disturbance which

may induce film rupture are mechanical disruption (stirring, shaking, etc.) and

evaporation. At the top of a foam exposed to the external atmosphere, evaporation

of water may reduce stability by reducing the film thickness to the value at which

there is spontaneous hole formation.

There are various empirical and semi-empirical equations that are used in the

quantitative description of the drainage process; their application, however, is

usually limited to short time intervals and narrow ranges of foam expansion

ratio.

5.11.7 Methods of improving foam stabilitySeveral methods have been developed for improving foam stability:

1 Stability increase caused by an increase in bulk viscosity. As a general rule, the

drainage rate of a foam may be decreased by increasing the bulk viscosity of

the liquid from which the foam is prepared. For many food foams, drainage

can easily be halted by formation of a hydrous gel, and the lamellae can be

stabilized at relatively large thicknesses (∼1 μm). The more viscous the liquid,

the slower is the drainage between layers.

2 Stability increase caused by an increase in surface viscosity. An alternative method

to slow down the foam drainage kinetics is to increase the surface viscos-

ity by packing a high concentration of surfactants or particles into the sur-

face, for example, by adding relatively high-molar-mass polymers, proteins

or polysaccharides or certain types of particles (e.g. castor sugar). In addi-

tion, high cohesive forces in the surface films can be achieved by using mixed

surfactant systems.

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Introduction to food colloids 255

3 An absorbed surfactant film can control the viscosity of the surface layer. The experi-

mentally measurable parameters that characterize the mechanical–dynamical

properties of monolayers are the surface elasticity and surface viscosity. The

surface viscosity reflects the speed of the relaxation processes which restore

equilibrium in a system after a stress has been imposed on it. The surface

viscosity (for simple Newtonian surface flow) is defined by the equation

𝜏s = 𝜂s

(dvdr

)

S

(5.113)

where 𝜏S is the surface shear stress (N/m), 𝜂S is the surface shear viscosity

(N s/m) and (dv/dr)S is the surface shear rate [m/(s m)]. The surface viscosity

is also a measure of the energy dissipation in the surface layer. In contrast,

the surface elasticity is a measure of the energy stored in the surface layer as a

result of an external stress. The surface elasticity (for simple Hookean surface

elasticity) is defined by

𝜏S = GS

(dLdr

)

S

(5.114)

where 𝜏S is the surface shear stress (N/m), GS is the surface shear modulus

(N/m) and (dL/dr)S is the surface shear deformation (m/m).

4 Gibbs–Marangoni effect. This is caused by adsorbed surfactants and heals thin-

ning surfaces and prevents the drainage of thin films that leads to rupture.

For thick lamellae, under dynamic conditions, the Gibbs–Marangoni effect

becomes important and operates on both expanding and contracting films.

The Gibbs–Marangoni effect is the transfer of mass on or in a liquid layer due

to differences in surface tension. Since a liquid with a high surface tension

pulls more strongly on the surrounding liquid than one with a low surface ten-

sion, the presence of a gradient in the surface tension will naturally cause the

liquid to flow away from regions of low surface tension. This surface tension

gradient may be caused by a concentration gradient or a temperature gradient,because surface tension is a function of temperature. The Gibbs–Marangoni

effect tends to oppose any rapid displacement of a surface and may, at fairly

high surfactant concentrations, provide a temporary restoring or stabilizing

force to dangerous thin films that can easily rupture. The Gibbs–Marangoni

effect is superimposed on the Gibbs elasticity, so that the effective restoring

force is a function of the rate of extension, as well as of the thickness.

5 Stabilization of films by a combination of surfactants (mixed films). In many cases

it has been found that the use of a combination of surfactants gives slower

drainage and improved foam stability through interfacial cohesion. There

are several possible explanations for the enhanced stability, including the

following:

∘ A non-ionic surfactant causes a reduction in the critical micelle concentra-

tion of a solution of an anionic surfactant.

∘ Although the anionic surfactant should not be too strongly absorbed, a low-

ering of the surface tension is expected to occur for the combination of a

non-ionic and an anionic surfactant.

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256 Confectionery and chocolate engineering: principles and applications

∘ An increase in surface viscosity and drainage is expected to occur when a

combination of surfactants is used. In many cases, a gelatinous surface layer

is believed to be formed, which gives a low gas permeability.

5.11.8 Oil foam stabilityWhile the understanding of the properties of aqueous foams has received con-

siderable attention, studies of non-aqueous foams have been remarkably scarce.

The reason for the discrepancy in scientific difference is believed to be related

to the fundamental difference in the stabilizing mechanisms. The fundamental

advancement of the stabilization of oil foams was recently reviewed by Friberg

(2010). In aqueous foams, surfactants adsorb at the interface changing its sur-

face properties which provides an important mechanism for foam stability; see

Langevin (2000). The inherent low surface tension of most oils implies that there

is little or no drive for hydrocarbon-based surfactants to adsorb to the interface.

As a result, the surface properties are only marginally changed by an increase in

the surfactant concentration and have no significant effect on the foam stability.

Vieira and Sundara (2011) studied the chocolate aeration processes, that is,

aeration by vacuum process, by dissolved process and by extrusion process.

Moreover, they discussed with the key factors governing chocolate aeration,

that is, the influence of the fat properties, the emulsifiers, the gas type, influence

of viscosity and tempering. For further references, see Jeffrey (1989), Haedelt

et al. (2005, 2007) and Haffar (2014).

5.12 Gelation as a second-order phase transition

5.12.1 Critical phenomena and phase transitionsSince the 1980s, a great deal of theoretical work has been devoted to the analysis

of the gelation process (Callen 1985, Ch. 12.7) following the ideas first pro-

posed by Stauffer in 1974 (Stauffer et al., 1982) and de Gennes (1979). These

authors established a parallel between gelation and a percolation process and studied

the process of gelation by analogy with a second-order phase transition, where

the fraction of reacted bonds p is equivalent to temperature and the gel frac-

tion is the order parameter of the transformation. The gel point corresponds to

the amount p= pc of reacted bonds for which an infinite cluster is formed. When

approaching the gel point, |p − pc| → 0, where p is the measure of connectivity.

Universal scaling laws have been predicted for the molecular weight of the finite

clusters (p< pc), for the mean size (p< pc) and for the gel fraction (p< pc).

Thermodynamic behaviour near critical point is governed by a set of critical

exponents. These are interrelated by scaling relations. The numerical values of the

critical exponents are determined by the physical dimensionality and by the

dimensionality of the order parameter; these two dimensionalities define uni-

versality classes of systems with equal critical exponents. Computer simulations

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Introduction to food colloids 257

allow an estimation of the critical exponents which are then compared to the

theoretical predictions (Djabourov et al., 1988).

Stauffer et al. (1982) determined that a gel fraction like (p− pc)𝛽 vanishes for

conversion factors p very close to the get point pc, the weight average molecu-

lar weight diverges as (pc − p)−𝛾 for p very slightly below pc, and the radius of

macromolecules at the gel point p= pc varies as the 𝜌th power of the number of

monomers in that macromolecule. Classical theories predict 𝛽 = 𝛾 = 1 and 𝜌= 1/4,

whereas the percolation theory gives 𝛽 ≅0.45, 𝛾≅ 1.74 and 𝜌≅ 0.40. Stauffer

et al. also generalize the percolation concept to include interaction effects and

concentration fluctuations; in this case the sol–gel phase transition may be con-

nected with a phase separation. Some experimental results are reviewed to check

whether the percolation theory agrees with reality; no clear answer has been

found so far, due to experimental difficulties. For instance, for the viscosity a

power law (pc − p)−0.8, which agrees with one of the percolation ideas, has been

established in several experiments; the shear modulus of the gel vanishes roughly

as (p− pc)3 in some experiments, which agrees better with the classical theory.

Marangoni and Tosh (2005) approach the topic of gelation on the basis of such

thermodynamical considerations.

Note: The phase transition and phase inversion are entirely different

phenomena.

5.12.2 Relaxation modulusThe transition strongly affects the molecular mobility, which leads to large

changes in rheology. For a direct observation of the relaxation pattern, one may,

for instance, impose a small step shear strain 𝛾0 on samples near the liquid–solid

transition (LST) while measuring the shear stress response 𝜏12(t) as a function

of time. The result is the shear stress relaxation function G(t)= 𝜏12(t)/𝛾0, also

called relaxation modulus. Since the concept of a relaxation modulus applies to

liquids as well as to solids, it is well suited for describing the LST, namely, at the

LST, the material behaves not as a liquid anymore and not yet as a solid. The

relaxation modes are not independent of each other but are coupled. The coupling is

expressed by a power law distribution of relaxation modes

G(t) = S t–n, for 𝜆0 < t <∞ (5.115)

where S is the gel stiffness and 𝜆0 is the lower crossover concerning the power

law. Parameters S, n and 𝜆0 depend on the material structure at the transition.

(The upper cut-off is infinite since the longest relaxation time diverges to infinity

at the LST.)

Beyond the LST, p> pc, the material is a solid. The solid state manifests itself in

a finite value of the relaxation modulus at long times, the so-called equilibrium

modulus:

Ge = limt→∞G(t). (5.116)

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258 Confectionery and chocolate engineering: principles and applications

Stresses cannot relax completely anymore. However, G% can be estimated

from log G versus log t plots. G% is zero at the gel point and grows with the extent

of reaction, p.

A tightly connecting topic is the scaling relations of gelation; for details, see

Stauffer et al. (1982).

5.12.3 Gelation theories5.12.3.1 Branching theoriesBranching models (Flory–Stockmayer model, recursive theory, the cascade the-

ory) are based on multifunctional molecules of different types between which

covalent bonds are formed to yield a network structure. Using combinatorial

approaches, they derived an expression for the molecular weight distribution and

subsequently the critical extent of reaction, pc, at which the molecular weight

diverges, Mw → ∞ (gel point).

5.12.3.2 Percolation theoryPercolation theory describes the random growth of molecular clusters on a

d-dimensional lattice. Imagine a very large lattice of empty sites. At random,

a site could be occupied with probability p or unoccupied with probability

(1− p). If we define a cluster as a set of occupied sites that can be traversed

by jumping from neighbour to occupied neighbour, then site percolation theory

is the study of such clusters. Two sites may also be attached with a bond with

probability b or unattached with probability (1− b). Bond percolation is the

study of clusters formed by such a procedure, where analogously a cluster is

defined as a collection of points that can be traversed by only travelling across

occupied bonds. Finally, site-bond percolation theory has both sites and bonds

that are filled at random, with bonds only permitted to be between occupied

sites.

5.12.3.3 Scaling near the LSTAll theories yield unique scaling relationships (power law∝ ∣p− pc∣exponent) for

molecular (e.g. mean cluster size, size distribution) and bulk properties (e.g.

equilibrium modulus) near the critical point, but critical exponent values and

relations between different critical exponents are different. This scaling is com-

mon for material behaviour near any critical point, that is, the polymeric material

near the gel point exhibits a behaviour analogous, for example, to a fluid near

its vapour–liquid critical point.

5.12.3.4 Critical gel as fractal structureBased on the fractal behaviour of the critical gel, which expresses itself in the

self-similar relaxation, several different relationships between the critical expo-

nent n and the fractal dimension df have been proposed recently.

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Introduction to food colloids 259

5.12.3.5 Kinetic theory (Smoluchowski equation)Kinetic theories based on Smoluchowski’s coagulation equation have

recently been applied more and more to describe the kinetics of gelation.

The Smoluchowski equation is able to describe and distinguish between gelling

and non-gelling systems. For more details, see Winter and Mours (1997) and

Leyvraz (2012).

5.12.4 The critical gel equationWinter and Mours (1997) provide a detailed survey on the viscoelastic properties

at and around LST, the constitutive modelling with the critical gel equation, the

rheometry near the gel point and the detection of LST. We are limited to the

following:

The linear viscoelastic constitutive equation of critical gels, called the critical gel

equation, is

𝜏(t) = nS∫

t

−∞(t − t′)−(n+1)C−1(t; t′)dt′, at p = pc (5.117)

where 𝜏(t) is the stress tensor and C−1(t;t′) is the Finger strain tensor proposed

by Lodge (1964) in his rubber-like liquid theory for describing the strain history.

(For details, see Appendix 3.4.1, also Joseph, 1990, p. 14.) Tanaka (2012) gives

a survey on the viscoelastic properties for sol–gel transitions.

5.12.5 Gelation of food hydrocolloids5.12.5.1 GelatinGelatin as a typical food gelling agent has become a frequented field of research

of gelation.

Dumas and Bacri (1980) studied the viscosity of a 7% gelation aqueous solu-

tion in a very close vicinity of the gelation transition by rotational relaxation

of ferromagnetic particles imbedded in the mixture. The viscosity critical expo-

nent s=0.95± 0.10, which is obtained over 3 decades in temperature, is well

accounted for by numerical calculations in the effective field treatment of perco-

lation theory. For the scaling of viscosity they found

𝜂cr = 𝜂0|p − pc|−s (5.118)

where p is the fraction of reacted bonds, pc is the gelation threshold and 𝜂0 is the

viscosity of the original solution of monomers at high temperature.

Djabourov (1988) studied the architecture of gelatin gels concerning the gela-

tion mechanism of a polymeric gel – the description of the system including both

the microscopic and the supramolecular scales – using different experimental

approaches (polarimetry, electron microscopy, rheology). The gelation process is

presented within the theoretical context of the scaling laws, which establish an

analogy with a second-order phase transition. This analogy is illustrated in the case

of the gelatin gel.

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260 Confectionery and chocolate engineering: principles and applications

Tose (2001) investigated the effect of setting temperature, T, on the scaling

properties of the structure of gelatin gels.

Normand and Parker (2003) showed that there are several striking parallels

between the dynamics of gelatin gels and spin glasses. In general, glassy systems

retain a memory of their past history. For the gelation kinetics, they found the

relation

G′(t)∕{𝜀𝛼(c − cc)𝜇

}= g

[t∕{𝜀𝛽(c − cc)𝜈

}](5.119)

where 𝜀= 1− T/Tc is the reduced temperature, c is the dimensionless concen-

tration, t is time and g(x) is a scaling function defining the shape of the master

curve. The four exponents and the critical concentration, cc, are fitting param-

eters. The form of equation (5.127) is evidence against (!) the presence of the

second-order phase transition, as the effects of concentration and temperature

are independent.

Forgacs et al. (2003) analysed the phase transition by the means of phase-

contrast microscopy and rotating disc rheometry, respectively, and by the terms

of percolation theory. The viscoelastic parameters (storage modulus G′ and loss

modulus G′′) were measured as a function of time for five different frequencies

ranging from 𝜔=0.2 to 6.9 rad/s. They found at the gel point both G′ and G′′

obey a scaling law G′(𝜔)∝G′′(𝜔)∝𝜔Δ, with the critical exponent Δ= 0.7 and a

critical loss angle 𝛿 (tan 𝛿 =G′′/G′) being independent of the frequency as pre-

dicted by percolation theory. Gelation of collagen thus presents a second-order

phase transition.

Parker and Povey (2012) measured the ultrasonic (8 MHz) speed and attenu-

ation of edible-grade gelatin in water, exploring the key dependencies on tem-

perature, concentration and time.

Samboon et al. (2014) studied agar (A) and fish gelatin (Fg) which are accept-

able gelling agents in halal food.

5.12.5.2 PectinAudebrand et al. (2003) studied mixtures of pectin and alginate. First, the gel

formation for the pure pectin and pure alginate was followed by recording the

evolution of the frequency-dependent mechanical spectra with time. For both

systems the sol–gel transition is of the classical scalar percolation type. Close to

the gel time, the viscosity behaves as 𝜂0 ∼ 𝜀−s and the static elastic modulus as

G0 ∼ 𝜀t, where 𝜀 is the time difference with respect to the gel time. Right at the gel

point the storage and loss moduli scale with frequency as G′ ∼G′′ ∼𝜔Δ. Theoreti-

cal values for the characteristic critical exponents are s= 0.75–0.04, t= 1.94–0.10

and Δ=0.72–0.04; furthermore the relations Δ= t/(s+ t) and G′′/G′ = tan(Δ𝜋/2)

are predicted to hold. Their results referring to alginate and pectin are consistent

with these theoretical results. At the gel point G′ and G′′ scale as 𝜔Δ with Δ∼ 0.7

for both systems, and the cited consistency relations are satisfied.

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Introduction to food colloids 261

Further reading

Adamson, A.W. and Gast, A.P. (1997) Physical Chemistry of Surfaces, 6th edn, Wiley, New York.

Anonymous (1985) The Dairy Handbook, Alfa-Laval AB, Lund.

Basak, R. and Bandyopadhyay, R. (2014) Formation and rupture of Ca2+ induced pectin

biopolymer gels. Soft Matter, 10, 7225–7233.

Brinker, C.J. and Scherer, G.W. (1990) Sol–Gel Science – The Physics and Chemistry of Sol–Gel Pro-

cessing, Academic Press, Inc., Boston.

Burt, D.J. and Thacker, D. (1981) Use of emulsifiers in short dough biscuits. Food Trade Review,

47, 344.

Bushella, G.C., Yan, Y.D., Woodfield, D. et al. (2002) On techniques for the measurement of

mass fractal dimension of aggregates. Advances in Colloid and Interface Science, 95, 1–50.

CABATEC (1991) Dairy Ingredients in the Baking and Confectionery Industries, An audio-visual

open learning module, Ref. C6. Biscuit, Cake, Chocolate and Confectionery Alliance, London.

Dickinson, E. (2001) Milk protein interfacial layers and the relationship to emulsion stability

and rheology: review. Colloids and Surfaces B: Biointerfaces, 20, 197–210.

Domb, C. and Lebowitz, J.L. (eds) (1991) Phase Transitions and Critical Phenomena, vol. 14, Aca-

demic Press, NY.

Eleya, M.M.O., Ko, S. and Gunasekaran, S. (2004) Scaling and fractal analysis of viscoelastic

properties of heat-induced protein gels. Food Hydrocolloids, 18, 315–323.

Friberg, S.E., Larsson, K. and Sjöblom, J. (2003) Food Emulsions, Marcel Dekker, New York.

Gabbrielli, R. (2009) Foam geometry and structural design of porous material. PhD theses. Uni-

versity of Bath.

Germain, J.C. and Aguilera, J.M. (2014) A close look at protein-stabilized foams: review. Food

Structure. doi: 10.1016/j.foostr.2014.01.001

Gilmore, R. (1993) Catastrophe Theory for Scientists and Engineers, Dover Publications, New York.

Hlynka, I. (ed.) (1964) Wheat Chemistry and Technology, American Association of Cereal Chemists.

Holmberg, K. (ed.) (2002) Handbook of Applied Surface and Colloid Chemistry, Wiley, Chichester.

Horn, J.D. (1970) Emulsifiers – A Practical Appraisal, British Chapter, A.S.B.E. Conference,

November.

Hutchinson, P.E. (1978) Emulsifiers in Cookies: Yesterday, Today and Tomorrow. 53rd Annual

Biscuit and Cracker Manufacturers Association Technologists’ Conference.

Hutchinson, P.E. et al. (1977) Effect of emulsifiers on texture of cookies. Journal of Food Science,

42, 2.

Ivanov, I.B., Danov, K.D. and Kralchevsky, P.A. (1999) Flocculation and coalescence of

micron-size emulsion droplets. Colloids and Surfaces A: Physicochemical and Engineering Aspects,

152, 161–182.

Juan, C., Germain, J.C. and Aguilera, J.M. (2014) A close look at protein-stabilized foams,

Review, Food Structure, http://dx.doi.org/10.1016/j.foostr.2014.01.001.

Kattenerg, H.R. (1994) (De Zaan) Cocoa-powder for the dairy industry. US Patent 4,704,292.

Kulp, K. (ed.) (1994) Cookie Chemistry and Technology, American Institute of Baking, Kansas.

Lebovka, N.I. (2012) Aggregation of charged colloidal particles. Advances in Polymer Science, 255,

57–96. doi: 10.1007/12_2012_171

Lübeck, S. (2004) Universal scaling behavior of non-equilibrium phase transitions. PhD thesis.

University of Duisburg-Essen, Germany.

Marangoni, A.G. and Narine, S.S. (2004) Fat Crystal Networks, Marcel Dekker, New York.

Meakin, P. (1992) Aggregation kinetics. Physica Scripta, 46 (4), 295.

Narine, S.S. and Marangoni, A.G. (2002) Physical Properties of Lipids, Marcel Dekker,

New York.

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262 Confectionery and chocolate engineering: principles and applications

Norn, V. (ed.) (2014) Emulsifiers in Food Technology, Wiley Online Library Print ISBN:

9780470670637, online ISBN: 9781118921265. doi: 10.1002/9781118921265

Payens, T.A. (1979) Casein micelles: the colloid chemical approach. Journal of Dairy Research, 46,

291–306.

Pocius, A.V. (2002) Adhesion and Adhesives Technology: An Introduction, 2nd edn, Hanser, Munich.

Segrè, P.N., Prasad, V., Schofield, A.B. and Weitz, D.A. (2001) Glass like kinetic arrest at the

colloidal-gelation transition. Physical Review Letters, 89 (26), 6042–6045.

Shih, W.H., Shih, W.Y., Kim, S.-I.I. et al. (1990) Scaling behavior of the elastic properties of

colloidal gels. Physical Review A, 42, 4772.

Shih, W.Y., Liu, J., Shih, W.-H. and Aksay, I.A. (1991) Aggregation of colloid particles with a

finite interparticle attraction energy. Journal of Statistical Physics, 62 (5/6), 961–984.

Stauffer, D. and Stanley, H.E. (1989) From Newton to Mandelbrot, Springer, Hamburg(4.3.10 Scal-

ing Theory).

Stephen, A.M., Phillips, G.O. and Williams, P.A. (eds) (2006) Food Polysaccharides and Their Appli-

cations, 2nd edn, Taylor and Francis Group, Boca Raton.

Stone, H.A., Koehler, S.A., Hilgerfeldt, S. and Durand, M. (2003) Perspectives on foam drainage

and the influence of interfacial rheology. Journal of Physics: Condensed Matter, 15, 283–290PII:

S0953-8984(03)55155-4.

Tamime, A.Y. and Robinson, R.K. (1999) Yoghurt: Science and Technology, CRC Press/Woodhead,

Cambridge.

Urbina-Villalba, G. (2009) An algorithm for emulsion stability simulations: account of floc-

culation, coalescence, surfactant adsorption and the process of ostwald ripening, review.

International Journal of Molecular Sciences, 10, 761–804. doi: 10.3390/ijms10030761.

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PART II

Physical operations

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CHAPTER 6

Comminution

6.1 Changes during size reduction

6.1.1 Comminution of non-cellular and cellular substancesThe role of comminution in food engineering has a peculiarity which is closely

connected to the cellular structure of the substances that are comminuted.

Taking into consideration the hierarchical structure of the materials, there is

an important difference between the properties of unbroken and broken cells.

Greater or lesser amounts of substances flow out of cells as a result of comminu-

tion, making it possible for many chemical and physical changes to take place

that were hindered by the original cellular structure. The degree of comminu-

tion (given, e.g. by the particle size distribution) is a factor that determines the

ratio of materials in unbroken and in broken cells.

The materials that are comminuted in food production may be grouped as

follows:

• Non-cellular substances, for example:

∘ Sucrose (sugar), which is ground as a powder itself and together with other

ingredients (cocoa derivatives, milk powder, etc.)

∘ Milk powder, which is ground together with other ingredients

• Cellular substances, for example, cocoa nibs and various nuts (almonds, hazel-

nuts, etc.)

The degree of comminution has to be high (the particle size has to be very

small) in the cases of cocoa mass and pastes of roasted almonds or hazelnuts.

In other words, the ratio of free substance to bound substance must be high; for

example, the entire content of cocoa butter should be free. However, if marzipan

is being prepared, the almonds ground together with sugar must not be finely

comminuted to prevent the marzipan paste leaking almond oil; that is, the ratio

of free to bound almond oil must be low.

6.1.2 Grinding and crushingSize reduction, or comminution, is an operation in which the particle size of a

bulk material is decreased, using various techniques and types of equipment. The

changes that take place during size reduction can be grouped as follows:

• Reduction of large, irregularly shaped solid particles to smaller sizes

• Creation of new free surfaces

Confectionery and Chocolate Engineering: Principles and Applications, Second Edition. Ferenc Á. Mohos.© 2017 John Wiley & Sons Ltd. Published 2017 by John Wiley & Sons Ltd.

265

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266 Confectionery and chocolate engineering: principles and applications

• Changes in the number and size of the particles and in the surface area of the

mass (These changes are connected with changes in the bonding in the crystal

lattice or, in general, changes in the structure of the material.)

The first type of process seems self-evident and is related to the coarse stage,

that is, crushing. The second type was highlighted by the theory of Rittinger,

which is more than 100 years old but is still useful today. This type of process

leads to new contact surfaces, which are highly important in chemical reaction

kinetics, and is characteristic of grinding. The changes of the third type, which

characterize the very fine stage of grinding, are more complex: besides the phe-

nomena of size reduction and surface area increase, agglomeration also occurs

and possibly prevails.

The materials used in the confectionery industry also have very different struc-

tures from the point of view of comminution, for example, crystalline (e.g. sug-

ars), cellular or amorphous (e.g. melted and cooled sugar) – every case has to be

studied separately.

Grinding, which is essential from the point of view of confectionery manu-

facture, is the fine phase of comminution. In the coarse stage, called crushing,

particles with sizes of millimetres to centimetres are produced, and this oper-

ation works down to millimetre sizes. However, grinding produces particles of

micron size, and its processes are more complicated.

6.1.3 Dry and wet grindingThe types of comminution can be distinguished according to whether or not

the material to be ground is suspended in a continuous medium. If not, as, for

example, in the case of the grinding of sugar, it is called dry grinding. The pro-

cessing of cocoa into cocoa mass or chocolate provides a typical example of wet

grinding: the continuous medium in which grinding takes place is cocoa butter or

some other kind of vegetable fat. The roll refiners and pearl mills used for these

purposes are continuously operated machines.

6.2 Rittinger’s surface theory

Rittinger’s surface theory, dating from 1867, deals with comminution by an imag-

inary process of slicing. The material, assumed to be homogeneous, in the form

of a cube xl m in size, is sliced in the three principal directions by parallel planes

with a spacing of x2 = x1/𝜈, producing 𝜈3 smaller cubes. The ratio 𝜈 = x1/x2 is called

the reduction ratio. According to the principle of Rittinger’s theory, each individual

slicing operation requires the same amount of energy, that is, the energy require-

ment for comminution is proportional to the area of the newly created surfaces.

We start with a cube of edge x1, which has an (initial) surface area 6x21. After

slicing, we get a final surface area of 6𝜏𝜈3x22, the increase in surface area being

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Comminution 267

equal to

ΔS = 6v3x22 − 6x2

1 (6.1)

According to Rittinger’s theory, the specific energy requirement w is the ratio of

the energy requirement W (J) to the volume V (m3) of material comminuted:

w = WV

= cΔSV

(6.2)

w = c1

(6v3x2

2

v3x22

−6x2

1

x31

)= c

(1x2

− 1x1

)(6.3)

After some algebraic transformation,

w =(

cx1

)(v − 1) (6.4)

Since in common cases 𝜈 ≫ 1, we can write

w =(

cx1

)v (6.5)

that is,

wRx2 = cR (6.6)

where c (J/m2) is a constant; its dimension is equal to that of the surface tension

of a liquid.

Equation (6.6) expresses the essence of the Rittinger’s theory: the reduction of the

particle size and the specific energy requirement for the size reduction process are inversely

proportional to each other. The Rittinger’s formula calculates only the effect of the

breaking of molecular bonds and neglects the work of elastic deformation pre-

ceding the fracture.

6.3 Kick’s volume theory

Kick’s volume theory, dating from 1885, takes into consideration also the work

of elastic deformation. Accordingly, the infinitesimal energy requirement for the

fracture of a cube of size x m is

dW = x2𝜎 d(x𝜆) (6.7)

where 𝜎 (Pa) is the fracture stress, x2𝜎 (N) is the force of fracture and 𝜆

(m/m)= 𝜎/E is the specific deformation (assuming the validity of Hooke’s law;

E (Pa) is Young’s modulus). From Eqn (6.7), we obtain

dW = x2𝜎

(𝜎

E

)dx (6.8)

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268 Confectionery and chocolate engineering: principles and applications

After integrating Eqn (6.7) between the initial and final states (characterized by

x1 and x2, respectively), we find that the energy requirement is

W =(x3

1 − x32)𝜎

2

3E=

x32(v

3 − 1)𝜎2

3E≈

x32v3𝜎2

3E=

x31𝜎

2

3E(6.9)

that is,

w = W

x32

= 𝜎2

3E(6.10)

The conspicuous defect of Eqn (6.10) is that it does not include the reduction

ratio; that is, the energy requirement for comminution according to Eqn (6.10)

is independent of the size reduction; it depends exclusively on the volume x31 of

the material to be fractured.

6.4 The third or Bond theory

The so-called third theory, also known as the Bond theory, aims to solve this con-

tradiction by calculating the energy requirement of the first fracture according to

the Kick’s (volume) theory but the energy requirement of subsequent fractures

according to the Rittinger’s (surface) theory. The specific energy requirement for

comminution according to the Bond theory is

wB = cB

(1√x2

− 1√x1

)(6.11)

or, expressed in terms of the reduction ratio,

wB =

(cB√x2

)(√

v − 1) ≈

(cB√

x

)√

v (6.12)

Equation (6.12) is empirical, but Bond demonstrated its suitability for practical

calculations by the results of very many tests. This can be considered to be a result

of the fact that the Kick’s theory has been proved suitable for crushing (large par-

ticles, the first step of comminution), and the Rittinger’s theory has been proved

suitable for grinding (small particles, the later steps of comminution).

6.5 Energy requirement for comminution

6.5.1 Work indexA work index can be defined by means of Eqn (6.12). The total energy Wi required

to comminute 1 short ton (=907.2 kg) of material to a particle size of 100 μm is

the work index, which can be calculated from test results for a size reduction from

x1 to x2:Wi

W=

1∕√

100

1∕√

x2 − 1∕√

x1

(6.13)

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Comminution 269

Table 6.1 Material behaviour with respect to hardness.

a: very soft b: soft c: medium hard d: hard

A: fibrous

B: elastic

C: plastic

D: tough

E: brittle

If the work index is determined for a material, then the energy requirement W

for any comminution of that material from xp to xr can be calculated:

W = 10Wi

(1√xr

− 1√xp

)(6.14)

However, work indices have not yet been determined for the materials used

in confectionery manufacture.

6.5.2 Differential equation for the energy requirementfor comminution

All of these three theories of comminution can easily be formulated as a single

differential equation,dWdx

= − cxn

(6.15)

where W is the energy requirement for comminution; x is the particle size, consid-

ered as the independent variable characterizing the comminution process; and c is

a constant, the dimension of which is dependent upon the value of n. n depends

on the theory: if n= 1, the equation represents the Kick’s theory; if n= 2, the

Rittinger’s theory; and if n=1.5, the Bond (third) theory.

Tarján (1981, p. 258) provided a set of codes of matrix type to indicate material

behaviour, as shown in Table 6.1. According to this classification, fresh fruit and

sugar beet are classified as Aa, sugar cane as Ab and sugar as Eb.

6.6 Particle size distribution of ground products

6.6.1 Particle sizeIn Chapter 5, the particle size was used as a concept without any definition, even

though homogeneity of size cannot be assumed in bulk grinding, that is, a set of

particle sizes is to be studied in reality. For this reason, the particle size distribu-

tion is the proper tool for studying ground products. The particle size concerns a

single particle; the particle size distribution shows how the sizes of the particles

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270 Confectionery and chocolate engineering: principles and applications

are distributed in a bulk sample of particles. Consequently, the particle size dis-

tribution concerns a given bulk sample.

A single particle is usually an irregular geometric body with several different

possible measures, and behind these measures one can imagine various tech-

niques of determination. The size of a particle is defined by the method of deter-

mination of the particle size.

According to Pabst and Gregorová (2007), sieve classification has lost its sig-

nificance for particle size analysis today, although it remains an important tool

for classification. Presently, the most important particle size analysis methods are

sedimentation methods, laser diffraction, microscopic image analysis and other methods

(dynamic light scattering, electrozone sensing, optical particle counting, XRD line

profile analysis, adsorption techniques and mercury intrusion).

In general, the masses of particles larger than about 40–60 μm can be deter-

mined by screening; below this range, determination is generally done by sedi-

mentation, microscopy or other techniques. Various recording apparatuses have

been developed to eliminate manual work; these use, for example, gravimetric

registration of settling, observation of the change of transparency of suspen-

sions (turbidimetry), microscopic particle counters with digital marking, electri-

cal resistance changes and light scattering in laser beams. A description of these

methods of particle size determination is beyond the scope of this book. Allen

(1981, p. 104) and Pabst and Gregorová (2007) have given a detailed overview

of these methods with many definitions of particle size.

Let us consider the most important methods used in the confectionery

industry.

6.6.2 ScreeningFrom a theoretical and practical point of view, screening plays an essential role

in comminution because the basic concepts of comminution are defined by ref-

erence to screening.

If a particle falls on a screen, there can be two outcomes of this event: the

particle passes or it does not. This decision of a given testing sieve divides the

bulk sample into two parts:

1 The passing part is labelled D; if the size of the openings of the sieve is d (m)

and the size of a tested particle is x (m) and if the relationship

x ≤ d (6.16)

is valid, then that particle belongs to the passing part.

2 The retained part, retained on the sieve, is labelled R (residue); it can be char-

acterized by the relationship

x > d (6.17)

The screening method makes decisions of this kind with a series of sieves; if

n sieves are used, n points are obtained for both D and R.

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Comminution 271

Table 6.2 Testing sieve data.

US sieve number Tyler sieve number Opening [mm (in.)]

100 100 0.149 (0.0059)

120 115 0.125 (0.0049)

140 150 0.105 (0.0041)

170 170 0.088 (0.0035)

200 200 0.074 (0.0029)

230 250 0.063 (0.0025)

270 270 0.053 (0.0021)

325 325 0.044 (0.0017)

400 400 0.037 (0.0015)

The usual form in which D(d) is presented is as a ratio (%) with respect to the

whole sample as a function of the size of the sieve. Data on the testing sieves of

particular interest to the confectionery industry are given in Table 6.2. IOCCC

(1970) recommends a ethanol/water-sieving method for the determination of

the sieve residue of cocoa powder and cocoa mass, which uses plate sieves with

square apertures (holes) of size 75 μm×75 μm or 125 μm×125 μm.

In practice, continuous functions R and D that approximate the real conditions

to a greater or lesser extent are used. These functions can be differentiated. So,

for example, D′(x) gives the frequency of particles of size x in the sample. The

maximum of the frequency is regarded as a characteristic value of the sample:

particles of that size are the most frequent in the sample. Table 6.3 shows data for

the particle size distribution of a chocolate mass, obtained by the Coulter counter

method (see Section 6.6.4). It can be seen from the first and second columns of

the table that the (cumulative) percentage of particles less than 25 μm in size is

97.18%, that is, D(x≤ 25)=97.18%. Figure 6.1 shows the differential curve, and

Figure 6.2 the cumulative curve. The maximum of the frequency in Figure 6.1

occurs at about 13 μm, the bell-curve character is evident.

10

8

6

4× 1

00%

2

00 10

Size (μm)

20 30

Figure 6.1 Particle size distribution of chocolate (differential curve): D′(x) versus log x;

evaluation due to log-normal distribution (see Section 6.7.3.).

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272 Confectionery and chocolate engineering: principles and applications

Table 6.3 Particle size distribution of a

chocolate mass measured by the Coulter

counter method.

x (𝛍m) Cumulative (%) Differential (%)

0.9 3.52 3.52

1.1 5.69 2.17

1.3 8.09 2.4

1.5 10.57 2.48

1.8 14.73 4.16

2.2 20.29 5.56

2.6 25.81 5.52

3.1 32.42 6.61

3.7 39.66 7.24

4.3 46.03 6.37

5 52.37 6.34

6 59.75 7.38

7.5 68.02 8.27

9 74.08 6.06

10.5 78.72 4.64

12.5 83.5 4.78

15 88.02 4.52

18 92 3.98

21 94.8 2.8

25 97.18 2.38

30 98.74 1.56

36 99.54 0.8

43 99.87 0.33

51 100 0.13

100

80

60

40

%

20

00 20

Size (μm)

40 60

Figure 6.2 Particle size distribution of chocolate (cumulative curve).

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Comminution 273

6.6.3 Sedimentation analysisThe other classical method is the sedimentation method, which is based on

Stokes’ law; this is valid in the laminar region (Re= du𝜌/𝜂 <4, where d= particle

size, u= velocity of sedimentation, 𝜌=density of medium and 𝜂 = dynamic

viscosity of medium). For further details, see Section 5.9.3.

To accelerate the speed of sedimentation in the size range below 10 μm, sed-

imentometers functioning in a centrifugal field have been developed (Németh

and Horányi, 1970).

6.6.4 Electrical sensing zone method of particle sizedistribution determination (Coulter method)

The Coulter technique is a method of determining the number and size of parti-

cles suspended in an electrolyte by causing them to pass through a small orifice,

on either side of which there is an immersed electrode. The changes in resistance

as particles pass through the orifice generate voltage pulses whose amplitudes are

proportional to the volumes of the particles. The pulses are amplified, sized and

counted, and the size distribution of the suspended phase may be determined

from the data derived. The technique was originally applied to blood cell count-

ing and then to counting of bacterial cells and the measurement of cell volume

distributions as well as number counting.

Modified instruments were soon developed to size and count particles. An

excellent description of the methods used in the confectionery industry to deter-

mine particle size distributions can be found in, for example, Minifie (1999,

pp. 825–843). For further details, see Allen (1981).

6.7 Particle size distributions

6.7.1 Rosin–Rammler (RR) distributionThe distribution function most often used in Europe is that of Rosin and Ramm-

ler. In the transcription given by Bennett, this is

1 − D(d) = R(d) = (100%) exp

[−(

dd0

)n](6.18)

where d is the particle size, D(d) is the cumulative passing function, R(d) is the

cumulative residue function, d0 is the mode and n is the uniformity coefficient.

If d= d0, then R (%)=100/e; that is, the particle size belongs to the residue in

100%/e= 36.8% of the sample (and D(p)= 63.2%), where e= 2.718, the Euler

constant and base of natural logarithms.

The standard deviation 𝜎(RR) of the Rosin–Rammler (RR) distribution is

inversely proportional to the uniformity coefficient:

𝜎(RR) =

(𝜋√6

)(1n

)≈ 1.282

n(6.19)

Equation (6.19) explains the meaning of the uniformity coefficient n.

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274 Confectionery and chocolate engineering: principles and applications

6.7.2 Normal distribution (Gaussian distribution, Ndistribution)

The normal distribution does not play an important role in the context of grind-

ing, since this distribution characterizes mainly natural processes, for example,

growth, crystallization and sublimation. However, it is mentioned here for the

sake of completeness.

6.7.3 Log-Normal (LN) distribution (Kolmogorov distribution)This distribution is frequently used in the context of grinding. Kolmogorov

(1937) demonstrated that particle sizes produced by crushing obey the

log-normal (LN) distribution law (see Gnedenko, 1988, p. 193).

If the variable used to characterize the particle size d is

x = log d (6.20)

where ‘log’ means the logarithmic function to base 10, and the logarithmic stan-

dard deviation is

𝜎log = log d2 − log d1 (6.21)

then the equation for the normal distribution can be applied unchanged as

follows:

D(d) = Φ(log d) (6.22)

where Φ is the error integral (i.e. the Gaussian function).

The frequency function of the LN distribution is

D′(d) = (5.772d0log𝜎log) exp

{−

log (d∕d0 log)2

2𝜎2log

}(6.23)

Whereas the mean value d0 in the normal distribution is an algebraic mean, it is

a geometric mean (d0log) in the LN distribution.

6.7.4 Gates–Gaudin–Schumann (GGS) distributionThis is used mostly in the United States. It can be expressed as

D(d) =(

dd0

)m

(6.24)

or

R(d) = 1 −(

dd0

)m

(6.25)

where d0 is the characteristic size of the particles and m is a parameter of homo-

geneity. For further details, see Beke (1981), Allen (1981) and Tarján (1981).

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Comminution 275

6.8 Kinetics of grinding

The decrease with time t of the weight percentage s of the oversize fraction

coarser than a limiting particle size x is given to a first approximation by the

following differential equation (Tarján, 1981):

dsdt

= −cs (6.26)

where c (s−1) is a constant. Equation (6.26) states that the rate of grinding varies

with the amount of oversize fraction remaining. The solution to Eqn (6.26) is

ss0

= exp(−ct) (6.27)

where s0 is the oversize fraction at the instant t= 0.

If the grindability of the material is not constant during the entire grinding

process (e.g. if it decreases owing to the gradual elimination of defects in crystals),

then the equationdsdt

= −csz (6.28)

holds, where the relative grindability z is a function of the decrease of s (Razumov,

1968). Experiments have shown the actual process to be well represented by the

functionss0

= exp(−Ktn) (6.29)

which is analogous in structure to the RR function (Eqn 6.18). (The units of K

are s−n.)

The analogy to the RR function means that plotting log s against t on

semi-logarithmic graph paper (as in the case of log R vs d) gives a straight line.

Differentiation with respect to time of the expression for the oversize fraction s

(Eqn 6.29) yields the equation

dsdt

= −snKtn−1 (6.30)

This implies that for n= 1, the rate of grinding is exponential; that is, it follows

the first-order kinetics of chemical reactions. The grinding rate decreases if n<1

and increases if n> 1, compared with first-order kinetics.

The constants K and n measured for different materials are contravariant: a

high value of K (easy grindability) entails a low value of n. The parameter K is a

sensitive function of the grain size x. For small sizes, K is proportional to xm, and

m is the slope of the RR distribution. The variation of n with x is slight for ball

mills; 0.7≤n≤ 1.3.

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276 Confectionery and chocolate engineering: principles and applications

6.9 Comminution by five-roll refiners

Five-roll (and also three-roll) refiners are traditionally used in the fine grinding

of chocolate, but they are used also in the manufacture of marzipan, compounds

and various filling masses.

6.9.1 Effect of a five-roll refiner on particlesThe effect is double:

• Comminution by stresses caused by the radial forces exerted by the rollers

• Comminution by shear caused by frictional forces, which are tangential to the

matt surfaces of the rollers

The usual arrangement of the five rollers is shown in Figure 6.3.

During the refining process, there is very intense heat production; therefore

cooling of the rollers by water (at ca. 15–18 ∘C) is necessary. A peculiarity of

R5

R4

R3

R1

R2

g(4–5)

g(4–5)

g(2–3)

g(2–3)

g(1–2)

g(1–2)

g(3–4)

g(3–4)

Figure 6.3 Five-roll refiner. R= roller. Source: Bertini (1996). Reproduced with permission of

Carle & Montanari SpA.

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Comminution 277

five-roll refining is that a special consistency of the product is necessary, which

can be achieved with a fat content of about 25–27%. If the fat content is lower,

the first roller pair refuses the mass; if it is higher, the rollers merely lick the mass

and do not pick it up.

6.9.1.1 Angle of pulling inLet us consider Figure 6.4 in order to study the quantitative relations in a roll

refiner.

The half-angle of pulling in, 𝜑, can be determined from the relationship

cos𝜑 = AOMO

=D∕2 + b∕2

D∕2 + d∕2= D + b

D + d(6.31a)

that is,

D = d cos𝜑 − b

1 − cos𝜑(6.31b)

where D is the cylinder diameter (m), b is the space between the cylinders (m)

and d is the particle diameter (m). If 𝜑 is given, this determines the minimum

value of the cylinder diameter.

The usual values of 𝜑 for various states of the surfaces of the cylinders are

• Lustrous, polished: 11∘

• Unpolished: 15∘

• Rough, unpolished: 17∘

6.9.1.2 Distance of rubbingAccording to Eqn (6.31b), cylinders of larger diameter are necessary only when

large particles are to be rolled. If the values of d and b are small, the minimum

cylinder diameter D can also be small, as Example 6.1 shows.

D/2

d/2 M

AO

φφ φ

Cylinders

b

Particle

Figure 6.4 Angle of pulling in and distance of rubbing in a roll refiner.

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278 Confectionery and chocolate engineering: principles and applications

Example 6.1Let d= 0.05 mm and b= 0.025 mm; cos 17∘ =0.9563. Then,

D = (0.05 × 0.9563 − 0.02) × 10−3

1 − 0.9563(mm) ≈ 0.6365 … mm

This is obviously a very low value. The essential reason for using refiners with

large-diameter rollers in chocolate manufacture is to make the distance of rubbing,

2s, in these machines as large as is required, and this makes it possible to approach

the necessary fineness of the particles in chocolate, which is an essential quality

requirement. From Figure 6.4, the half-distance of rubbing can be calculated:

s2 = (AM)2 = (MO)2 − (AO)2 =(

D2+ d

2

)2

−(

D2+ b

2

)2

(6.32)

and

s =√(D

2

)(d − b) + (d2 − b2)

4

Since D≫ d and D≫ b, we can write

s ≈√(D

2

)(d − b) (6.33)

that is,

s ∼√

D (6.34)

Example 6.2Let us calculate the distances of rubbing for two sizes of cylinders, D(1)=0.35 m

and D(2)= 0.45 m; in both cases, d= 0.030 mm and b=0.020 mm:

s(1) =√(0.35

2

)(0.030 − 0.020) × 10−6 ≈ 0.0418 mm

s(2) =√(0.45

2

)(0.030 − 0.020) × 10−6 ≈ 0.0474 mm

Therefore, the diameter of the rollers in modern refiners is a minimum of

300 mm.

6.9.2 Volume and mass flow in a five-roll refinerThe calculation of the power requirement of a five-roll refiner seems to be an

unsolved problem. However, a relationship between the revolution rates of the

rollers can be determined on the basis of continuity if it is supposed that the vol-

ume (or mass) flow remains unchanged during the refining process, namely, that

the moisture loss accompanying the work of the rollers is practically negligible.

This is represented in Figure 6.3 (see Bertini, 1996). The volume flow dV/dt

between two rollers can be expressed as

dVdt

(m3∕s) =g(i − (i + 1))𝜋D(i + 1)L(i + 1)n(i + 1)

60(6.35)

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Comminution 279

Five-roll refiner, 1800 mm

Milk chocolate (25.4% fat)40

40 60

Increase (%) in velocity of roller 1

Part

icle

siz

e (

μm

)

80 100

2320

2030

1740

1450

Yie

ld (

kg/h

)

1160

870

580

30

20

20010

Figure 6.5 Particle size and yield as functions of the velocity increase of roller 1. Source:

Bertini (1996). Reproduced with permission of Carle & Montanari SpA.

where g(i− (i+1)) is the gap (m) between rollers i and (i+ 1), 𝜋D(i+ 1) L(i+1)

is the surface area (m2) of roller (i+ 1) and n(i+ 1) is the revolution rate (min−1)

of roller (i+ 1). Evidently, for rollers 1 and 2, for example, the following relation

is valid:

g(1 − 2)v(2) = g(2 − 3)v(3) = g(3 − 4)v(4) = g(4 − 5)v(5) (6.36)

where, for example, v(3)=D(3)n(3) since the lengths of the rollers are equal.

Figure 6.5 shows the effect of an increase in the velocity of roller 1 on pro-

ductivity. This figure shows the particle fineness and the yield as a function of

the percentage increase in the velocity of a type HFE five-roll refiner. Roller 2

remains in a fixed position, which roller 1 is drawn near to. If the input created

by roller 1 becomes more intense, the productivity increases, but the particle

fineness becomes poorer (Bertini, 1996). The usual solution is to use pre-refining

with a two-roll refiner; its effect is represented in Figure 6.6, which shows results

for five-roll refiners of three different types. As both Figures 6.5 and 6.6 show,

linearity seems to be a good approximation.

The relationship between the length of the rollers and the productivity is pre-

sented in Table 6.4, assuming that the characteristic particle size of the product

is 20 μm.

According to the manufacturer’s technical information, the specific energy

requirement for modern machines of the kind described here varies between

30 and 70 kW h/t.

Example 6.3In a five-roll refiner, the parameters of the rollers are L= 1.8 m and D(5)= 0.4.

The productivity is 1500 kg/h, and the specific weight of the refined product is

1200 kg/m3. Let us calculate the revolution rate of roller 5 if the gap between

rollers 4 and 5 is 0.020 mm (=2×105 m).

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280 Confectionery and chocolate engineering: principles and applications

35

Type 1

Type 2

Type 3

Yield (kg/h)

500 1000 1500 2000

Upper lines: with pre-refiningLower lines: without pre-refining

2500 3000

30

25

Part

icle

siz

e (

μm

)

20

15

10

Figure 6.6 Particle size versus productivity for a five-roll refiner with and without pre-refining.

Source: Bertini (1996). Reproduced with permission of Carle & Montanari SpA.

Table 6.4 Relationship between length of rollers and

productivity for Carle & Montanari machines.

Type Length of rollers (mm) Productivity (kg/h)

HF 513 1300 700–850

HF 518 1800 1000–1200

HF 525 2500 1400–1600

Source: Bertini (1996). Reproduced with permission of Carle

& Montanari SpA.

Evidently,

dmdt

= 𝜌 dV

dt=𝜌g(4 − 5)D(5)𝜋Ln(5)

60

1500 kg∕h =1500 kg

3600 s= 0.42 kg∕s

0.42 kg∕s = 1200 kg∕m3 × 2 × 10−5 m × 0.4 m × 3.14 × 1.8 m × n(5)60

n(5) = 464.43∕min = 7.741∕s

If g(1 − 2)=2 × 10−5 m, then n(2)=(464.43∕min) × 2∕6=154.81min−1 = 2.58 s−1

6.10 Grinding by a melangeur

The melangeur cannot be regarded as a true machine for comminution; it is actu-

ally a mixer, as suggested by its name. However, it is perhaps one of the most

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Comminution 281

versatile machines in the confectionery industry and is almost indispensable in

small plants because it can be used, although not very effectively, for mixing,

comminution and conching.

Let us consider the forces on a particle in a melangeur (Fig. 6.7). At the point

A, a force F acts on the particle. This force can be analysed into a tangential force

t and a radial force r, that is,

F= t+ r (6.37)

These forces are made up as follows:

t=p+ q (6.38)

r= m+ n (6.39)

The forces q and m are compensated by a rotating table (or plate). However, the

condition for comminution is

p > n (6.40)

Since p= t cos𝜑 and n= r sin𝜑, this requirement can be expressed as

t cos 𝜑 > r sin 𝜑 (6.41)

that is,tr> tan 𝜑 (6.42)

where 𝜑 is the angle of pulling in; its usual value for a melangeur is about 25–30∘.Since

tr> tan 𝜌 (6.43)

Figure 6.7 Forces on a particle in a melangeur.

Rotating

cylinder

Rotating

cylinder

F

A n

tr

mdp

D/2

q

a

r

Rotating

table

Rotating

table

φ

φφ

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282 Confectionery and chocolate engineering: principles and applications

where 𝜌 is the angle of friction, it follows from Eqn (6.42) that

tan 𝜌 > tan𝜑, i.e. 𝜌 > 𝜑 (6.44)

On the basis of geometric considerations (see Fig. 6.7), the following equation

for 𝜑 is valid:D − dD + p

= cos 𝜑 (6.45)

that is,

d = D(1 − cos 𝜑)1 + cos 𝜑

(6.46)

where d is the size of the largest particle that can be pulled in by the melangeur.

Example 6.4If D= 0.6 m, 𝜑=30∘ and cos𝜑=0.8660, then d=0.6× 0.0718≈0.04309 m=43.09 mm.

In the optimal case the ratio D/d is about 40, which determines the value of D

if d is given. The rolling of the cylinders (rollers) is slip free at their centre line,

but at the edges of the rollers, the slipping effect is strong, and this causes both

mixing and some comminution (see Fig. 6.7).

The peripheral velocity vm of the table at the centre line of a cylinder is

vm(m∕s) = 2π(

r + a2

) n60

(6.47)

where n is the revolution rate (min−1) of the table, r is the distance (m) of the

inner edge of the cylinder from the centre of the rotating table and a is the length

(m) of the surface of the cylinder. It can be assumed that there is no slip at the

centre line, that is,

vm = peripheral velocity of cylinder (6.48)

The peripheral velocity vi of the table at the inner edge of a cylinder is

vi (m∕s) = 2𝜋rn60

(6.49)

and the peripheral velocity ve of the table at the external edge of a cylinder is

ve(m∕s) = 2𝜋(r + a)n60

(6.50)

The maximum slip relative to vm is

w = ve − vm = vm − vi =(ve − vi)

2= 𝜋an

60(6.51)

If P is the pulling force (N) at the centre line of a cylinder, and 𝜇 is the friction

coefficient, then the P(N) friction force is

P = 𝜇K (6.52)

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Comminution 283

and the power balance (W1) for one cylinder is

W1 = Pw (6.53)

W1 = 𝜇K𝜋an∕60 (6.54)

Since a melangeur has two cylinders, the power required to overcome friction

for the two cylinders is

W2 = 2W1 = 𝜇K𝜋an∕30 (6.55)

Example 6.5If the surfaces of the rollers have a length a= 0.9 m, and n=12 min−1,

K=3× 104 N and 𝜇= 0.35, then from Eqn (6.55),

N = K𝜇𝜋an

30= 3 × 104 × 0.35 × 3.14 × 0.9 × 12

30= 11.87 kW

It should be emphasized that N is the power requirement of friction only; the total

power requirement of a melangeur contains additionally the power consumption

for moving the machine.

To determine n (the revolution rate of the table), we suppose that the frictional

force mg𝜇 on a particle must exceed the centrifugal force originating from the

revolution of the cylinder:

mg𝜇 >mv2

m

𝜌(6.56)

where 𝜌= r+ a/2 is the radius of the cylinder from the centre of the table at the

centre line. The value of n is then obtained from

√g𝜇𝜌 > vm = 2𝜋

(r + a

2

) n60

(6.57)

that is,30

√g𝜇𝜌

𝜋(r + a∕2)> n (6.58)

Example 6.6The parameters of a melangeur are r= 0.3 m, a= 0.9 m and 𝜇= 0.35. Let us cal-

culate the maximum revolution rate n (min−1) of the table.

𝜌 [m] = r + a2= 0.3 + 0.9

2= 0.75 m

From Eqn (6.58) (using that numerical 𝜋 ≈√

g),

n < 30 ×[√(0.35 × 0.785)]

0.75= 20.49 min−1 ≈ 1

3s−1

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284 Confectionery and chocolate engineering: principles and applications

6.11 Comminution by a stirred ball mill

Stirred (or agitated) ball (or pearl) mills became indispensable machines for com-

minution in cocoa processing and chocolate manufacture in the second half of

the 20th century. From the beginning it was clear that stirred ball mills were suit-

able for refining cocoa mass (cocoa liquor) if the cocoa nibs were pre-ground. The

question was whether they could refine milk chocolate, taking into considera-

tion the heat sensitivity of milk protein and the particular properties of sucrose

and lactose. Extensive research work has addressed these questions, examples of

which are Anonymous (1971, 1981, 1995), Niediek (1973, 1978), Bauermeister

(1978), Goryacheva et al. (1979), Shlamas et al. (1984), Lucisano et al. (2006) and

Alamprese et al. (2007).

For further details, see Hoepffner and Patat (1973), Hörner and Patat (1975),

Kirchner and Aigner (1979), Freiermuth and Kirchner (1981, 1983), Bühler

(1982), Kipke (1982), Stehr and Schwedes (1983), Rolf and Vongluekiet (1983),

Kersting (1984), Kirchner and Leluschko (1986), Weit and Schwedes (1986,

1988), Stehr (1989), Ulfik (1991) and Bunge and Schwedes (1992).

A frequently cited review of the mathematical modelling of grinding kinetics

was given by Austin and Bathia (1971/1972a).

6.11.1 Kinetics of comminution in a stirred ball millA simple kinetics of batch comminution in the micrometre and submicrometre

range (1–40 μm) was presented by Strazisar and Runovc (1996) on the basis of

experiments where barite, magnetite, dolomite and calcite in aqueous suspen-

sion were ground by a stirred ball mill, a vibratory mill and a planetary mill. These

authors interpreted the results of the grinding experiments using a cumulative

LN distribution

Q(d) =

(1√2𝜋

)

{exp

[−(1

2

)x2]}

dx (6.59)

where d is the particle size, x= (1/s) ln (d/d50) is a variable and s= ln(d84/d50) is

the standard deviation.

The dependence of d50 on the grinding time can be approximated by an expo-

nential equation,

d50(t) = d50(∞) + {d50(0) − d50(∞)} exp(− t𝜏

)(6.60)

where d50(t) is the median particle size at time t, d50(0) is the median particle

size of the feed material, d50(∞) is the expected median particle size after a long

grinding time and 𝜏 is the characteristic time. For further details, see Dück et al.

(2003).

Example 6.7The particle size of the input cocoa mass into a stirred ball mill is d50(0)= 120 μm;

after t= 60 s, the particle size of the output is d50(t)= 50 μm; and the probable

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Comminution 285

value of d50(∞) is 50 μm. Let us calculate the value of the characteristic time 𝜏 of

this stirred ball mill.

From Eqn (6.60),

In( 50 − 10

120 − 10

)= −1.0116 = −60 s

𝜏→ 𝜏 = 59.312 s

6.11.2 Power requirement of a stirred ball millAccording to Stiess (1994, Vol. 2, pp. 307–309), the power requirement of a

stirred ball mill can be expressed by means of the dimensionless Newton number

Ne = P𝜌Sn3d5

(6.61)

where P is the power requirement (W), 𝜌S is the density of the solid being com-

minuted (kg/m3), n is the rotation rate of the mixer (s−1) and d is the diameter of

the mixer (m). Since stirred ball mills work in the turbulent region, Ne is constant.

The effective energy requirement can be calculated using the formula

EV =P − P0

(dV∕dt)cV

(6.62)

where EV is the energy requirement per unit volume (J/m3), P0 is the power

requirement for free running (W), dV/dt is the volume flow of the suspension

(m3/s) and cV is the volume concentration of solids in suspension. We may also

write

Em =EV

𝜌S

(6.63)

where 𝜌S (kg/m3) is the density of the material being ground.

In the turbulent region, Ne= 𝜉 is independent of the Reynolds number and the

viscosity of the fluid, and the usual value of Ne is approximately 0.1–5 (Stiess,

1995, Vol. 1, p. 231). The value of Ne is more than unity if there are objects

bumping in the mixing space.

Weit and Schwedes (1986) gave a relationship between EV and the mean par-

ticle size x,

x =655 μm

E0.84V1

(6.64)

or

x =223 μm

E0.84V2

(6.65)

where x (μm) is a weighted mean particle size, calculated from the volume dis-

tribution as x= ∫ xq(x)dx between the boundaries x(min) and x(max), and EV1

(J/cm3) and EV2 (kW h/m3) are values of the volumetric energy requirement.

Comment: Equations (6.64) and (6.65) hold (and are equivalent) over a rather

broad range of parameters of the process (e.g. concentration of solid material,

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286 Confectionery and chocolate engineering: principles and applications

volume flow and particle size). Note that

1 kWh = 3.6 × 106 J, 1 m3 = 106 cm3 and655 μm

3.60.84≈ 223 μm

Example 6.8The power requirement of a pearl mill for refining cocoa mass is to be calculated

for a mean particle size after milling of 65.5 μm; P0 is 60% of the total power

requirement, dV/dt= 0.72 m3/h= 2×10−4 m3/s and 𝜌S =1100 kg/m3.

To calculate cV, we take the following data into account: the concentration of

cocoa solids in cocoa liquor is 45 m/m% and its density 𝜌S is 1100 kg/m3, and the

density of cocoa butter 𝜌B is 850 kg/m3. The volume (in litres) of 1 kg of cocoa

liquor is V=0.45/1.1+0.55/0.85=0.409+0.647= 1.056 l. Consequently,

cV = 0.4091.056

(V∕V) = 0.387

From Eqn (6.64),

65.5 μm =655 μm

E0.84V1

→ EV1 = 101∕0.84 = 12.6 × 106 J∕m3

From Eqn (6.62),

EV =P − P0

(dV∕dt)cV

P(1 − 0.6) = 12.6 × 106 J∕m3 × (2 × 10−4 m3∕s) × 0.387 = 0.97524 kW

P = 0.97524 kW0.4

= 2.4381 kW

Em =EV

𝜌S

=12.6 × 106 J∕m3

1100 kg∕m3= 11.45 kJ∕kg

6.11.3 Residence time distribution in a stirred ball millIn a continuously operated stirred ball mill, a two-phase mixture consisting of a dis-

persed solid and a continuous liquid phase is transported through a fixed cylinder

equipped with a stirring device. This formal similarity to a ball mill used for batch

processing leads us to choose an axial transport model for describing the trans-

port through the ball mill. The following treatment follows the method of Stehr

(1984).

The differential equation for the model of axial dispersion, with normalized

variables, is𝜕C𝜕𝜏

= − 𝜕C𝜕X

+( 1

Pe

)𝜕2C𝜕X2

(6.66)

where C= c/c0 is the normalized concentration of a tracer, c is the tracer concen-

tration at time t, c0 is the maximum concentration of the tracer, 𝜏 = t/tm is the

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normalized time variable, t is the time, tm is the mean residence time, X= x/L is

the relative position in the mill, x is the distance from the input, L is the length

of the grinding chamber, Pe= 𝜈mL/D is the Peclet number, 𝜈m is the mean axial

transport velocity and D is the axial dispersion coefficient.

The solid fraction of the feed suspension can itself be considered to be a tracer.

The first term on the right-hand side of the differential equation represents

convection and the second term represents diffusion, both related to the mean

axial transport velocity. To solve the differential equation, a close–close system

is assumed, although the ideal boundary conditions of a close–close system are

valid only if no dispersion occurs in the inlet and outlet regions. With regard to

the substantial difference between the cross-sectional areas of the pipes attached

to the inlet and outlet and the grinding chamber, it can be assumed that the

dispersion in the pipes, and hence at the boundaries of the system, is negligible.

Consequently, the model of a close–close system, where both convection and

dispersion occur, applies to the stirred ball mill.

Molerus (1966) pointed out that only the aforementioned conditions

(close-close system) does the concentration cimp(t) measured at the outlet yield

the residence time density distribution E(t) of an injected tracer of quantity q as

follows:

E(t) =(

dVdt

) cimp(t)q

(6.67)

where dV/dt is the flow rate. In addition, Molerus pointed out that the transport

coefficients in the differential equation can be determined using the first and

second moments of the residence time density distribution E(t):

𝜎2 = 𝜇(2) − {𝜇(1)}2 =(

2D

v3m

){1 −

(Dvm

)[1 − exp

(−

vmL

D

)]}(6.68)

where 𝜎2 is the variance. The zeroth moment is the normalization; 𝜇(1) = ∫ tE(t)dt

= tm is the first moment, defining the mean value of E(t); and 𝜇(2) = ∫ t2E(t)dt is

the second moment. (All of these integrals are evaluated from 0 to ∞.) Hence,

the mean axial transport velocity can be defined by

vm = Ltm

= L𝜇(1) (6.69)

From response data, E(t), 𝜇(1) = tm, 𝜇(2), 𝜎2 and D can be calculated by iteration

from Eqn (6.68). For details, see Levenspiel (1972).

Stehr (1984) determined a relationship between the stirrer parameters and the

Peclet number, referring to the residence time distribution of a single-phase flow

in rotating-disc contactors:

Pe =vmL

D= 6

1 + 1.33 × 10−3dRSn∕vm

(6.70)

where dRS is the diameter of the discs in the grinding chamber and n is the num-

ber of discs. In the investigations of Stehr (1984), the range of the dimensionless

number dRSn/𝜈m was 419–6534, that is, the range of Pe was 3.854–0.619.

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288 Confectionery and chocolate engineering: principles and applications

Example 6.9Let us calculate the residence time distribution in a rotating-disc contactor for

the following parameters: L= 1.5 m, 𝜈m =0.01 m/s, n=14 and dRS = 0.4 m.

From Eqn (6.69),

vm = 0.01 = 1.5𝜇(1) → 𝜇(1) = 150 s

From Eqn (6.70),

Pe =vmL

D= 6

1 + 1.33 × 10−3dRSn∕vm

= 6

1 + 1.33 × 10−3 × 0.4 × 14∕0.01≈ 3.44

Pe =vmL

D= 3.44 = 0.01 × 1.5

D→ D = 4.36 × 10−3 m2∕s

From Eqn (6.68),

𝜎2 = 𝜇(2) − {𝜇(1)}2 =(

2D

v3m

){1 − D

vm

[1 − exp

(−

vmL

D

)]}

=(

2 × 4.36 × 10−3

10−6

)× {1 − 0.436 × [1 − exp(−3.44)]}

= 8.72 × 10−3{1 − 0.436 × (1 − 0.033)} = 3.68 × 10−3 s2

6.11.3.1 Effect of comminution behaviourUp to now, studies of stirred ball mills have concerned their use as stirrers. In

order to determine the grinding effect of a stirred ball mill, it can be assumed that

the result of comminution for a differential amount of material is a function of

residence time only. Hence, the particle size distribution of the product obtained

in the continuous mode is calculable, using the residence time distribution of the

total amount of material. In addition, the results of batch-grinding experiments

are required.

In principle, the calculation can be accomplished using the equation

Qcont(S) = ∫Qbatch(t; S) × E(t)dt (6.71)

where Qcont is the cumulative mass percentage finer than the stated size S in

continuous mode, and Qbatch is the corresponding quantity for the batch mode.

Equation (6.71) expresses the essence of this calculation method: the cumulative

mass percentage finer than a given particle size is constructed from the cumu-

lative particle size distribution data for the batch mode and the residence time

distribution.

For details, see Stehr (1984), and for the modelling of comminution in a stirred

ball mill, see Bernhardt et al. (1999) and Schwedes (2003).

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Comminution 289

Further reading

Atiemo-Obeng, V.A., Penney, W.R. and Armenante, P. (2003) Solid–liquid mixing, in Handbook

of Industrial Mixing: Science and Practice (eds E. Paul, V.A. Atiemo-Obeng and S.M. Kresta),

Wiley Interscience, pp. 543–584.

Bauermeister (Probat Group). Technical brochures.

Beckett, S.T. (ed.) (1988) Industrial Chocolate Manufacture and Use, Van Nostrand Reinhold, New

York.

Beckett, S.T. (2000) The Science of Chocolate, Royal Society of Chemistry, Cambridge.

Erdem, A.S., Ergün, L. and Benzer, H. (2004) Calculation of the power draw of dry

multi-compartment ball mills. Physicochemical Problems of Mineral Processing, Fizykochemiczne

Problemy Mineralurgii, 38, 221–230.

FrymaKoruma. Technical brochures.

Kempf, N.W. (1964) The Technology of Chocolate, Manufacturing Confectioner Publishing Co.,

Glen Rock, NJ.

NETZSCH. Technical brochures.

Nopens, I. and Biggs, C.A. (2005) Advances in Population Balance Modelling, Elsevier, Oxford.

Posner, E.S. and Hibbs, A.N. (2005) Wheat Flour Milling, 2nd edn, American Association of Cereal

Chemists, St Paul, MN.

Pratt, C.D. (ed.) (1970) Twenty Years of Confectionery and Chocolate Progress, AVI Publishing, West-

port, CT.

Remény, K. (1974) The Theory of Grindability and the Comminution of Binary Mixtures, Akadémia

Kiadó, Budapest.

Wieland, H. (1972) Cocoa and Chocolate Processing, Noyes Data Corp, Park Ridge, NJ.

Williams, S.H., Wright, B.W., Troung, V.D. et al. (2005) Mechanical properties of foods used

in experimental studies of primate masticatory function. American Journal of Primatology, 67,

329–346.

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CHAPTER 7

Mixing/kneading

7.1 Technical solutions to the problem of mixing

Mixing is any process that increases the randomness of the distribution of two

or more materials with different properties. In practice, mixing can take place

between solids, between liquids, between solids and liquids, or between other

combinations. In certain cases, gases, particularly air, can be incorporated, either

intentionally or accidentally.

Mixing can be obtained by any one of the following techniques:

• The ingredients are placed in a vessel that is rotated or tumbled, subjecting the

ingredients to a variety of motions. The blending of solids in double-cone, vee,

tumbler and mushroom-type mixers provides good examples.

• The ingredients are placed in a vessel in which an arm or an agitator stirs

the mass. Examples are provided by stirred tanks for making liquid mixtures,

kneading machines for mixing bread or cookie doughs, mixers for solids or

pasty materials, and ribbon and screw mixers.

• The mixture of ingredients is pumped through an orifice, valve, nozzle or other

static device, which causes mixing. Examples are provided by the homogeniza-

tion of milk and the blending of pastes with static mixers.

In all cases, the operation can be carried out in discrete batches or continu-

ously by feeding the separate (or partially premixed) ingredients to the mixer

and continuously withdrawing the mixed product.

The mixing is caused by splitting of the flow at the beginning of each mixingelement, by changes in flow direction caused by alternate right- and left-handed

helices and by acceleration and deceleration of a fluid as boundary layers are

built up and destroyed at the beginning and end of each element.

7.2 Power characteristics of a stirrer

According to dimensional analysis, the power consumption P of mixing can be

calculated using a function Ne= f(Re), where

P𝜌d5n3

= Ne (Newton number) (7.1)

d2nv

= d2n𝜌

𝜂= Re (Reynolds number for mixing) (7.2)

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290

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Mixing/kneading 291

Here 𝜌 is the density of the fluid (kg/m3), d is the diameter of the mixing element

(m), n is the characteristic velocity of mixing (s−1), 𝜈 is the kinematic viscosity of

the fluid (m2/s) and 𝜂 is the dynamic viscosity of the fluid (kg/m s).

The determination of the function Ne= f(Re) is an experimental task. If Re<20,

then Ne×Re= constant. This is in the laminar flow region. If Re> 50 (for a vessel

with baffles) or Re>5× 104 (for an unbaffled vessel), then Ne= constant. This is

in the turbulent flow region.

Stiess (1995, Vol. 1, pp. 228–231) gave a general characterization of the rela-

tionship between Ne and Re for mixing. Three regions can be distinguished:

1 In the laminar region (Re≈ 10–50),

Ne =KI

Re(7.3)

where KI ≈ 50–150 depending on the type of mixer.

2 In the transitional region (Re≈ 150–1000),

Ne =KII

Rem(7.4)

where 0<m< 1. The boundaries of the transitional region and the value of

KII vary to a great extent depending on the type of mixer.

3 In the turbulent region (Re> 1000 in general),

Ne = KIII = constant ≈ 0.1 − 0.5 (7.5)

For a baffled mixer, Ne is higher than for an unbaffled one.

The number Ne and the Euler number Eu are closely connected with each

other (sometimes the Newton number is called the modified Euler number):

Eu=pressure force/inertial force

Ne=drag force/centrifugal force

The influence of baffles is nil in the laminar flow region but extremely strong

at Re>5× 104. The installation of baffles under otherwise unchanged operating

conditions increases the stirrer power.

Reher (1969) dealt in detail with the power requirements of mixing for blade,

turbine and spiral impellers, taking into account the effect of the geometric con-

ditions as well. His results can be summarized by the formula

Ne = CReu(H

D

)v(Dd

)w

(7.6)

where Ne= P/n3d5𝜌; Re= 𝜌nd2/𝜂rep (where 𝜂rep is the representative viscosity; see

Section 7.4); u, v and w are exponents; H is the height of the fluid level (m); D is

the inner diameter of the tank (m) and d is the diameter of the impeller (m).

For a blade impeller:

C= 82.8

u=−1 if 2.3×10−5 <Re<5

v= 0.19 if 0.7<H/D< 1.25

w=0.685 if 1.363<D/d< 2.00

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292 Confectionery and chocolate engineering: principles and applications

For a turbine impeller:

C= 36.4

u=−1 if 1.4×10−5 <Re< 7

v= 0.43 if 0.9<H/D< 1.3

w= 0.52 if 1.743<D/d<2.56

For a spiral impeller:

C= 48.7

u=−1 if 1.2×10−4 <Re< 1

v= 0.59 if 0.7<H/D< 1.25

w= 0.423 if 1.82<D/d<3.33

For further types of impeller, see Reher (1970).

7.3 Mixing time characteristics of a stirrer

Zlokarnik (1991) obtained the following formula using dimensional analysis:

n𝜃 = f (Re, Sc) (7.7)

where 𝜃 is the mixing time (s), Sc= 𝜈/D is the Schmidt number, n𝜃 is the char-

acteristic time of mixing (dimensionless) and the function f is to be determined

experimentally.

7.4 Representative shear rate and viscosity for mixing

For ideal Newtonian fluids, the viscosity 𝜂 is independent of the shear rate D;

therefore, the calculation of the Reynolds number is simple (Re= dv𝜌/𝜂) since

the shear rate, which is a function of v, has no effect on 𝜂.

A representative viscosity 𝜂rep is used if the viscosity 𝜂 depends on the shear rate

or stress. At the working point, the coordinates of the flow curve 𝜏 = f(𝜂; D) are

𝜏w and Dw, and, by definition (Fig. 7.1),

𝜂rep =𝜏w

Dw

(7.8)

For real Newtonian fluids, the Reynolds number is defined by Eqn (7.2) using

the representative viscosity 𝜂rep instead of 𝜂 (Riquart, 1975).

7.5 Calculation of the Reynolds number for mixing

For the mixing of ideal Newtonian fluids, the Reynolds number can be calculated

from Eqn (7.2). For Ostwald–de Waele fluids, the corresponding flow curve is

𝜏 = KDm (7.9)

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Mixing/kneading 293

Flow curve

Working point

Shear

str

ess (τ)

Shear rate DDw

τ

τw

α

Figure 7.1 Definition of representative viscosity.

where K is a constant (kg m−1 s−(2+m)) and m is the flow index. The representative

viscosity at the working point is

𝜂rep = 𝜏

D= KDm

D= KDm−1 (7.10)

The value of D (the shear rate) for mixing is calculated using the formula

D = ksn (7.11)

where n is the revolution rate and ks is a constant value that is characteristic of

the type of impeller used. For the leaf impeller, disc impeller and propeller mixer,

ks = 11 (7.12)

in the case of viscoelastic fluids, and

ks =22s2

s2 − 1(7.13)

in the case of dilatant fluids, where s= dt/dm, dt is the inner diameter of the tank

and dm is the width of the impeller.

For the anchor impeller,

ks = 9.5 + 9s2

s2 − 1(7.14)

For the spiral impeller,

ks = 4𝜋 (7.15)

In the case of viscoelastic fluids, 0.512≤m (Reher, 1970).

Example 7.1Let us calculate the value of Re for a viscoelastic fluid mixed using a spiral

impeller.

According to Eqns (7.11) and (7.15), D = ksn = 4𝜋n.

According to Eqn (7.10), 𝜂rep = KDm−1 = K(4𝜋n)m−1.

According to Eqn (7.2), Re = nd2m𝜌∕𝜂rep = nd2

m𝜌(4𝜋n)1−m∕K.

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294 Confectionery and chocolate engineering: principles and applications

7.6 Mixing of powders

7.6.1 Degree of heterogeneity of a mixtureA peculiarity of the mixing of powders is that it can be more complicated to

achieve the required homogeneity of the mixture than is the case for the mixing

of gases or liquids with each other or the mixing of liquids with solids. Therefore,

the degree of homogeneity and the rate of mixing are important technological

parameters in the mixing of powders.

Among the most objective procedures for estimating the degree of homogene-

ity, and among the simplest, are those of Hixson and Tenney (1935) and Coulson

and Maitra (1950), which consist of collecting a given number of samples from

time to time and determining by inspection the number or fraction of each set of

samples that appears to be homogeneous. Very often, however, it is preferable to

analyse random samples of a predetermined constant mass. Whatever the pro-

cedure used, the degree of heterogeneity is expressed conveniently by either the

variance or the standard deviation.

A thorough review of the topic of the mixing of solids has been given by

Muzzio et al. (2003).

7.6.1.1 Homogeneity: effectiveness of mixingThe effectiveness of mixing can be expressed by the duration of mixing neces-

sary to reach a given homogeneity. The usual degrees of homogeneity are 75%,

90% and 95%, where, for example, 75% means that the difference from the

final value of the concentration is ±25% (and 90% and 95% mean differences

of ±10% and ±5%, respectively) and 𝜏75 means the time (s) taken for a homo-

geneity of 75% to be reached.

According to Hoogendoorn and Den Hartog (1967), the product n𝜏75 definitely

decreases if the Reynolds number is increased. Also, the use of a leading tube

strongly improves the effectiveness of mixing, and it holds in general that

n𝜏75 ≈ 140 (7.16)

where n is the rotation rate.

The true variance is obtained from the expression

𝜎2 = (N − 1)−1∑

(x − xm)2 (7.17)

where xm is the true value of the mean concentration of a constituent and x

is each of the values obtained by analysing each of the N samples. If the true

value of the mean concentration is not known, the experimental variance is used,

that is,

s2 = (N − 1)−1∑

(x − xe)2 (7.18)

where xe is the arithmetic mean of the results obtained. An evident measure of

homogeneity is

M = 1 − 𝜎

xm

or M = 1 − sxe

(7.19)

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Mixing/kneading 295

If M= 0.50, the mixture is not yet homogeneous. If V= s/xe = 0.05, the homo-

geneity may be sufficient for a given purpose. Here V is the variance coefficient,

that is,

M + V = 1 (7.20)

Precautions must be taken that the samples are collected completely at ran-

dom; during sampling, one must also endeavour not to enhance the mixing,

which would distort the results obtained for subsequent samples.

It is important to note that there is a fundamental difference between a uniform

distribution, corresponding to a theoretical variance of zero, and a random distri-

bution, for which the variance tends towards a final limiting value, designated by

𝜎2r , which can always be determined experimentally. For liquids or gases, where

mixing takes place at a molecular level, a random distribution leads very nearly

to a uniform distribution for any sample of the size that is normally encountered

in analysis.

In summary, the quality of mixing can be determined by:

• Estimating the proportion of samples that appear homogeneous

• Determining the variance or standard deviation by analysis of samples of fixed

size

• Determining the mass of the sample which must be taken in order to have a

chosen standard deviation

In addition, the degree of heterogeneity can be estimated by other procedures,

such as by determination of the amount of contact area between phases or deter-

mination of the droplet size in the case of emulsions. For further details, see Hiby

(1979) and Söderman and Laine (1990).

7.6.1.2 Range prescriptionThe simplest way to characterize the homogeneity of a component i is to prescribe

a range within which the concentration xi of this component will be found when

the mixing is stopped, that is,

xi min ≤ xi,j ≤ xi max (7.21)

If n samples (labelled by j= 1, … , n) are taken at different points in time, with

concentrations xi,j, all n samples have to meet this requirement.

7.6.1.3 Prescription of ratio of componentsThe standard deviation itself cannot characterize the ratio p/q of two compo-

nents (of concentrations p and q). If we take n samples at different points in time

(labelled by j= 1, 2, …), the ratios of them will be pi/qi where i= 1, 2, … , n, and

the mean value Xj of these ratios is given by

Xj =(1

n

)∑(pi

qi

)

j

, i = 1,2, … ,n and j = 1,2, … (7.22)

where j is the serial number of the sample.

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296 Confectionery and chocolate engineering: principles and applications

If the quality requirement is that the difference between the planned value of

p/q and Xj cannot be more than w%, then mixing has to be carried on until

|||||1 −

Xj

p∕q

|||||<

w100

(7.23)

where p/q is the prescription in the recipe (the planned value).

7.6.1.4 Rate of mixingThe driving force for mixing is the degree of heterogeneity, 𝜎2 − 𝜎2

r . The rate

of mixing depends on this driving force and on a rate coefficient k, which is

characteristic of the equipment and the material being mixed.

An equation proposed by Oyama (see Weidenbaum, 1958) is

d𝜎2

dt= −k(𝜎2 − 𝜎2

r ) (7.24)

or, integrated,

ln

(𝜎2

0 − 𝜎2r

𝜎2 − 𝜎2r

)= kt (7.25)

where 𝜎20 is the initial variance. By definition, the rate coefficient k (s−1) is con-

stant for a given product in a given apparatus. It must be measured experimen-

tally, for example, as a function of the rate of rotation.

7.6.1.5 Separation during mixing of powdersThe results of mixing can sometimes be influenced by factors that are difficult

to foresee. For example, during the mixing of certain powders, stratification can

take place, where the larger particles come to the surface or separation of particles

of different density occurs if the mixing is prolonged. In certain cases, especially

for pastes, the addition of very small quantities of additives such as surface-active

agents can radically modify the rate coefficient. There is a simple model that takes

separation during mixing into consideration.

The differential equation in this model is

dMdt

= A(1 − M) − BΦ (7.26)

where M is the measure of homogeneity according to Eqn (7.19), Φ is the

potential of separation (≤1, possibly negative; see Eqn (7.29)), A is the coef-

ficient of mixing and B is the coefficient of separation. The following relation

applies:

M = 1 − Φ2 (7.27)

If the heavier component is the upper one (Φ is positive),

M = 1 −{(1 − r) exp

(−At

2

)+ r

}2

(7.28)

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Mixing/kneading 297

If the heavier component is the lower one (Φ is negative),

M = 1 −{

r − (1 + r) exp(−At

2

)}2

(7.29)

where t is the duration of mixing (s) and r=A/B. Equations (7.28) and (7.29) are

the integrals of Eqn (7.26).

The actual circumstances in mixing processes are slightly different, and,

according to Rose (1959a,b), this can be taken into account by an internal

degree of efficiency 𝜒 , which characterizes the equipment:

if t → ∞, M → M(equivalent) = 𝜒(1 − r2) (7.30)

For further details, see Sommer (1975).

Example 7.2Let us calculate the velocity constant k of mixing supposing that Eqns (7.16)

and (7.25) are valid for the mixing process used; in addition, 𝜎0/xm = 0.8,

𝜎r/xm = 0.02, 𝜏75 ↔ 𝜎75/xm =0.25 and n= 0.5 s−1:

ln

(𝜎2

0 − 𝜎2r

𝜎2 − 𝜎2r

)= ln

(0.82 − 0.022

0.252 − 0.022

)= 2.332 = k𝜏75

From Eqn (7.16),

n𝜏75 ≈ 140, 𝜏75 ≈ 140∕0.5 = 280s → k = 2.332∕280 s = 8.33 × 10−3 s−1

In addition, we can calculate the value of 𝜏95 according to Eqn (7.25):

ln

(𝜎2

0 − 𝜎2r

𝜎2 − 𝜎2r

)= ln

(0.82 − 0.022

0.052 − 0.022

)= 5.719 = 8.33 × 10−3 × 𝜏95 → 𝜏95 = 686.6 s

7.6.2 Scaling up of agitated centrifugal mixersIt is nearly impossible to formulate generalized scaling-up equations for the

mixing of solids. However, extensive experimental investigations conducted

by Scheuber et al. (1980), Merz and Holzmüller (1981) have resulted in the

following useful criteria. Two regions are demarcated by a Froude number of 3.

The improvement in mixing coefficient for a given mixer at Fr> 3 is dramatic.

The coefficient of mixing M proposed by Müller is a parameter used in his

semi-empirical one-dimensional model of horizontal mixers. This mixing coeffi-

cient determines how quickly concentration equalization will occur in a mixer.

A large mixing coefficient will result in a short mixing time for a given quality

of mix. The mixing coefficient is assumed to remain constant at all points in the

mixer for the duration of the mixing process. It should be noted that M depends

on the type of mixer, the geometry of the internal components and the operating

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298 Confectionery and chocolate engineering: principles and applications

conditions, but it does not depend on the properties of the components of the

mixture (e.g. size or density).

If Fr < 3, thenM

D2n= constant (7.31)

If Fr > 3, thenM

D2n≈ Fr2 (7.32)

where D (m) is the diameter of the mixer, n (rpm) is the revolution rate and Fr,

the Froude number, is defined as

Fr = v2

gR= R𝜔2

g(7.33)

where v (m/s) is the peripheral velocity of the mixing element (plough, paddle,

etc.), R (m) is the mixer radius (=D/2), 𝜔 (rad/s) is the angular velocity of the

agitators and n=30𝜔/𝜋.

Two common approaches are used for scaling these mixers, assuming geomet-

ric similarity and the same quality of mixing:

1 Keep the peripheral speed constant between the pilot mixer and the full-scale

mixer, that is,n (pilot)

n (full scale)= R (full scale)

R (pilot)(7.34)

2 Keep the Froude number constant between the pilot mixer and the full-scale

mixer, that is,

n (pilot)n (full scale)

=

√R (full scale)

R (pilot)(7.35)

Both of these approaches are used by mixer equipment manufacturers, and

this suggests that more research and development are required to increase our

understanding of the mixing processes of solids.

It is common practice to use a Froude number of 7 for mixing non-friable mate-

rials. For friable materials, the effect of breakage caused by agitator impact must

be evaluated. Attrition is non-linear with impact velocity, whereas it is linear with

mixing time. Therefore, an optimum can be found through experimentation.

7.6.3 Mixing time for powdersRumpf and Müller (1962) have shown experimentally that the mixing coefficient

can also be related to the mixer length L if the mixer diameter D is kept constant:

MtL2

= constant (7.36)

where M is the mixing coefficient, t (s) is the mixing time and L (m) is the mixer

length.

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Mixing/kneading 299

For Froude numbers below 3 and for geometrically similar mixers operating

at the same peripheral speed of the agitator, the mixing time increases linearly

with the mixer diameter:

t ∼( L

D

)2 Dv

(7.37)

At higher Froude numbers (>3), the mixing time is linear with the volume (not

the diameter) of the mixer. The effect of the agitator speed v is significant in this

range:

t ∼( L

D

)2 D3

v5(7.38)

7.6.4 Power consumptionA relationship between power consumption and Froude number for agitated

centrifugal mixers was given by Müller (1982). The power consumption is

expressed in a non-dimensional form using the Newton number Ne:

Ne = P𝜌s(1 − 𝜀)D5n3(L∕D)

(7.39)

where 𝜌s is the density of the mixture (kg/m3), 𝜀 is the voidage of the packed bed

and n (s−1) is the rotation rate. The Froude number Fr has the form

Fr = R𝜔2

g

where R is the radius of the mixer, 𝜔= 2𝜋n is the angular velocity and g is the

gravitational acceleration.

For Fr< 1, where the acceleration forces are relatively small and the material

is not fluidized or under plastic shear, the following relationship holds:

Ne ∼ 1Fr

(7.40)

At higher Froude numbers, the configuration of paddles/agitators (i.e. the rough-

ness and shape) and the size of the particles have a significant influence on the

shape of the curve of log Ne versus log Fr: the linear region in the plot becomes

curved.

Example 7.3A mixture of sugar and cocoa powder is being homogenized in a vessel, where

D=1 m, L= 1 m, 𝜀=0.3, 𝜌s =1350 kg/m3 and n= 90 min−1. What is the approx-

imate power requirement?

𝜔 = n𝜋30

= 3𝜋, n = 1.5s−1

Fr = R𝜔2

g= 0.5 × 9𝜋2

9.81≈ 4.5 (> 3)

Ne ≈ 4 (Müller, 1982)

P = 4𝜌s(1 − 𝜀)D5n3( L

D

)= 4 × 1350 × 0.7 × 1.53 = 12757.5W ≈ 12.6kW

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300 Confectionery and chocolate engineering: principles and applications

7.7 Mixing of fluids of high viscosity

According to Schmidt (1968), the flow pattern in the case of a propeller mixer

changes with the Reynolds number. If the viscosity is low and the Reynolds num-

ber is high (Re>104), a propeller mixer can work efficiently, since the mixer

generates an axial movement of the liquid and the flow pattern is determined

by the mass forces. If the viscosity is higher and the Reynolds number is lower

(103 <Re< 50), the flow rays generated by the propeller spread out in a radial

direction, since the effect of the viscous forces is increased. At high viscosity and

low Reynolds number (Re<20, in the laminar flow region), the axial flow disap-

pears entirely. Under these conditions the shape of the mixer has no importance,

but the size of it is important because this determines the volume of flow moved.

When a fluid of high viscosity is mixed, places can often be found in the tank

where the flow is very slow or does not develop, because the energy dissipation

caused by the viscous forces rapidly consumes the kinetic energy of the mixer

within a short distance from the mixer. According to Schmidt (1968), the effective

distance of a mixer can be expressed by the formula

R ≈ C

√P𝜂

(7.41)

where R is the effective distance of the mixer measured from the axle.

In the case of high viscosity, mixers work in the laminar flow region, and the

active region of mixing is decreased in size. Therefore, the geometric shape of the

mixing region and the mixer must be tailored to a specific objective: the basis of

achieving mixing efficiency is to increase the velocity difference between the

parts that are unmoved and moved. In this case mixers have to work on the

principle of volume displacement. For this reason, the mixer often fills almost

the whole volume of the tank: this ensures that the effective distance of the

mixer reaches every point of the tank.

There are batch and continuous agitators with various structural shapes,

and in both types there can be one or more mixers in the place where mixing

is done.

An important characteristic of the mixing fluids of high viscosity is that

the power requirement per unit volume is higher than in the case of lower

viscosity.

Further references for the making of suspensions and dispersions are Brauer

and Mewes (1973), Zielinski et al. (1974), Kale et al. (1974), Nagel and Kürten

(1976), Staudinger and Moser (1976), Einenkel (1979), Kipke (1979, 1985,

1992), Mersmann and Grossmann (1980), Becker et al. (1981), Koglin et al.

(1981), Herndl and Mershmann (1982), Kneuele (1983), Ebert (1983), Bertrand

(1985), Zehner (1986), Geisler et al. (1988), Xanthopoulos and Stamatoudis

(1988), Kraume and Zehner (1988, 1990), Pörtner and Werner (1989), Brauer

et al. (1989), Markopoulos et al. (1990), Fleischli and Streiff (1990) and Pörtner

et al. (1991).

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Mixing/kneading 301

Further references for helical screw agitators and for static and continuous

mixers are Chapman and Holland (1965), Henzler (1979), Riedel (1979), Pahl

(1985), Gyenis (1992) and Sarghini and Masi (2008).

Further references for the topic of the just-suspended speed in stirred tanks are

Zwietering (1958), Baldi et al. (1978), Volt and Mersmann (1985), Davies (1986),

Latzen and Molerus (1987), Mak (1992), Atiemo-Obeng et al. (2003), Ibrahim

and Nienow (1994) and Joosten et al. (1977).

Further references for the residence time distribution are Schönemann and

Hein (1993) and Schönemann et al. (1993).

7.8 Effect of impeller speed on heat and mass transfer

7.8.1 Heat transferDetailed discussions with a rich list of references have been given by Gaddis and

Vogelpohl (1991) and Sprehe et al. (1999)

The principal relationship for heat transfer is

Nu = C Rea Prb

(𝜂FL

𝜂W

)c

(7.42)

where Nu= 𝛼D/𝜆 (Nusselt number), 𝛼 is the heat transfer coefficient (W/m2 K),

D is the inner diameter of the vessel (m), 𝜆 is the thermal conductivity of the fluid

at the temperature in the centre (W/m K), Re= d2n𝜌/𝜂FL (Reynolds number), d is

the diameter of the impeller (m), 𝜂FL is the dynamic viscosity of the fluid at the

temperature in the centre (Pa s), n is the rotation rate (s−1), 𝜌 is the density of the

fluid at the temperature in the centre (kg/m3), Pr= 𝜈FL/a, 𝜈FL is the kinematic

viscosity of the fluid at the temperature in the centre (m2/s), a is the thermal

diffusivity of the fluid at the temperature in the centre (m2/s), 𝜂W is the dynamic

viscosity of the fluid at the temperature of the wall and a, b and c are exponents

depending on the conditions of mixing (construction of mixer, type of fluid, etc.).

The actual form of the relationship in Eqn (7.42) can be strongly influenced by

the type of impeller and fluid. Further discussion is beyond the scope of this book.

For further references, see Pawlowski and Zlokarnik (1972), Poggemann et al.

(1979), Kahilainen et al. (1979), Schulz (1979), Yüce and Schlegel (1990) and

Fingrhut (1991).

7.8.2 Mass transferThe diffusional mass transfer rate is affected primarily by the impact of agitation

on the hydrodynamic environment near the surfaces of the particles, in partic-

ular on the thickness of the diffusional boundary layer surrounding the solid

particles. The hydrodynamic environment near a particle surface depends on

the properties of the fluid and of the particles. In addition, the diffusivity DA also

influences the diffusional mass transfer.

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302 Confectionery and chocolate engineering: principles and applications

In general, the specific impact of agitation must be determined experimen-

tally for each system. The correlations (Sherwood number and Froessling type

equation) discussed in the following are presented to provide a guide to and some

insight into the expected effects of various variables on solid–liquid mass transfer.

Referring to solid–liquid mass transfer, several correlations for the quantity

kSL that appears in the Sherwood number have been reported in the litera-

ture. The following Froessling-type equation, developed by Nienow and Miles

(1978), is based on the theory of the slip velocity between a liquid and a solid

particle:

Sh = 2 + 0.44 Re1∕2 Sc0.38 (7.43)

where Sh= kSLd/DA is the Sherwood number (where DA is in m2/s), d is the

characteristic size of the particles (m), Re= 𝜌LV(s)d/𝜂L is the Reynolds number,

V(s) is the settling velocity or slip velocity (m/s), 𝜂L is the viscosity (Pa s) of

the fluid, Sc= 𝜂L/𝜌LDA = 𝜈L/DA is the Schmidt number and 𝜈L is the kinematic

viscosity (m2/s) of the fluid. This has proven useful for estimating kSL and for

establishing the effect of the properties of the solid and fluid and the effect of the

agitation parameters. The Froessling correlation is not applicable to solid–liquid

systems where the settling velocity or slip velocity is small, that is, where

V(s)≪ 0.0005 m/s.

For further details, see Nienow (1975), Baldi et al. (1978), Doriaswarmy and

Sharma (1984) and Davies (1986).

7.9 Mixing by blade mixers

Blade mixers are used with various deformable or plastic solids and high-

consistency pastes to achieve a kneading and mixing action accompanied by

heating or cooling. They are used for mixing the components of chocolate, soft

sugar confectioneries containing fondant mass, chewing/bubble gum, etc.

The process involves compressing the fluid mass flat, folding it over on itself

and then compressing it again. The material is usually torn apart, and high shear

is produced between the moving and stationary fluid elements. The mixing is

usually performed by two Z-shaped heavy blades rotating in opposite directions

at different speeds on parallel horizontal shafts.

The following formula was derived from dimensional analysis for highway

mixers:

N = 150 × d4.56 × n2.78 ×(𝛾

g

)0.78

× 𝜂0.22a (7.44)

where d is the diameter of the circle traced out by the blade (m), n is the rotational

velocity of the blade (rot/s) and 𝜂a is the apparent viscosity of the mixture (Pa s).

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Mixing/kneading 303

Example 7.4Let us calculate the approximate power consumption of a blade mixer with the

parameters d=0.5 m, n= 0.5 s−1 and 𝜂a = 30 Pa s.

We substitute these parameters into Eqn (7.44) and obtain N= 87.8 kW.

For approximate calculations of power, Kharkhutta et al. (1968) recommended

the following formulae:

If Q<1400 kg, then

N = 0.035Q (kW) (7.45)

where Q is the mass of the mix (kg).

If Q>1400 kg, then

N = 30 + 0.01Q (kW) (7.46)

For details of the measurement of the performance of blade mixers, see

Cheremisinoff (1988, pp. 788–790).

Example 7.5Let us calculate the approximate power consumption for a batch of size

Q=250 kg.

According to Eqn (7.45), N= 8.75 kW.

7.10 Mixing rolls

Mixing rolls subject pastes and deformable solids to intense shear by passing them

between smooth or corrugated metal rolls that revolve at different speeds. These

machines are widely used in the cocoa, confectionery and biscuit industries. A

typical area of application is in five-roll refiners, which mix and comminute

chocolate paste at the same time.

The material enters the mixing rolls in the form of lumps, powder or friable

laminated material. As a result of rotation, adhesion and friction, the material is

entrained into the gap between the rolls, and upon discharge it sticks to one of the

rolls, depending on their temperature difference and velocities. The rolls are tem-

perature controlled. The rolling process is also influenced by the gap between the

rolls. Both the shearing action and the entrainment of material into the gap are

very important in the mixing process and in transporting the material through

the unit.

The hydrodynamic theory of mixing rolls was originally developed by von

Kármán (1925). For a detailed discussion of the mechanism governing the rolling

process, see Cheremisinoff (1988), who cites work by Bernhard (1962), Soroka

and Soroka (1965), Bekin and Nemytkov (1966) and Lukach et al. (1967).

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304 Confectionery and chocolate engineering: principles and applications

The power requirements of mixing rolls can be calculated on the basis of similar-

ity theory, and the type of formula obtained is

N = K𝛾𝜔DaLbhcf dB3 (7.47)

where K is a constant, 𝛾 is the specific weight, 𝜔 is the angular velocity, D is the

roll diameter, L is the length of the roll, h is the minimum gap between rolls

(cm), f is the friction and B is the batch weight. Equation (7.47) was obtained

in experiments on various types of plastic with the parameters h=0.6–2.6 mm,

v1 =6.28–18 m/s, f=1–3, L= 150–1050 mm and D= 200–400 mm. The expo-

nents obtained were a= 2 and 2.3, b= 0.6, c=0.1 and d=−0.2. No data have

been found by the author for the mixing rolls used in the confectionery industry.

For further details, see Section 14.2.3.

7.11 Mixing of two liquids

This is a typical task in the manufacture of emulsions. This topic was discussed

in Section 5.8.7.

Holmes et al. (1964) determined a formula called the Holmes–Voncken–Dekker

formula for baffled turbine-stirred machines, which are frequently used for pro-

ducing emulsions:

n𝜏

(dD

)2

≈ constant (7.48)

where 𝜏 is the mixing time (s) and n is the revolution rate (s−1). For geometrically

similar machines, d/D= constant, that is,

n𝜏 ≈ constant (7.49)

It is worth mentioning the formal similarity of Eqns (7.16) and (7.49): the former

refers to powders and the latter to emulsions.

Further reading

Baldyga, J. and Bourne, J.R. (1999) Turbulent Mixing and Chemical Reactions, Wiley, Chichester.

Baldyga, J., Bourne, J.R., Pacek, A.W., Amanullah, A., Nienow, A.W. (2001 ): Effects of agitation

and scale-up on drop size in turbulent dispersions: allowance for intermittency, Chem.Eng.Sci.,

56, 11, pp. 3377–3385

CABATEC (1992) Biscuit Mixing. Audio-visual open learning module, Ref. S10. The Biscuit, Cake,

Chocolate and Confectionery Alliance, London.

Gassis, E.S. and Vogelpohl, A. (1991) Wärmeübergang in Rührbehältern, in VDI-Wärmeatlas, 6th

Ma 1 edn, VDI-Verlag, Düsseldorf.

Kempf, N.W. (1964) The Technology of Chocolate, Manufacturing Confectioner Publishing, Glen

Rock, NJ.

Levins, D.M. and Glastonbury, J. (1972) Application of Kolmogoroff’s theory to particle-liquid

mass transfer in agitated vessels. Chemical Engineering Science, 27, 537–542.

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Mixing/kneading 305

Lienhard, J.H., IV and Lienhard, J.H., V (2005) A Heat Transfer Textbook, 3rd edn. Phlogiston

Press, Cambridge, MA.

Manley, D.J.R. (1981) Dough mixing and its effect on biscuit forming. Cake and Biscuit Alliance

Technologists’ Conference.

Manley, D.J.R. (1998) Biscuit, Cookie and Cracker Manufacturing Manuals, vol. 3, Biscuit Dough Piece

Forming, Woodhead Publishing, Cambridge.

McCarthy, J.J. (2009) Turning the corner in segregation. Powder Technology, 192, 137–142.

NETZSCH. (0000) Technical brochures.

Pabst, W. and Gregorová, E. (2007) Characterization of Particles and Particle Systems, ICT Prague,

Czech Republic.

Povey, M.J.W. and Mason, T.J. (1998) Ultrasound in Food Processing, Blackie Academic & Profes-

sional, London.

Pratt, C.D. (ed.) (1970) Twenty Years of Confectionery and Chocolate Progress, AVI Publishing, West-

port, CT.

Rohsenow, W.M., Hartnett, J.P. and Cho, Y.I. (eds) (1998) Handbook of Heat Transfer, 3rd edn,

McGraw-Hill Handbooks. McGraw-Hill, New York.

Sollich. (0000) Technical brochures.

Tanguy, P.A., Bertrand, J. and Xuereb, C. (2005) Innovative studies in industrial mixing pro-

cesses. Chemical Engineering Science, 60 (8–9), 2099.

Wade, P. (1965) Investigation of the Mixing Process for Hard Sweet Biscuit Doughs. Part I, Comparison

of Large and Small Scale Doughs. BBIRA Report 76.

Wade, P. and Davis, R.I. (1964) Energy Requirement for the Mixing of Biscuit Doughs under

Industrial Conditions. BBIRA Report 71.

Werner & Pfleiderer. (0000) Technical brochures.

Wieland, H. (1972) Cocoa and Chocolate Processing, Noyes Data Corporation, Park Ridge, NJ.

Yianneskis, M. (ed.) (2006) Fluid Mixing, 8th International Conference. Special issue. Chemical Engi-

neering Science, 61 (9), 2753–3052.

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CHAPTER 8

Solutions

8.1 Preparation of aqueous solutions of carbohydrates

8.1.1 Mass balanceThe first step in the manufacture of sugar confectionery is the preparation of

aqueous solutions of carbohydrates such as sucrose, starch syrup and invert

syrup. It is useful to study the mass balance for the case of two components,

Aa + Bb = x(A + B) (8.1)

where a is the concentration (m/m) of component A (mass A kg), b is the con-

centration (m/m) of component B (mass B kg) (m/m) and x is the resultant

concentration of the mixture. For example, if sugar (A) is dissolved in water (B),

then the sugar concentration of pure sugar is a= 1 and the (sugar) concentration

of water is b= 0, that is,

A × 1 + B × 0 = x(A + B) → x = AA + B

(8.2)

For a multicomponent mixture where the components are labelled by an index i,

∑mici = x

∑mi (8.3)

Sometimes the equation

(a − x)A = (x − b)B (8.4)

is more practical for calculations because it relates to differences in percentages.

An important property of Eqns (8.1) and (8.4) is that

a < x < b or a > x > b (8.5)

that is, the value of x is between those of a and b. The value of x can exceed

the values of a and b because of evaporation. Therefore, a more general mass

balance is

Aa + Bb = x(A + B − V ) (8.6)

where V is the mass of vapour (kg) that is extracted by evaporation from the mix-

ture. Equation (8.6) makes a common treatment of the operations of dissolution

and evaporation possible.

Confectionery and Chocolate Engineering: Principles and Applications, Second Edition. Ferenc Á. Mohos.© 2017 John Wiley & Sons Ltd. Published 2017 by John Wiley & Sons Ltd.

306

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Solutions 307

8.1.2 Parameters characterizing carbohydrate solutionsVarious types of concentrations are used:

1 Mass ratio concentration:

c =mass of dissolved material (kg)

100 kg of solution(8.7)

This is the most frequently used concentration; it is usually expressed as a mass

ratio (m/m) or as a mass percentage (m/m%). The latter is also referred to as

degrees Brix (see later).

2 The volume concentration v is used only rarely, but it is used for solutions con-

taining alcohol:

v = volume of dissolved material (l)100l of solution

(8.8)

3 Mixed concentration:

C =mass of dissolved material (kg)

100l of solution(8.9)

The use of this type of concentration is complicated because the density of the

solution is dependent on its solid content.

4 The Raoult concentration or molality (not molarity!) is defined as

m = number of dissolved moles1000 g of solvent

(8.10)

It is used in connection with the elevation of the boiling point (see Chapter 9)

and the depression of the freezing point of solutions, although the latter plays

hardly any role in the confectionery industry.

5 Degrees Baumé. The number Bé of degrees Baumé (symbol ∘Bé) is a kind of

concentration, although it has a close connection to the density of the solution

(denoted by d and expressed in g/cm3), measured at 20 ∘C and related to the

density of water at 4 ∘C. For solutions heavier than water, that is, if d>1 g/cm3,

then

d (g∕cm3) = 145145 − Be

(8.11)

For solutions lighter than water, that is, if d< 1 g/cm3, then

d (g∕cm3) = 140130 + Be

(8.12)

See Examples 8.1 and 8.2.

6 Degrees Brix. The number Bx of degrees Brix (symbol ∘Bx) is a measurement of

the mass ratio of dissolved sucrose to the mass of aqueous sugar solution; for

example, a 25∘Bx solution contains 25 g of sucrose per 100 g of solution. The

number of degrees Brix can be approximated as

Bx = 261.3 − 261.3d

= 261.3(

1 − 1d

)(8.13)

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308 Confectionery and chocolate engineering: principles and applications

where d (>1) is the density (g/cm3) of the sugar solution measured by a refrac-

tometer at 20 ∘C. After some algebraic transformation, we obtain the following

result from Eqns (8.11) and (8.13) for heavy solutions:

d = 261.3261.3 − Bx

= 145145 − Be

that is,

Bx = 261.3145

Be = 1.8021Be (8.14)

It should be emphasized that Eqn (8.14) is only an approximation, but it can

sometimes be used for engineering purposes. The exact relations between

degrees Brix and Baumé (at 68 ∘F= 20 ∘C) are given in Appendix 2; for

a detailed scale (at intervals of 0.5∘B), see Meiners et al. (1984, Vol. 1/I,

p. 11).

Example 8.1Sugar solutions are heavy. If Bé=18∘, then

d = 145145 − 18

= 1.1417 g∕cm3

Example 8.2If the concentration of an alcoholic solution (light) is 18∘Bé, then

d = 140148

= 0.8459 g∕cm3

8.2 Solubility of sucrose in water

An essential point in relation to the preparation of sugar solutions is the solu-

bility of sugar in water at given temperatures. Table A1.5 gives the solubility of

sugar and the density of saturated sugar solutions as a function of temperature

(Antokolskaja, 1964).

According to Junk and Pancoast (1973), the concentration of a saturated

sucrose/water solution as a function of temperature (in the interval 0–100 ∘C)

can be approximated by the following formula (at atmospheric pressure):

c = 64.397 + 0.07251t + 0.0020569t2 − 0.000009035t3 (8.15a)

where c is the amount of dissolved sucrose (g) per 100 g of saturated solution and

t is the temperature (∘C) of the solution.

Vavrinecz (1955a,b) proposed the following formula:

c = 64.347 + 0.10236t + 0.001424t2 − 0.000006020t3 (8.15b)

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Example 8.3From Table A1.5, a saturated aqueous solution contains 260.4 g of sucrose

per 100 g of water at 50 ∘C. According to Eqn (8.15a), when t= 50 ∘C,

c=74.294125 g/100 g saturated solution, that is, 25.705875 g of water dissolves

74.294125 g of sucrose= 289.0161 g sucrose/100 g water. The difference shows

the incorrectness of Eqn (8.15a): 289.0161/260.4= 1.1099 …, that is, an error

of ≈11%!

Under similar conditions, Eqn (8.15b) results in c=73.9745 g of sucrose

in (100− 73.9745)=26.0255 g of water, that is, 284.2385 g sucrose/100 g

water (instead of 260.4 g). The error is a little less: 284.2385/260.4=1.0915…(≈9.2%).

8.2.1 Solubility number of sucroseFor saturated sucrose solutions, the solubility number, denoted by 𝜎, is defined as

𝜎 = mass of dissolved substancemass of solvent

(8.16)

For example, from Table A1.6 the concentration of saturated sugar/water solu-

tion at 30 ∘C is 68.7%. Since the amount of water is (100− 68.7)%= 31.3%, the

solubility number is 𝜎 = (68.7/31.3)×100=219.49.

For further details, see Sokolovsky (1958) and Maczelka (1962).

8.3 Aqueous solutions of sucrose and glucose syrup

Starch syrup is usually characterized by two parameters: the dry content D and

the so-called dextrose equivalent DE – the reducing sugar content of the dry content

of the starch syrup expressed in terms of dextrose. A basic task in the manufac-

ture of sugar confectionery is the preparation of sucrose–starch syrup solutions

of given dry content and given reducing sugar content.

Example 8.4The usual parameters of starch syrup are D= 80% (m/m) and DE=40% (m/m),

which means that starch syrup contains 20% (m/m) water+ 80% (m/m) dry

content, and this dry content consists of 80%×0.40=32% reducing sugars

and 48% non-reducing sugars (carbohydrates): 100 kg starch syrup= 20 kg

water+ 32 kg reducing sugars+ 48 kg non-reducing sugars.

If the dry content is to be calculated, the mass balance is

Aa + BD = x(A + B) (8.17)

where A is the amount of sugar of concentration a and B is the amount of starch

syrup of dry content D.

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310 Confectionery and chocolate engineering: principles and applications

Example 8.550 kg of a sugar solution with a sucrose content a=75% and 40 kg of starch syrup

with D= 82% are mixed. The resultant dry content of the solution is

50 × 0.75 + 40 × 0.82 = x(50 + 40) x = 78.11 …%

Let us calculate the reducing sugar content of this solution. The reducing sugar

content of sucrose is practically zero: a= 0. The reducing sugar content of starch

syrup is determined by the value of DE. In this case we assume that DE=43, so

50 × 0 + 40 × 0.82 × 0.43 = xred(50 + 40) → xred = 15.671 …%

8.3.1 Syrup ratioA parameter commonly used to characterize sugar–starch syrup solutions is the

syrup ratio, which is expressed as follows, by definition:

Syrup ratio(SR) = 100 kg sugar∶ X kg starch syrup dry content (8.18)

Example 8.6If SR=100:50, then 100 kg sugar and 50 kg starch syrup dry content are dissolved

in the solution prepared.

The value of X used with advanced machinery (about 50–60) is higher than

that used with traditional machinery (about 30–40).

The syrup ratio and water content of the solution unambiguously determine

how to prepare an aqueous sucrose–corn syrup solution. The water content can

be prescribed in two ways: by the concentration (m/m%) or by the amount (kg).

(If another type of concentration is not specified, it should be assumed that it is

in mass per cent.)

Example 8.7If the water content of a solution is 20%, SR= 100 : 60 and DE= 38%, then

100 kg of solution consists of the following components:

20 kg water

80 kg dry content, which is divided according to SR as:

80×100/160= 50 kg sugar

80×60/160=30 kg starch syrup dry content

The reducing sugar content of the solution is 30 kg× 0.38= 11.4%.

It should be mentioned that, in addition to the 30 kg dry content of the starch

syrup, the starch syrup has a water content; if D= 80%, this water content is

30 kg× [(1/0.8)−1]=7.5 kg, which is included in the 20 kg of water.

Example 8.8If the amount of water W is 15 kg and the dry content is 90 kg, the solution

consists of the following components (assuming SR= 100 : 60 again):

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15 kg water

90 kg dry content, which is divided according to SR as:

90×100/160=56.25 kg sugar

90×60/160= 33.75 kg starch syrup dry content

The reducing sugar content of the solution is 33.75 kg× 0.38/(90+ 15)=12.214%. (The water content included in the starch syrup is 33.75 kg× [(1/0.82)

− 1]=7.41 kg water if D= 82%.)

Because the reducing sugar content of sugar–starch syrup solutions is an

important parameter in the technology of sugar confectionery, the following

general formula for its calculation is useful:

R = (1 − W ) × DESR + 1

(8.19)

where R is the reducing sugar content of the solution (%), W is the concentration

of water in the solution, DE is the dextrose equivalent of the starch syrup (%)

and SR is the syrup ratio. For the previous two examples, we have the following

results:

Example 8.7: if W=0.20 and SR=100 : 60= 1.66,

R = 0.8 × 38%2.66

= 11.42%

Example 8.8: if W=15/(15+ 90)=0.14029,

R = (1 − 0.1429) × 38%2.66

= 12.214%

8.4 Aqueous sucrose solutions containing invert sugar

A similar calculation needs to be done if invert sugar solution is mixed with sugar

solution or starch syrup. Invert sugar solutions can also be characterized by two

technological parameters: the dry content and the reducing sugar content.

Invert sugar is formed when sucrose is chemically split by acid (inverted):

sucrose (in presence of acids or invertase) → glucose + fructose

As a general rule, the inversion of sucrose is mostly regarded as undesirable in the

confectionery industry because the resulting fructose makes the product sticky.

However, there are special applications of invert sugar solutions in which the

strong hygroscopic property of fructose is exploited for conservation of the water

content against drying. In these cases, the correct way to use invert sugar is to add

invert sugar solution to the system, rather than to invert the sucrose content of

the system, because the control of inversion is difficult. For details, see Sections

2.2.2 and 16.1.

The main sources of invert sugar solution are fluid sugars. These fluid sugars are

prepared from acidic or enzymatic conversion of starch, which results in glucose,

and then the glucose is partly (or entirely) transformed to fructose by enzymatic

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312 Confectionery and chocolate engineering: principles and applications

catalysis. In an invert sugar solution prepared from sucrose, the proportion of

glucose to fructose is always 50 : 50; however, in fluid sugars, this proportion can

change according to the target use.

The calculations of the dry content and reducing sugar content of solutions

containing invert sugar are similar to those presented earlier, see Eqn (8.17), for

starch syrup.

8.5 Solubility of sucrose in the presence of starchsyrup and invert sugar

In the presence of both starch syrup and invert sugar, the solubility of sucrose

is decreased; however, the total dry content of the saturated solution is higher

than when sucrose alone is dissolved. This fact makes it possible to produce sugar

solutions of high dry content and, in the end, to produce sugar confectionery.

Table A1.12 gives solubility data for sucrose–starch syrup–water solutions

(Sokolovsky, 1958; p. 16) and Table A1.13 gives data for sucrose–invert

sugar–water solutions (Sokolovsky, 1958; p. 17). It can be seen that the presence

of invert sugar reduces the solubility of sucrose less than the presence of starch

syrup does, and, in addition, it increases the total soluble dry content of the

solution far more than starch syrup does. For example, at 50 ∘C the solubility

of sucrose is 260.36 g/100 g water, which changes under the effect of starch

syrup to 176.56 g sucrose+188.56 g starch syrup dry content (both values per

100 g water); however, under the effect of invert sugar, the values are 196.43 g

sucrose+ 253.2 g invert sugar (both values again per 100 g water).

It is evident from the solubility data that the amount of water required to dis-

solve sugar ingredients is more than the water content of sugar confectionery,

which ranges from 1.5 m/m% (for hard-boiled bonbons) up to 22 m/m%. Con-

sequently, the evaporation of surplus water is necessary. For example, at 20 ∘C,

100 g of water dissolves 257.89 g dry content (154.82 g sucrose+ 103.07 g starch

syrup dry content); however, the minimum water content of the saturated solu-

tion is about 27.94% at room temperature. To achieve evaporation, the solution

is warmed, and at higher temperatures the solubility of the dry components is

increased. A fundamental condition for successful evaporation is that while the

solution is becoming more and more concentrated, no component should start

to crystallize. Since the rate of evaporation is speeded up by mixing, the crystal-

lization of sucrose is a real danger if the syrup ratio is not high enough.

8.6 Rate of dissolution

The dissolution of solid substances is a process of diffusion. The process of disso-

lution can be accelerated by intensive mixing, which, on the one hand, disperses

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the solid particles in the solvent and, on the other hand, causes a turbulent flow

that reduces the thickness of the laminar boundary layer on the surface of the

particles, through which the movement of the soluble material into the solvent

is relatively slow.

The differential equation for the dissolution process is

dSdt

= kA(cSAT − c) (8.20)

where S is the mass of dissolved substance (kg), t is the time (s), k is the mass

transfer coefficient (m/s), A is the surface area of the soluble substance (m2), c

is the concentration of the solution (kg/m3) and cSAT is the concentration of the

saturated solution (kg/m3). If it may be assumed that S= Zc, where Z (m3) is a

constant, then

ln

(cSAT − c0

cSAT − cTERM

)=(

kAZ

)Δt (8.21)

where c0 is the concentration of the dissolved substance when t= 0, cTERM is the

concentration of the dissolved substance when t=Δt, Δt is the duration of the

process and A/Z is the specific surface area (1/m). The difficult question is the

need to suppose that A is constant, because the surface area of a substance that

is dissolving will not remain constant.

The mass transfer coefficient k can be calculated according to the Colburn–

Chilton analogy (see Section 1.4.2):

Sh = CReaScb (8.22)

where Sh is the Sherwood number (the Nusselt number for mass transfer), Re is

the Reynolds number, Sc is the Schmidt number= 𝜈/CD, a and b are exponents,

𝜈 is the kinematic viscosity of the solvent (m2/s) and CD is the diffusion coeffi-

cient of the solid substance (m2/s). The Sherwood and Reynolds numbers can be

calculated in various ways:

If the characteristic length (m) is the diameter d of an impeller,

Shi =kdCD

, Rei =d2n

v

If the characteristic length is the diameter D of a tank,

Sht =kDCD

, Ret =D2n

v

If the characteristic length is the mean equivalent diameter dp of the particles,

Shp =kdp

C, Rep =

dpv

v

where v is the peripheral velocity of the impeller (m/s).

Fejes (1970, p. 67) has reviewed studies of the various types of agitators for

different flow regions (see Table 8.1).

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314 Confectionery and chocolate engineering: principles and applications

Table 8.1 Constants in Eqn (8.22) according to type of impeller.

Type of mixer Characteristic lengths C a b Flow region

Propeller D d 0.66 0.667 0.3 4× 104 < Re<18× 104

Turbine, flat blade D d 3.3 0.55 0.3 2.3×104 < Re<11× 104

Turbine, oblique blade d d 0.625 0.62 0.5 7500<Re<6.7×105

Source: From Fejes (1970).

Example 8.9100 g of sugar is to be dissolved in 100 g of water at 20 ∘C; the particle size is

0.2 mm, and the particles are assumed to be homogeneously of cubic form. The

diameter d of the impeller of the mixer is 0.2 m, n= 1/s, and the diffusion constant

of sucrose is 2.5×10−10 m2/s (Rohrsetzer, 1986; p. 15).

We choose an impeller of the oblique blade turbine type. From Table 8.1,

C= 0.625, a=0.62 and b= 0.5, and hence

Rei =d2n

v= 0.22 × 1

10−6= 40000

Sc = 10−6

(2.5 × 10−10)

Shi = kd∕CD = k × 0.2∕(2.5 × 10−10)

= 0.625 × (40000)0.62 ×√

4000 → k = 3.52 × 10−5 m∕s

The surface area of a cubic particle is

A = 6 × (2 × 10−4 m)2 = 24 × 10−8 m2

The density of sugar is about 1500 kg/m3, thus the volume of 100 g of sugar is

Vsugar =66.67×10−6 m3. The volume of a cubic particle is v= 8×10−12 m3. Con-

sequently, 100 g of sugar consists of

N = V∕v = 66.67 × 10−6 m3∕8 × 10−12 m3 = 8.33 × 106 particles

the total surface area of which is

Atotal = (24 × 10−8 m2∕particle) × 8.33 × 106 particles ≈ 2 m2

In Eqn (8.21), c0 =0 and cTERM =100 g sugar in 100 g water; however, in

Eqns (8.20) and (8.21), the concentrations must be given in kg/m3. Since

cTERM =100/200= 50∘Bx, for this solution of cTERM concentration, we obtain

d= 1.2367 g/cm3 = 1236.7 kg/m3 density from Eqn (8.13).

We have 200 kg solution, the volume of which is (200/1236.7) m3 =0.1617 m3.

This solution contains 100 kg sugar, that is,

cTERM =100 kg

0.1617 m3= 618.43 kg∕m3

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Solutions 315

From Table A1.6,

cSAT =67.09 g

100 cm3= 670.6 kg∕m3 at 20 ∘C

From Eqn (8.21),

ln[670.6∕(670.6–618.43)] = 2.5537 = (kAtotal∕Z)Δt

Z = Vsugar + Vwater = (66.67 + 100) × 10−6 m3 = 166.67 × 10−6 m3

(For checking: S= Z c= 166.67×10−6 m3 ×618.45 kg/m3 =103 073 g, i.e. the sup-

position S= Z c approximately holds.)

From Eqn (8.21),

Δt = 2.5537 × Z∕(kAtotal)

= 2.5537 × 166.67 × 10−6 m3∕(3.52 × 10−5 m s−1 × 2 m2) ≈ 6 s

(It seems a too optimistic result.)

In practice, dissolving is accelerated by warming the solution.

8.7 Solubility of bulk sweeteners

The number of approved sweeteners has increased substantially in the last

three decades. Food product developers now have a number of sweeteners

from which to choose in order to provide more product choices to meet

the increasing demand for good-tasting products that have reduced calo-

ries. Some references on the applications of alternative sweeteners in food

technology: Grenby (1996), O’Brien-Nabors (2011), O’Donnell and Kears-

ley (2012). Confectionery applications of various polyols are discussed by

Belscak-Cvitanovic et al. (2010) – this study contains a lot of values of moisture

content (%), particle size range (μm), loose bulk density(kg/m3), wettability

(s), solubility (%), dispersibility (%) and cohesion index of sucrose, glucose,

fructose, trehalose, isomaltulose, erythritol, stevia, aspartame/acesulfame K

maltodextrin, inulin and oligofructose. On water solubility of polyols, a detailed

discussion is given by Evrendilek (2012) and Meiners et al. (1984), Vol. 2,

p. 587–603.

Because of volume reasons indicative solubility values of polyols can be given

here only:

The solubility of isomalt in water (t= 20–60 ∘C) can be described by the approx-

imative equation:

m (%) = 8.5 + 0.7975t (∘C) (8.23)

(On the basis of data given by Zentralblatt der Südzucker AG, Offstein, 1979,

published by Infopac, Palatinit Süssungs-mittel GmbH, ISOMALT, 5th ed.)

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316 Confectionery and chocolate engineering: principles and applications

Table 8.2 Melting point and water solubility of some

polyols.

Polyol Melting point (∘C) Solubility (m/m%), 25 ∘C

Erythritol 121 37

Xylitol 94 64

Mannitol 165 20

Sorbitol 97 70

Maltitol 150 60

Isomalt 145–150 25

Lactitol 122 57

Heat stability (∘C)>160; that is, they are available for baking.

Source: Adapted from Goossens and Gonze (2000).

Example 8.10If t= 40 ∘C, then the isomalt concentration is m= 40.4%.

If t= 25 ∘C → m= 28.4% (in Table 8.2: m= 25%; cautiously use data in refer-

ences!).

More detailed solubility data relating to the temperature dependence and data

concerning other physico-chemical properties (viscosity, compressibility, etc.) of

polyols can be found in the handbooks mentioned earlier.

Further reading

A.V.P. Baker. Technical brochures,

Alikonis, J.J. (1979) Candy Technology, AVI Publishing, Westport, CT.

Cakebread, S.H. (1975) Sugar and Chocolate Confectionery, Oxford University Press, Oxford.

Jónsdóttir, S.Ó., Cooke, S.A. and Macedo, E.A. (2002) Modeling and measurements of

solid-liquid and vapor-liquid equilibria of polyols and carbohydrates in aqueous solution.

Carbohydrate Research, 337, 1563–1571.

Lees, R. (1980) A Basic Course in Confectionery, Specialized Publications Ltd, Surbiton.

Lienhard, J.H., IV and Lienhard, J.H., V (2005) A Heat Transfer Textbook, 3rd edn. Phlogiston

Press, Cambridge, MA.

Meiners, A. and Joike, H. (1969) Handbook for the Sugar Confectionery Industry. Silesia-Essenzen-

fabrik, Gerhard Hanke K.G. Norf, Germany.

Pratt, C.D. (ed.) (1970) Twenty Years of Confectionery and Chocolate Progress, AVI Publishing, West-

port, CT.

Robert Bosch/Hamac. Technical brochures

Schwartz, M.E. (1974) Confections and Candy Technology, Food Technology Review, 12, Noyes, Park

Ridge, NJ.

Stephen, A.M., Phillips, G.O. and Williams, P.A. (2006) Food Polysaccharides and Their Applications,

2nd edn, Taylor & Francis Group, LLC, Boca Raton, London, New York.

Sullivan, E.T. and Sullivan, M.C. (1983) The Complete Wilton Book of Candy, Wilton Enterprises

Inc., Woodridge, IL.

Ter Braak. Technical brochures.

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CHAPTER 9

Evaporation

9.1 Theoretical background: Raoult’s law

For the theoretical background to the various formulae for the boiling-point

elevation and vapour pressure of aqueous solutions of carbohydrates such as

sucrose, dextrose, starch syrup and invert sugar, we need to study Raoult’s law.

This law states that the elevation Δtb of the boiling point of a solution is given by

Δtb = mΔtm;b (9.1)

where m, the so-called Raoult concentration or molality, is the number of dis-

solved moles per 1000 g of solvent and Δtm;b is the molar elevation of the boiling

point (in units of K/mol), given by

Δtm;b =RT2

b

1000Lb

(9.2)

that is,

Δtb =mRT2

b

1000Lb

(9.3)

where R, the universal gas constant, is equal to 8.31434 J/mol K; Tb (K) is the

boiling point of the solvent at the given pressure and Lb (J/1000 g solvent) is the

molar latent heat of vaporization of the solvent at the given pressure (Erdey-Grúz

and Schay, 1954; Vol. 2, p. 51; Lengyel et al., 1960; p. 73).

According to Raoult’s law, which is strictly valid only for dilute solutions, if 1 g

of a substance is dissolved in 1000 g of solvent, then

ΔtbΔtm;b

=g

M(9.4)

where M is the molar mass of the dissolved substance.

In other words, the elevation of the boiling point is dependent on the number

m of moles of the dissolved substance (see Eqn 9.3); moreover, it is dependent on

the qualitative nature of the solvent, defined by the molar elevation of the boiling

point of the solvent (Eqn 9.2), but independent of the nature of the dissolved

substance.

Confectionery and Chocolate Engineering: Principles and Applications, Second Edition. Ferenc Á. Mohos.© 2017 John Wiley & Sons Ltd. Published 2017 by John Wiley & Sons Ltd.

317

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318 Confectionery and chocolate engineering: principles and applications

In the case of aqueous solutions of carbohydrates, the solvent is water, and

for water, Δtm;b = 0.52 K. For dilute aqueous solutions, the appropriate form of

Eqn (9.4) isΔtb

0.52 K=

g

M(9.5)

at atmospheric pressure (750 mmHg).

Example 9.1Let us calculate the molar elevation of the boiling point of water at atmo-

spheric pressure using Eqn (9.2). The molar heat of vaporization of water is

Lb =9710 cal/18 g= 539.44 cal/g= 2258.53 J/g, and Tb =373.1 K (Erdey-Grúz

and Schay, 1962; Vol. 1, p. 715). We obtain

Δtm;b =RT2

b

1000Lb

=8.31434J∕molK × (373.1K)2

1000g × 2258.53J∕g= 0.51245K∕mol

In practice, the value Δtm;b =0.52 K/mol is used.

It should be emphasized that at higher concentrations, Raoult’s law is not valid;

for example, if 1 mol (180 g) of dextrose is dissolved in 1000 g of water (so that the

concentration s is 180/1180= 15.25%), the elevation of the boiling point should

be 0.52 ∘C. However, according to Bukharov’s measurements (see Table 9.2), this

value is merely ≈0.35 ∘C. For 1 mol (342 g) of sucrose (s= 342/1342= 25.48%),

the actual elevation of the boiling point is ≈0.45 K according to Bukharov’s mea-

surements (see Table 9.2 and Sokolovsky, 1958; p. 20). That is, these solutions

cannot be regarded as dilute.

9.2 Boiling point of sucrose/water solutionsat atmospheric pressure

Sokolovsky (1958, p. 19) gives a simple formula for the boiling point of

sucrose/water solutions:

T(s) = 100 + 2.33s1 − s

(9.6)

where T(s) is the boiling point (∘C) of a sucrose/water solution at atmospheric

pressure and s is the concentration of sucrose in the solution (m/m or m/m%).

Equation (9.6) can be regarded a modification of Raoult’s law. Table 9.1 shows

the relation between measured values of the boiling point and the corresponding

values calculated on the basis of Eqn (9.6).

For higher concentrations of sucrose, Eqn (9.6) cannot be correct, because

it becomes divergent when s→ 1. Exclusively for the interval 15%>W> 2% of

the water content W (m/m%), a better approximation has been obtained by the

present author using the formula

T(s) = 146.7 − 4.2W + 0.138W2 (9.7)

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Evaporation 319

Table 9.1 Boiling points of aqueous sucrose solutions of various

concentrations (m/m%), measured by Bukharov (1935) and

calculated according to Eqn (9.6).

Boiling point (∘C)Sugarconcentration (%) Measured Calculated

10 100.1 100.2589

20 100.3 100.5825

30 100.6 100.9986

40 101 101.5533

50 101.8 102.33

60 103 103.495

70 105.5 105.4367

80 109.4 109.32

90 119.6 120.97

Source: Adapted from Bukharov (1935).

9.3 Application of a modification of Raoult’s lawto calculate the boiling pointof carbohydrate/water solutions at decreasedpressure

9.3.1 Sucrose/water solutionsValues of the boiling-point elevation of sucrose/water solutions at decreased pres-

sures have been given by Sokolovsky (1958, p. 20), following Bukharov (1935);

see Table 9.2.

9.3.2 Dextrose/water solutionsValues of the boiling-point elevation of aqueous solutions of dextrose at

decreased pressures have been summarized by Sokolovsky (1958, p. 41); see

Table 9.3.

9.3.3 Starch syrup/water solutionsThe elevation of the boiling point of aqueous starch syrup solutions as a function

of concentration at various pressures, according to Bukharov (1935), is given in

Table 9.4.

9.3.4 Invert sugar solutionsSokolovsky (1951, p. 18) has also published data on the elevation of the boiling

point of aqueous invert sugar solutions (Table 9.5).

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Table 9.2 Elevation of boiling point (∘C) of aqueous sucrose solutions as a function of

concentration at various pressures.

p (105 Pa)

0.12279 0.19916 0.31157 0.47393 0.70096 1.01325

t (∘C)Concentration(m/m%) 50 60 70 80 90 100

5 0.05 0.05 0.05 0.06 0.06 0.06

10 0.1 0.1 0.11 0.11 0.12 0.12

15 0.17 0.18 0.18 0.19 0.19 0.2

20 0.26 0.27 0.28 0.28 0.29 0.3

25 0.39 0.4 0.42 0.43 0.44 0.45

30 0.52 0.54 0.55 0.57 0.58 0.6

35 0.69 0.71 0.73 0.76 0.78 0.8

40 0.8 0.85 0.9 0.95 1 1.05

45 1.02 1.1 1.18 1.25 1.32 1.4

50 1.32 1.4 1.52 1.61 1.72 1.8

55 1.7 1.82 1.94 2.06 2.18 2.3

60 2.3 2.45 2.6 2.75 2.9 3.05

65 2.8 3 3.2 3.4 3.6 3.8

70 3.65 3.9 4.18 4.46 4.75 5.05

75 5.05 5.4 5.8 6.2 6.6 7

80 6.8a 7.3 7.85 8.35 8.9 9.4

85 a 10a 10.75 11.5 12.25 13

90 a a 16a 17.2 18.4 19.6

aData uncertain or unknown.

Source: Adapted from Sokolovsky (1958).

9.3.5 Approximate formulae for the elevation of the boilingpoint of aqueous sugar solutions

Equation (9.6), T(s)=100+2.33s/(1− s), which refers to atmospheric pressure,

means that if s=0.5 (50%) then the elevation of the boiling point (in ∘C) is equal

to the factor 2.33. This consideration helps us to construct approximate formulae

similar to Eqn (9.6). A detailed calculation shows that this factor is dependent

on the pressure applied. The resulting approximate formulae are

T(s) = Ts=0 +(1.1 + 0.012Ts=0)s

1 − s(9.8)

T(d) = Td=0 +(1.2 + 0.0154Td=0)d

1 − d(9.9)

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Table 9.3 Elevation of boiling point (∘C) of dextrose solutions as a function of concentration at

various pressures.

p (105 Pa)

0.12279 0.19916 0.31157 0.47393 0.70096 1.01325

t (∘C)Concentration(m/m%) 50 60 70 80 90 100

5 0.08 0.08 0.09 0.1 0.11 0.11

10 0.16 0.17 0.18 0.19 0.21 0.22

15 0.25 0.26 0.28 0.3 0.32 0.35

20 0.39 0.41 0.44 0.48 0.51 0.55

25 0.51 0.55 0.59 0.63 0.67 0.7

30 0.62 0.66 0.7 0.75 0.8 0.85

35 0.78 0.84 0.9 0.96 1.02 1.05

40 1.04 1.11 1.2 1.28 1.36 1.45

45 1.45 1.55 1.66 1.78 1.9 2

50 1.98 2.12 2.28 2.42 2.59 2.75

55 2.7 2.9 3.1 3.3 3.59 3.75

60 3.63 3.9 4.17 4.45 4.75 5.05

65 4.73 5.07 5.43 5.89 6.19 6.6

70 6.04 6.47 6.93 7.4 7.9 8.4

75 7.47 8.02 8.58 9.17 9.79 10.45

80 9.29 9.98 10.69 11.42 12.17 13

85 12.01 13.6 14.69 15.59 16.65 17.75

90 19.14 20.5 21.08 23.62 25.27 27

Source: Adapted from Sokolovsky (1958).

T(st = y) = Td=0 +(0.63 + 0.0077Ty=0)y

1 − y(9.10)

T(i) = Ti=0 +(1.47 + 0.0188Ts=0)i

1 − i(9.11)

where Ts=0 = Td=0 = Ty=0 = Ti=0 is the boiling point (∘C) of pure water at the

given pressure (decreased or atmospheric), and s, d, y and i are the concentrations

(m/m%) of sucrose, dextrose, starch and invert sugar, respectively.

Example 9.2The boiling point of pure water at atmospheric pressure is 100 ∘C. Therefore,

according to Eqn (9.8), for sucrose solutions,

T(s) = Ts=0 +(1.1 + 0.012Ts=0)s

1 − s= 100 + (1.1 + 1.2)s

1 − s

which agrees with Eqn (9.6).

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Table 9.4 Elevation of boiling point (∘C) of aqueous starch syrup solutions as a function of

concentration at various pressures.

p (105 Pa)

0.12279 0.19916 0.31157 0.47393 0.70096 1.01325

t (∘C)Concentration(m/m%) 50 60 70 80 90 100

5 0.04 0.04 0.04 0.04 0.04 0.04

10 0.06 0.06 0.07 0.07 0.08 0.08

15 0.1 0.1 0.11 0.11 0.13 0.15

20 0.14 0.15 0.16 0.18 0.19 0.2

25 0.18 0.19 0.21 0.22 0.24 0.26

30 0.27 0.28 0.31 0.33 0.35 0.38

35 0.33 0.35 0.37 0.4 0.44 0.5

40 0.405 0.48 0.52 0.55 0.59 0.63

45 0.57 0.61 0.66 0.7 0.75 0.8

50 0.74 0.79 0.85 0.91 0.97 1.03

55 1.02 1.09 1.17 1.25 1.33 1.4

60 1.4 1.51 1.62 1.74 1.89 1.95

65 1.94 2.07 2.23 2.38 2.53 2.7

70 2.62 2.81 3.12 3.21 3.43 3.65

75 3.49 3.74 4 4.28 4.55 4.85

80 4.62 4.96 5.3 5.66 6.05 6.45

85 6.44 6.97 7.4 7.89 8.43 9

90 9.73 10.45 11.2 11.97 12.79 13.6

92 12.11 13.01 13.94 14.91 15.91 17

94 16.18 18.07 18.85 19.96 21.33 22.75

96 24.92 26.82 28.84 30.85 33.28 40

Source: Adapted from Sokolovsky (1958).

Table 9.5 Elevation of boiling point (∘C) of aqueous invert sugar solutions as a function of

concentration at various pressures.

p (105 Pa)

0.12279 0.31157 0.70096 1.01325

t (∘C)Concentration(m/m%) 50 70 90 100

70 5.8 6.8 a 8.1

75 7.53 8.65 9.86 10.5

80 9.66 11.17 12.54 13.5

85 12.83 14.76 16.94 18

90 17.42 20.09 22.99 24.55

aData uncertain or unknown.

Source: Adapted from Sokolovsky (1951).

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Example 9.3If the boiling point of pure water is 50 ∘C, then, according to Eqn (9.9), for dex-

trose solutions,

T(d) = Td=0 +(1.2 + 0.0154Td=0)d

1 − d= 50 + (1.2 + 0.0154 × 50)d

1 − d= 50 + 1.97d

1 − d

Let d= 0.7; then T(d)= 50+1.97×0.7/0.3= 54.6 ∘C. The value in Table 9.3 is

56.04 ∘C.

More detailed data for aqueous solutions of various monosaccharides and dis-

accharides can be found in the handbook by Junk and Pancoast (1973).

9.4 Vapour pressure formulae for carbohydrate/watersolutions

9.4.1 Vapour pressure formulaeThe vapour pressure function most often used has the form

log p = −AT

+ B (9.12)

where p is the vapour pressure, T is the boiling point of the liquid (K), and A and

B are constants. For pure water (Erdey-Grúz and Schay, 1962; p. 708),

log pw = − 103134.576Tw

+ 8.9296 = −2253.715Tw

+ 8.9296 (9.13)

where pw is the vapour pressure of water (mmHg); the subscript ‘w’ denotes

water vapour.

Let us now write Tw − 273= Ts=0 = Td=0 = Td=0; that is, we transcribe Eqns

(9.8)–(9.11) into formulae using Tw, which is expressed in kelvin. After some

simple algebraic transformations, the following equations are obtained:

T(s) = Tw(1 + 0.012S) − 2.176S (9.14)

T(d) = Tw(1 + 0.0154S) − 3.0042S (9.15)

T(st) = Tw(1 + 0.0077S) − 1.4721S (9.16)

T(i) = Tw(1 + 0.0188S) − 3.6624S (9.17)

where, for the sake of simplicity, S denotes the ratios of concentrations s/(1− s),

d/(1− d), y/(1− y) and i/(1− i), and st refers to aqueous starch syrup solutions.

Expressions for Tw can be obtained from Eqns (9.14)–(9.17); for example, from

Eqn (9.14), we obtain

Tw = T(s) + 2.176S

1 + 0.012S

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324 Confectionery and chocolate engineering: principles and applications

When these expressions are substituted into Eqn (9.13), the following pressure

functions are obtained.

For aqueous sucrose solutions:

log pw = −2253.715(1 + 0.012S)T(s) + 2.176S

+ 8.9296 (9.18)

For aqueous dextrose solutions:

log pw = −2253.715(1 + 0.0154S)T(d) + 3.0042S

+ 8.9296 (9.19)

For aqueous starch syrup solutions:

log pw = −2253.715(1 + 0.0077S)T(st) + 1.4721S

+ 8.9296 (9.20)

For aqueous invert sugar solutions:

log pw = −2253.715(1 + 0.0188S)T(i) + 3.6624S

+ 8.9296 (9.21)

In the previous equations (Equations 9.18–9.21), pw is in mmHg.

Example 9.4An aqueous sucrose solution has a concentration s= 0.3, that is, S= 0.3/0.7=0.4286. The boiling point of this solution (measured value) is 60 ∘C+ 0.54 ∘C=333.54 K=T(s) (see Table 9.2). What is the vapour pressure at this temperature?

According to Eqn (9.18),

log pw = −2253.715(1 + 0.012 × 0.4286)333.54 + 2.176 × 0.4286

+ 8.9296

From this, pw = 147.23 mmHg= 0.19629×105 Pa. The correct value is

0.19916×105 Pa (see Table 9.2).

Example 9.5An aqueous starch syrup solution has a concentration s= 0.7, that is,

S= 0.7/0.3=2.33. The boiling point of this solution (measured value) is

80 ∘C+3.21 ∘C= 356.21 K=T(st) (see Table 9.4). What is the vapour pressure at

this temperature?

According to Eqn (9.20),

log pw = −2253.715(1 + 0.0077 × 2.33)356.21 + 1.4721 × 2.33

+ 8.9296

From this, pw = 355.3 mmHg= 0.473694×105 Pa. The correct value is

0.47393×105 Pa (see Table 9.4).

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Example 9.6An aqueous dextrose solution is evaporated at pw = 250 mmHg and 75 ∘C= 348 K.

What is the equilibrium concentration (S and s) in these circumstances?

Using Eqn (9.19),

log 250 = −2253.715(1 + 0.0154 × S)348 + 3.0042 × S

+ 8.9296

By solving this equation, we obtain S= 1.2806= s/(1− s) and s= 0.562 (m/m).

It should be emphasized that all of these equations concerning the elevation

of boiling point and the vapour pressure of carbohydrate solutions are only the-

oretical, although they are based on the laboratory measurements of Bukharov.

Moreover, the concentration interval in which they work acceptably is only

about c= 0.3–0.7, and the data referring to aqueous invert sugar solutions are

insufficient. Consequently, they must be regarded as being for information only

and must not replace trials.

9.4.2 Antoine’s ruleEquations (9.14)–(9.17) can be transcribed into a general form. For example,

T(s) = Tw(1 + 0.012S) − 2.176S (9.14)

can be written as

T(s) − Tw = Δtb = Tw × 0.012S − 2.176S = S(Tw × 0.012 − 2.176)

that is,

Δtb = S(Twa − b) (9.22)

where a and b are constants (Table 9.6).

Equation (9.22) can be transformed to

Δtb = Ti − Tw = Sb

(Tw

Tr

− 1

)(9.23)

Table 9.6 Constants in Eqns (9.22) and (9.23).

Carbohydrate a b (K) Tr (K)=b/a

Sucrose 0.012 2.176 181.330

Dextrose 0.0154 3.0042 195.078

Starch syrup 0.0077 1.4721 191.182

Invert sugar 0.0188 3.6624 194.809

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326 Confectionery and chocolate engineering: principles and applications

where Tr ≡ b/a and Ti is the boiling point of any of the sugars discussed earlier.

A consequence of Eqn (9.23) is that Tw ≥ Tr. From Eqns (9.13) and (9.23), an

equation for the vapour pressure of carbohydrate solutions can be constructed:

log pw = −2253.715

(1 +

Sbi

Tri

)∕(Ti + Sbi) + 8.9296 (9.24)

where i refers to the type of carbohydrate dissolved and Ti is the boiling point of

the solution.

There is a well-known general relationship for the vapour pressure of solutions

called Antoine’s rule:

log pw = − AT + C

+ B (9.25)

where A, B and C are constants; in most cases C=−43 K. Equation (9.24) can

be regarded as an equation of Antoine type, where A= 2253.715(1+ Sbi/Tri),

B=8.9296 and C= Sbi. C is dependent on the composition (i.e. on S) and

is positive.

For further details, see Elliot and Lira (1999).

Example 9.7Let us calculate the Antoine equation for a starch syrup/water solution in which

the concentration of starch syrup is s= 75%.

We have

S = 0.750.25

= 3

From Table 9.6, bi = 1.4721 K and Tr = 191.182 K.

A = 2253.715

(1 +

Sbi

Tri

)= 2253.715

(1 + 3 × 1.4721

191.182

)= 2314.565

B = 8.9296

C = Sbi = 3 × 1.4721K = 4.4163K

log pw = − AT + C

+ B = − 2314.565T + 4.4163

+ 8.9296

9.4.3 Trouton’s ruleEquation (9.2) can be expressed with the help of the Trouton constant:

Δtm =mRT2

b

1000Lb

= m ×18RTb

1000Tr(9.26)

where

Tr =Lb

Tb

is the Trouton constant, which is equal to 26.0 cal/K (=108.784 J/K) for water

(Erdey-Grúz and Schay, 1962; p. 715). S and m are proportional to each other:

m = 1000SM

(9.27)

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Evaporation 327

where M is the molar mass (in grams) of the carbohydrate. For example, if

M/2= 342 g/2= 171 g of sucrose is dissolved in 1000 g of water, then m= 1/2.

Since S= 171/1000= 0.174, we obtain from Eqn (9.27) the result m= 1000×0.171/342=1/2.

These facts can be explained as a loose relationship between Eqn (9.22) and

Raoult’s law:

Δtb =mRT2

w

1000Lw

= m ×18RTw

1000Tr= S(Twa − b) (9.28)

An important question can be asked: How to calculate the elevation of the boiling

point of aqueous solutions of carbohydrate mixtures? A possible interpretation of

this question is how to calculate the value of S? The starting supposition is that the

values of the constants a and b have taken into account the molar masses of the

carbohydrates in question. Thus, for the values of both a and b, the following

sequence of magnitudes can be observed:

starch syrup < sucrose < dextrose < invert sugar

which agrees with the sequence of molality of these carbohydrates if their masses

are the same.

There are no data on the DE value of the starch syrup used in Bukharov’s inves-

tigations. If an estimated value DE≈ 40%, which is usual in the confectionery

industry, is assumed, then the dissolved dry substance of the starch syrup consists

roughly of 40% reducing sugar (expressed as dextrose)+ 60% other compo-

nents, which are dissolved as well. Consequently, 100 kg of dextrose, when dis-

solved, produces roughly double the number of molecules that 100 kg of starch

syrup does. This can be observed in the values of a and b.

Therefore the simple mass ratios can presumably be used to approximate the

real conditions by a type of equation of mixture:

Δtb = S(Twa − b) =

∑sj(Twaj − bj)

1 − s=

∑sj(Δtbj

)

1 − s(9.29)

Table 9.7 Elevation of boiling point for aqueous carbohydrate solutions, for S=1.a

Elevation of boiling point (K) if S=1Pressure(105 Pa)

Boilingpoint Tw (K) Sucrose Dextrose Starch syrup Invert sugar

0.12279 323 1.700071 1.969998 1.014998 2.409985

0.19916 333 1.820073 2.123998 1.091998 2.597984

0.31157 343 1.940076 2.277998 1.168997 2.785984

0.47393 353 2.060078 2.431998 1.245997 2.973983

0.70096 363 2.18008 2.585998 1.322997 3.161983

1.01325 373 2.300082 2.739998 1.399997 3.349982

aA maximum of two decimal places is sufficient.

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328 Confectionery and chocolate engineering: principles and applications

where Δtbi is the elevation of the boiling point for each carbohydrate if S= 1;

s=Σsj is the total solid content dissolved (m/m); j= 1, 2, … , n; and aj and bj are

constants for each particular type of substance. In order to facilitate the calcula-

tion, Table 9.7 gives the values of Δtbi for the carbohydrates in question.

Example 9.8At p= 0.19916×105 Pa (Tw = 60 ∘C=333 K), the distribution of the dissolved

solid content is (concentrations in m/m) sucrose= 0.45, starch syrup=0.20

and invert sugar=0.05. The elevation of the boiling point is to be calculated

(s=0.70).

Using Eqn (9.29),

Δtb = {0.45(333 × 0.012 − 2.176) + 0.2(333 × 0.0077 − 1.4721)

+ 0.05(333 × 0.0188 − 3.6624)}∕0.3

= 3.891K

(According to Bukharov (Table 9.2), the measured value is 3.9 K for a sucrose

solution of s=0.7.)

The calculation can easily be done for this example by using the values in

Table 9.7:

Δtb = (0.45 × 1.82 + 0.2 × 1.092 + 0.05 × 2.6)∕0.3 = 3.8915K

9.4.4 Ramsay–Young ruleThe Ramsay–Young rule makes it possible to calculate the boiling point of a solu-

tion at a pressure p that differs from atmospheric pressure (1 bar):[

T(p)T(1bar)

]

water

=[

T(p)T(1bar)

]

solution

(9.30)

where T(p) is the boiling point (in K) of water at a (decreased) pressure p, T(1 bar)

is the boiling point of water at atmospheric pressure, T(p) is the boiling point of

the solution at the pressure p and T(1 bar) is the boiling point of the solution at

atmospheric pressure.

For pure water, the vapour pressure function is

log pw = − 103134.576Tw

+ 8.9296 = −2253.715Tw

+ 8.9296 (9.13)

For aqueous solutions of the carbohydrates in question, the vapour pressure

function is

log pw = −2253.715(1 + Sbi∕Tri)

Ti + Sbi

+ 8.9296 (9.24)

The Ramsay–Young rule concerns the same pressures, that is, the equality of

Eqns (9.13) and (9.24), and therefore

(pure water) 1Tw

=1 + Sbi∕Tri

Ti + Sbi

(solution) (9.31)

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Evaporation 329

Since Eqn (9.31) refers to any pressure p, it can be written for atmospheric

pressure:

(pure water) 1373

=1 + Sbi∕Tri

Ti0 + Sbi

(solution) (9.32)

where Ti0 is the boiling point of the solution at atmospheric pressure. From Eqns

(9.31) and (9.32),

Tw∕373 =Ti + Sbi

Ti0 + Sbi

(9.33)

which is a modified form of the Ramsay–Young rule.

Example 9.9Let us apply the Ramsay–Young rule to an aqueous dextrose solution with

s=60% at the pressures 0.12279× 105 Pa and 0.31157×105 Pa.

From Table 9.6, bi =3.0042 K; S= 0.6/0.4= 3/2, and therefore Sbi =6.634. For

this solution, from Table 9.3,

Δtb = 5.05K at atmospheric pressure

Δtb = 3.63K at0.12279 × 105 Pa

Δtb = 4.17K at0.31157 × 105 Pa

At 0.12279× 105 Pa, the boiling point of pure water is 50 ∘C= 323 K. Supposing

that the Ramsay–Young rule is valid, we write

323373

= 0.866,323 + 3.63 + 6.634373 + 5.05 + 6.634

= 0.866

At 0.31157×105 Pa, the boiling point of pure water is 70 ∘C= 343 K:

343373

= 0.9196,343 + 4.17 + 6.634373 + 5.05 + 6.634

= 0.9204

In both cases, the two ratios for the same pressure can be regarded as equal (e.g.

0.9196≈ 0.9204); our supposition was correct.

9.4.5 Dühring’s ruleAccording to Dühring’s rule for two substances 1 and 2, the boiling points are in

a linear relationship:

T1(p) = k1T2(p) + k2 (9.34)

where T1(p) is the boiling point (K) of substance 1 at pressure p, T2(p)

is the boiling point (K) of substance 2 at pressure p, and k1 and k2 are constants.

The Ramsay–Young rule can be regarded as a special case of Dühring’s rule: in

the former case, k2 =0. In general, Dühring’s rule can be assumed to be valid for

less familiar substances.

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330 Confectionery and chocolate engineering: principles and applications

Equation (9.31) provides a starting point for applying Dühring’s rule to the

aqueous carbohydrate solutions previously studied:

(pure water) 1Tw

=1 + Sbi∕Tri

Ti + Sbi

(solution) (9.35)

that is,1 + Sbi∕Tri

Ti + Sbi

=1 + Sbj∕Trj

Tj + Sbj

(9.36)

where i and j refer to two different carbohydrates. The equation

Ti + Sbi

Tj + Sbj

=1 + Sbi∕Tri

1 + Sbj∕Trj

= K (9.37)

or

Ti = KTj + S(Kbj − bi) (9.38)

where K is a constant, agrees with Dühring’s rule as expressed in Eqn (9.34).

9.5 Practical tests for controlling the boiling pointsof sucrose solutions

In the production of hard-boiled and low-boiled sugar sweets by confection-

ers, the end point of boiling can be checked without special equipment, using

experiments based on assessment of the sugar mass by the confectioner’s own

senses (Table 9.8).

Table 9.8 Sugar-boiling tests used in practice. a

Hungarian Germanb Englishc Boiling point (∘C)

Szirup Crystal syrup 104

Gyenge szál Schwach. Faden 105

Erös szál Starker Faden 107.5

Szál Thread 108

Gyöngy Pearl 110

Kis gyöngy Kleine Perlen 110

Nagy gyöngy Grosse Perlen 111

Gyenge pflúg Schwach. Pflug 112.5

Pflúg (fújás) Blow/soufflé 113

Erös pflúg Starker Pflug 116

Gyenge golyó Soft ball 118

Golyó Ballen 122.5

Kemény golyó Hard ball 123

Törés Bruch Crack 131

Karamel Karamel Caramel 150

Cukor (nyilt lángon) Bonbons/Feuer 156

aFor doctor solution (Läuter-Lösung in German), a boiling point of 102.5 ∘C=82 ∘R is recommended by

Földes and Ravasz (1998).bFor German test names, see Besselich (1951).cFor English test names, see Meiners et al. (1984).

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Evaporation 331

Example 9.10Conversion between the various temperature scales is a common task. A tem-

perature of 32 ∘F is assigned to the melting point of ice and 212 ∘F to the boiling

point of water, so that the temperature interval between these points is divided

into 180 parts; 32 ∘F= 0 ∘C and 212 ∘F= 100 ∘C.

The following equation makes it very simple to convert temperatures from one

scale to another by the help of the Sena formula:

(t − 273)K∕5 = t∘C∕5 = t∘R∕4 = (t − 32)∘F∕9 (9.39)

Here, absolute zero (0 K) is calculated to be equal to −273 ∘C (the exact value is

−273.16 ∘C). For example, if t(K)=573 K, then

(573 − 273)K∕5 = t∘C∕5 → 573K = 300 ∘C

= t∘R∕4 → 573K = 300 ∘R × (4∕5) = 240 ∘R

= (t − 32)∘F∕9 → (573 − 273)∕5 = (t − 32)∕9 → t = 572 ∘F

→ 573K = 572 ∘F

(As a check, we can calculate t ∘F if t ∘C= 300 ∘C:

300 ∘C∕5 = (t − 32)∘F∕9 → t = 572 ∘F

If t ∘F= 0, what is t ∘C?

t∘C∕5 = (0 − 32)∕9 → t∘C = 32 × (5∕9)∘C = −17.77 ∘C

Comments:

• The equality 573 K= 572 ∘F does not mean that the two scales are similar; see

previous text.

• The scale in which the magnitude of a degree is the same as in the Fahrenheit

scale, but where the temperature is counted from absolute zero is called

the Rankine scale. In this scale, a temperature of 459.67∘ corresponds to

0 ∘F, 491.67∘ to the freezing point of water and 671.67∘ = (491.67+ 180)∘ to

the boiling point of water. (Since Δt ∘C= 1.8Δt ∘F, −273.16 ∘C (=0 K)= 1.8×273.16 ∘Rankine=491.688 ∘Rankine – the difference derives from the value

of absolute zero.)

• The Réaumur scale (∘R) is used in old recipes (0 ∘R= 0 ∘C; 80 ∘R= 100 ∘C).

9.6 Modelling of an industrial working process forhard boiled sweets

This section presents a study by Oliveira et al. (2008) of the use of a hybrid mod-

elling approach that consists of a phenomenological model of the evaporation

step and an artificial neural network (ANN) to model the vacuum-drying step of

a cooking process for chewy candy.

Figure 9.1 presents a schematic illustration of a classical candy-cooking

machine. An aqueous sugar/starch syrup solution (with a boiling point of

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332 Confectionery and chocolate engineering: principles and applications

12 8

7

6

911

10

13

4

3

25

1

Figure 9.1 Schematic diagram of an industrial candy-cooking machine: 1, feed pump; 2,

vapour chamber; 3, stainless steel coil; 4, vapour input valve; 5, vapour purge; 6, expansion

chamber; 7, tempering piston; 8, outlet; 9, vacuum chamber; 10, air inlet valve; 11, paste

reservoir; 12, PT100 sensor; 13, temperature controller. Source: Oliveira et al. (2008).

Reproduced with permission from Elsevier.

about 106 ∘C) is pumped through a stainless steel coil located inside a vapour

chamber. The temperature of the vapour chamber is controlled by a control

loop composed of a PT100 sensor, a PID controller and a control valve. The

candy solution enters the expansion chamber at atmospheric pressure, where

the evaporated water is removed through an outlet. The resulting paste (candy

mass) is accumulated in this chamber and then transferred to the vacuum

chamber through an outlet by a tempering piston. The air inlet valve is then

opened, allowing the candy mass to flow into the reservoir for the cooling

step. The cooking process must be done to meet the requirement of a total

solids concentration of around 98%; it is conducted in a temperature range of

125–132 ∘C.

9.6.1 Modelling of evaporation stageThe following assumptions were made:

• Homogeneity of composition and temperature inside the steel coil

• Constant amount of contents in the steel coil

• Thermodynamic equilibrium of the system

The global balance for the evaporation stage is given by

dMdt

= q′b − q′ − q′

v (9.40)

where dM/dt (kg/s) is the mass flow, M (kg) is the total mass in the evaporation

stage, q′b

(kg/s) is the feed flow, q′ (kg/s) is the concentrate product flow and

q′v (kg/s) is the evaporate flow. The total mass in the system was assumed to be

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Evaporation 333

constant, that is, dM/dt= 0, and thus

q′b = q′ + q′

v (9.41)

The mass balance for the total solids is given by

M

(dXdt

)= Xbq′

b − Xq′ (9.42)

where X (expressed as a ratio) is the total solids concentration and Xb is the solids

concentration of the feed. The energy balance is given by

M

(dHdt

)= Hbq′

b − XHq′ − Hvq′v + Q′ (9.43)

where H (kJ/kg) is the enthalpy of the concentrated product, Hb (kJ/kg) is the

enthalpy of the feed, Hv (kJ/kg) is the enthalpy of the evaporate and Q′ (kJ/s) is

the heat exchange through the wall, which is given by

Q′ = 𝜅ΔTML (9.44)

where 𝜅 (kJ/s K) is the overall heat transfer coefficient and ΔTML (∘C) is the

logarithmic mean of the temperature.

The overall heat transfer coefficient of the cooker used was determined from

a steady-state evaporation model and from steady-state data for the industrial

process, using the following equation:

𝜅 =XHq′ − Hvq′

v − Hbq′b

ΔTML

(9.45)

where q′v was computed from Eqn (9.42). The enthalpy of the candy solution

was defined by

H = CP(X)T (9.46)

Hb = CP(Xb)Tb (9.47)

where the subscript ‘b’ denotes the feed.

To calculate the specific heat capacity of the candy solution as a function of

the percentage composition mi of the system, the following equation (Singh and

Heldman, 1993) was used:

CP = 1.424mc + 1.549mp + 1.675mf + 0.837ma + 4.187mw (9.48)

where c is carbohydrate, p is protein, f is fat, a is ash and w is water. The enthalpy

of the saturated vapour Hv was given by

Hv = 2509.2888 + 1.6747Tv (9.49)

and the enthalpy of the condensate Hcond was given by

Hcond = 4.187Tcond (9.50)

where Tv and Tcond are the corresponding temperatures.

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334 Confectionery and chocolate engineering: principles and applications

140

135

130

125

120

115

110

105

100

95

9030 40 50 60

Total solids concentration (wt%)

Syru

p b

oili

ng

te

mp

era

ture

(°C

)

70 80 90 100

This work (BPR data)Adjusted BPR modelIndustrial process

Lees and jackson (1999)

Figure 9.2 Boiling point of candy solution as a function of the total solids concentration at

100 kPa (=1 bar). BPR= boiling-point rise. Source: Oliveira et al. (2008). Reproduced with

permission from Elsevier.

To correlate the boiling-point elevations ΔTeb measured, the ‘boiling-point rise

(BPR) model of Capriste and Lozano (1988) was adopted:

ΔTeb = aXbecXPd (9.51)

where a= 0.4846×10−2, b=−1.0718, c= 8.5714, d= 0.09689, e=2.71828…(the base of natural logarithms) and P (bar) is the absolute pressure of the

system. The parameters a, b, c and d were obtained by fitting the measured

boiling-point elevation data for the candy solution (R= 0.9882; mean absolute

error 0.56 ∘C). Figure 9.2 shows values of the boiling point versus total solids

concentration for the candy solution at 1 bar pressure.

The experimental data measured in this work are in good agreement with val-

ues presented in the literature (Lees and Jackson, 1999) and with data obtained

from industrial processes, despite differences in the compositions of the solutions

used. It is worth noting, in addition, that a plot of the boiling-point elevation data

for the solution versus boiling-point elevation data for water was linear for solids

concentrations of 0.6, 0.7, 0.745 and 0.8 (at atmospheric pressure), and thus the

model used was capable of satisfactorily representing the experimental data on

boiling-point elevation for chewy candy solutions.

9.6.2 Modelling of drying stageIt should be noted that while evaporation is a continuous process with this type

of machine, the drying stage is a batch operation. A multilayer perceptron ANN

with one hidden layer was used to represent the variation of moisture content in

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Evaporation 335

Table 9.9 Elevation of boiling point (∘C) of

aqueous isomalt solutions.

w: Water%

T: Boilingpoint (∘C)

16 111

15 114

14 116

13 117

12 118

11 122

10 124

9 127

8 130

7 133

6 137

5 141

4 145

3 150

2 157

1 168

Source: Reproduced with permission from Infopac.

the vacuum chamber. The inputs to the ANN were the total solids concentration

X in the vacuum chamber feed, the absolute pressure P of the system and the

process time t; the moisture content of the candy mass at the vacuum chamber

outlet was the output of the ANN. For details, see Oliveira et al. (2008).

9.7 Boiling points of bulk sweeteners

The boiling-point elevation of aqueous solutions of lactitol is similar to sucrose

(Mitchell, 2006; O’Brien-Nabors, 2011; O’Donnell and Kearsley, 2012).

Isomalt is available for producing hard-boiled confectioneries (drops); there-

fore, the boiling point elevation of its aqueous solutions is an important infor-

mation (see Table 9.9).

Further reading

Alikonis, J.J. (1979) Candy Technology, AVI Publishing, Westport, CT.

AVP Baker. Technical brochures.

Andreasen, G. (1972) Are traditional sugar boiling techniques really the best way. Confect Prod,

38 (12), 641–656.

Cakebread, S.H. (1972) Confectionery ingredients – vapour pressures of carbohydrate solutions

II. Confect Prod, 38 (9), 486–492496.

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336 Confectionery and chocolate engineering: principles and applications

Cakebread, S.H. (1972) Confectionery ingredients – vapour pressures of carbohydrate solutions

III. Confect Prod, 38 (10), 524–526550.

Cakebread, S.H. (1975) Sugar and Chocolate Confectionery, Oxford University Press, Oxford.

Lees, R. (1972) High boiled sweets – simple in composition but physical structure is complex.

Confect Prod, 38 (9), 456–457.

Lees, R. (1972) High boiled sweets – products should not grain nor become sticky. Confect Prod,

38 (9), 484.

Lees, R. (1980) A Basic Course in Confectionery, Specialized Publications Ltd, Surbiton.

Lienhard, J.H. IV, and Lienhard, J.H. (2005) A Heat Transfer Textbook, 3rd edn, Phlogiston Press,

Cambridge, MA.

Meiners, A. and Joike, H. (1969) Handbook for the Sugar Confectionery Industry, Silesia-

Essenzenfabrik, Gerhard Hanke K.G., Norf, Germany.

Pratt, C.D. (ed.) (1970) Twenty Years of Confectionery and Chocolate Progress, AVI Publishing, West-

port, CT.

Robert Bosch/Hamac. Technical brochures.

Rohsenow, W.M., Hartnett, J.P. and Cho, Y.I. (eds) (1998) Handbook of Heat Transfer, 3rd edn,

McGraw-Hill, New YorkChapter 15.

Schwartz, M.E. (1974) Confections and Candy Technology, Food Technology Review, 12, Noyes,

Park Ridge, NJ.

Sullivan, E.T. and Sullivan, M.C. (1983) The Complete Wilton Book of Candy, Wilton Enterprises

Inc., Woodridge, IL.

Ter Braak. Technical brochures.

VDI-GVC (2006) VDI-Wärmeatlas, Springer, Berlin.

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CHAPTER 10

Crystallization

10.1 Introduction

Crystallization is a process in which an ordered solid phase is precipitated from

a gaseous, liquid or solid phase. The liquid phase may be either a melt or a solu-

tion; both cases occur in confectionery practice. Crystallization from molten fat is

characteristic of chocolate and similar products, the continuous phase of which

is a molten fat. On the other hand, crystallization from solution is characteris-

tic of various types of candies, primarily fondant and some hard-boiled sugar

confectioneries.

10.2 Crystallization from solution

10.2.1 NucleationA solid phase is precipitated from a solution if the chemical potential of the solid

phase is less than that of the dissolved components to be precipitated from the

solution. A solution in which the chemical potential of a dissolved component

is the same as that of the corresponding solid phase is in equilibrium with this

solid phase under the given conditions and is termed a saturated solution. In order

for crystallization to proceed, this equilibrium concentration must be exceeded

as the result of some method for producing supersaturation: cooling the solution

and evaporation of the solvent are both used in confectionery technology. These

methods can be carried out both continuously and batchwise.

In both of these methods, the concentration of the solution (i.e. the chemi-

cal potential of the component) is somewhat greater than that corresponding to

equilibrium. This excess concentration or chemical potential, which is actually

the driving force for crystallization, is termed the supersaturation. If the super-

saturation is obtained by cooling, then the difference between the temperature

corresponding exactly to saturation and the actual temperature of the solution

is termed the supercooling.

Provided the supersaturation is not too great, the rate of formation of new crys-

tal nuclei is negligible, and the state of the solution corresponds to a metastable

region: new crystals are formed only to a limited extent, and crystals already

present grow.

Confectionery and Chocolate Engineering: Principles and Applications, Second Edition. Ferenc Á. Mohos.© 2017 John Wiley & Sons Ltd. Published 2017 by John Wiley & Sons Ltd.

337

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338 Confectionery and chocolate engineering: principles and applications

If the supersaturation is increased further, then the maximum permissible

supersaturation is attained, which defines the boundary of the metastable region.

When this boundary is exceeded, the rate of nucleation increases rapidly, and

the crystallization process becomes uncontrolled. Thus, it is expedient to con-

trol the crystallization process so that the state of the solution is characterized by

a point lying inside the metastable region, which is limited on one side by the

aforementioned boundary and on the other side by the solubility curve.

According to Nyvlt et al. (1985), the kinetics of crystallization can be divided

into two stages: formation of crystal nuclei (or nucleation) and crystal growth

proper. Both of these stages occur simultaneously in a crystallizer, but they will

be considered separately in the study of crystallization processes presented later.

It is usual to subdivide the formation of crystal nuclei according to the follow-

ing scheme, depending on the mechanism involved:

1 Primary nucleation (in the absence of solid particles), which may be either

homogeneous or heterogeneous (catalytically initiated by a foreign surface)

2 Secondary nucleation, which can be classified further into apparent, true and

contact secondary nucleation

A basic criterion for this distinction is the presence or absence of a solid phase.

Secondary nucleation is contingent on the presence of crystals.

10.2.2 SupersaturationTo study the nucleation and growth of crystals as a function of the driving force

for crystallization, we define the concept of supersaturation as follows:

Δc = c − ceq. (10.1)

We can also use the relative supersaturation

s =c − ceq

ceq

= Δcceq

(10.2)

or the supersaturation ratio

S = cceq

= s + 1 (10.3)

where c is the concentration of the dissolved substance in the supersaturated

solution and ceq is the concentration in the saturated solution.

The numerical values of Δc, s and S are dependent on the choice of units in

which the concentration of the substance in solution is given. This dependence

is demonstrated in the following example.

Example 10.1In an example given by Mullin (1973), the concentration of a saturated aqueous

solution of sugar is ceq =2040 kg sugar/1000 kg water, and the concentration of a

supersaturated solution is c=2450 kg sugar/1000 kg water (both values at 20 ∘C).

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Crystallization 339

Taking these concentrations into account, we obtain

s = Δcceq

= (2450 − 2040)kg sugar∕1000kg water

= 410kg sugar∕1000 kg water

s = Δcceq

= 410 kg sugar∕2040kg sugar = 0.2001, and S = s + 1 = 1.2001.

If we work with concentrations in kg sugar/kg solution, then

c = 2450kgsugar∕3450kgsolution = 0.7101kgsugar∕kg solution, and

ceq = 2040kg sugar∕3040kg solution = 0.6711kg sugar∕kg solution

Δc = (0.7101 − 0.6711)kg∕kg solution = 0.039kg sugar∕kg solution

s = Δcceq

= 0.039kg sugar∕0.6711kg sugar = 0.058, and S = s + 1 = 1.058.

If we work with molarities x, where M(sugar)= 342 and M(water)= 18,

xeq =2040∕342

2040∕342 + 1000∕18= 0.097

x =2450∕342

2450∕342 + 1000∕18= 0.114

Δx = 0.114 − 0.097 = 0.017

s = Δxxeq

= 0.0170.097

= 0.175, and S = s + 1 = 1.175.

10.2.3 Thermodynamic driving force for crystallizationThe driving force for crystallization is expressed thermodynamically by the dif-

ference between the chemical potentials of a crystalline substance 1 in the super-

saturated solution (state ′) and in the saturated solution (state ′′):

Δ𝜇1 = 𝜇′1 − 𝜇

′′1 . (10.4)

The expression for the chemical potential of a substance i in a solution is

𝜇i = 𝜇∘i + RT ln ai (10.5)

where 𝜇∘i

is the chemical potential in the standard state, R is the gas constant,

T is the temperature (K), ai = xi𝜉i is the chemical activity of substance i in the

solution, xi is the molarity (molar concentration) of substance i in the solution

and 𝜉i is the activity coefficient of substance i in the solution.

Taking Eqn (10.5) into account, the form of Eqn (10.4) is

Δ𝜇1

RT= ln

(a1

aeq

)= ln Sa (10.6)

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340 Confectionery and chocolate engineering: principles and applications

where a1 and aeq are the chemical activities of substance 1 in the supersaturated

and the saturated state, respectively, and Sa is the thermodynamic supersatura-

tion ratio calculated from the chemical activities.

Carrying on from Example 10.1, if Sa = 1.175, then from Eqn (10.6),

Δ𝜇1

RT= ln

(a1

aeq

)= ln Sa = 0.1613

and

Δ𝜇1 = 0.1613RT = 0.1613 × 8.31434 (J∕molK) × 293K = 392.94J∕mol.

A simplification of Eqn (10.6) can be used:

Δ𝜇RT

≈ s (10.7)

where s is calculated as a ratio of molarities, if the following assumptions are

fulfilled:

• The ratio of the activity coefficients 𝜉i/𝜉i.eq is equal to 1.

• Dissociation of the substance in the solution can be neglected.

• ln(1+ s)≈ s in the whole supersaturation region.

In theoretical studies, the driving force for crystallization must always be

expressed by means of the exact expression Δ𝜇/RT and not simply on the basis

of concentrations (e.g. ln 1.175= 0.1613≠ 0.175).

10.2.4 Metastable state of a supersaturated solutionThe phase diagram of a two-component solid phase is given in Fig. 10.1. The

lower limit of the metastable zone is the solubility of the substance, and the upper

limit is the metastable boundary of the solution. The liquid system contains a

substance with a positive temperature coefficient of solubility in the temperature

interval considered, that is, dceq/dT> 0.

According to Ting and McCabe (1934), the metastable zone is separated into

two parts, separated by the dashed line in Fig. 10.1. In the region between the

dotted line and the upper boundary of the metastable zone, spontaneous nucle-

ation is possible. The position of the metastability boundary is expressed by the

maximum attainable supercooling:

ΔTmax = T2 − T1 (10.8)

which corresponds to the maximum attainable supersaturation:

Δcmax = ceq.T(2) − ceq.T(1) ≈ ΔTmax

(dceq

dT

)(10.9)

Preparation of a solution by the route A′ →A→B represents the polythermal

method.

Isothermal preparation of a supersaturated solution begins at point A′′ and

involves the evaporation of solvent at a constant temperature up to the

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Crystallization 341

Region of

spontaneous

nucleation

No spontaneous

nucleation

A'A

B

Cc3

c2

c1

T1

T2

T3

B' A"

Solubility

Temperature, T

Metastability

limit

••

Equili

bri

um

concentr

ation, C

c

Figure 10.1 Metastable zone. Source: Nyvlt et al. (1985). Reproduced with permission from

Elsevier.

saturation point A and then proceeds through the metastable region up to point

C at the metastability boundary. After this limit is passed, the solution is in a

labile state, and the solid phase is immediately and spontaneously precipitated.

Since the lines of solubility and the metastability boundary are not parallel in

general (see later text),

ceq.T(2) − ceq.T(1) ≈ ceq.T(3) − ceq.T(2), (10.10)

that is, the value of Δcmax obtained by the polythermal method does not agree

with that obtained by isothermal preparation.

The width of the metastable zone can be measured either using the isothermal

method or using the Nyvlt polythermal method; details can be found in Nyvlt

et al. (1985, pp. 47–65).

10.2.5 Nucleation kineticsThe initial concept of nucleation is the formation and decomposition of clusters

of molecules of the dissolved substance – aggregates – as a result of local fluctua-

tions. For each value of the supersaturation of the solution, a critical cluster size

can be determined – the critical nucleus – which is in equilibrium with the sur-

rounding medium and has the same probability of growth as of disintegration. If

an aggregate is smaller than the critical size, then the probability of its decompo-

sition is large, whereas clusters larger than the critical size grow spontaneously.

In order for a stable nucleus to be formed in a solution, a certain degree of

supersaturation must be exceeded. The solubility of small particles depends on

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342 Confectionery and chocolate engineering: principles and applications

their size L according to a relationship given by Ostwald and Freundlich:

lncL

c∞=

2𝜎slM

RT𝜌cL(10.11)

where cL is the solubility of small crystals of size L; c∞ is the solubility of large

crystals, that is, c∞ = ceq, and cL/c∞ ≥ 1; 𝜎sl is the specific surface energy of the

solid–liquid surface (J/m2); M is the molar mass of the substance dissolved

(kg/mol); R=8.31434 J/mol K is the gas constant; T is the temperature (K); and

𝜌c is the density of the substance dissolved (kg/m3).

The fact that small particles are more readily recognized from Eqn (10.11). If L

increases, cL is decreased, and vice versa. This phenomenon is known as Ostwald

ripening.

For some values of 𝜎sl, see Nyvlt et al. (1985, pp. 71–73, 309). For example, the

values of 𝜎sl for KCl, cholesterol and BaSO4 are 35 J/m2, 17 J/m2 and 116 J/m2,

respectively. The usual values are between 20 and 200 J/m2 (the values for spar-

ingly soluble substances are in the region of 100 or higher).

Example 10.2Let us calculate the ratio of the solubilities of crystals of radii L10 = 10 μm

and L1 = 1 μm (the corresponding concentrations are denoted by c10 and c1,

respectively), supposing that all other parameters in Eqn (10.11) are unchanged.

With such a supposition, Eqn (10.11) can be written as ln (c10∕c∞) = K∕10 and

ln(c1∕c∞) = K, where K is a dimensionless constant.

ln

(c1

c∞

)= K → c1 = c∞eK ; ln

(c10

c∞

)= K

10→ c10 = c∞e0.1K .

Thus, c1/c10 = e0.9K > 1 since 0.9K>0.

The classical theory of nucleation states that clusters of particles are formed in

solution according to the following scheme:

a + a ↔ a(2)

a(2) + a ↔ a(3)

a(i − 1) + a ↔ a(i).

As soon as these clusters attain a critical size corresponding to the relationship

given in Eqn (10.10), the intermolecular forces between the particles within a

cluster begin to predominate over the effect of the surrounding particles, and the

cluster becomes stable. Taking this mechanism into consideration, a relationship

can be given for the rate of nucleus formation:

dNdt

= k′ exp[−ΔG

kT

](10.12)

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Crystallization 343

where dN/dt is the rate of increase of the number of nuclei (s−1), k′ is a constant

(s−1), k= 1.38062×10−23 J/K (the Boltzmann constant), T is the temperature (K)

and G is the Gibbs free enthalpy (J). According to the classical expression of

Nielsen (1964, 1969),dNdt

= Ω exp

(− K′

T3log2S

)(10.13)

where Ω is a pre-exponential factor (s−1), K′ is a constant (K3), T is the tem-

perature (K) and S is the supersaturation ratio (calculated from the chemical

activity).

It follows from Eqn (10.13) that the width of the metastable region decreases

with increasing saturation temperature of the equilibrium solution. An empir-

ical relationship has been proposed by Tobvin and Krasnova (1949, 1951) and

Akhumov (1960) for the dependence of Smax on temperature:

Smax = 1 + A exp(B

T

)(10.14)

where A and B are constants.

During cluster formation, N particles (atoms, molecules or ions) of the given

substance in the bulk of the original phase are transferred from the original phase

1 into the final phase 2. This process is accompanied by a change in the Gibbs

free enthalpy of

ΔG = −Δ𝜇N + G1(N) (10.15)

where Δ𝜇 is the free enthalpy difference of a single species in the phase consid-

ered and G1(N) is the free enthalpy, which depends on the formation of an inter-

phase boundary and on the translational and rotational movement of the cluster.

Although there are other approaches to the kinetics of nucleation, it should be

emphasized that a correct application of the classical theory leads in most cases

to an interpretation of any given experiment with equal success. Moreover, it

seems that the rate of homogeneous nucleation in melts is generally described

well by the classical theory.

10.2.6 Thermal history of the solutionOf the many factors affecting the width of the metastable zone, the thermal

history of the solution is particularly interesting. It has long been known that

solutions that have been maintained at a temperature sufficiently higher than

the equilibrium temperature for several hours have broader metastable zones

or slower nucleation than solutions whose temperature has not increased much

above the equilibrium temperature.

Theoretical considerations have demonstrated that the experimental data can

be explained by assuming that there is a change in the mean subcritical cluster

size, produced by a deviation from its steady-state value, and that the rate of

change of this deviation can be described by a first-order kinetic equation:

− dN(n)dt

= const.(N − Neq) (10.16)

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344 Confectionery and chocolate engineering: principles and applications

or

ln(N − Neq) = −const. t + C (10.17)

where N is the number of characteristic cluster sizes at time t, Neq is the equilib-

rium number of characteristic cluster sizes corresponding to the temperature of

the solution, t is the time of overheating, C is an integration constant, n is an arbi-

trary degree of aggregation and N(n) is the number of characteristic sizes of clus-

ters which have an aggregation degree n. (N−Neq) is proportional to the width

of the metastable zone, and it decreases if t (the time of overheating) is increased.

For details, see Nyvlt and Pekárek (1980) and Nyvlt et al. (1985, pp. 85–94).

10.2.6.1 Influence of mechanical action on the metastable zoneUnstirred solutions have broader metastable zones than have stirred solutions

(Mullin and Osman, 1973; Garside et al., 1972). According to the theory of local

isotropy, regions with an isotropic character are formed even in very strongly

stirred solutions, with a size corresponding to the intensity of stirring. The over-

all volume of the solution can be divided into a large number of elementary

volumes. The number of elementary volumes in an isotropic region depends on

a quantity w characterizing the intensity of stirring. The greater the effect of stir-

ring, the greater are the supersaturation and the temperature of the solution.

This effect can be described by the following equation:

dcn

dw= k(c0 − cn) or cn − cmin = (c0 − cn)[1 − exp(−kw)] (10.18)

where w is the intensity of stirring, cmin is the minimum value of the concentra-

tion in the vicinity of a cluster provided that the stirring does not lead to exchange

of elementary volumes, c0 is the average concentration in the solution, cn is the

decreased concentration of the substance in the isotropic region around a cluster

and k is a constant.

10.2.6.2 Effect of viscosity of solution on the width of the metastablezone

In very viscous solutions, the nucleation rate and thus also the width of the

metastable zone are a function of the viscosity of the solution (Mullin and Leci,

1969; Pacák and Sláma, 1979). Above a certain critical viscosity, the nucleation

rate in the solution decreases with increasing viscosity, even if the supersatura-

tion of the solution increases at the same time.

10.2.7 Secondary nucleationThe mechanisms of nucleation resulting from the presence of crystals in a super-

saturated solution are generally termed secondary nucleation. These mechanisms

can be separated into three groups, according to Botsaris and Denk (1970) and

Nyvlt (1973b, 1978); these groups differ in the source of crystal nuclei:

1 Apparent secondary nucleation. The types of apparent secondary nucleation are

as follows:

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Crystallization 345

∘ Seeding with crystal dust (dust breeding), which occurs when a supersatu-

rated solution is seeded with untreated crystals.

∘ Polycrystalline breeding: Here, it is necessary for the crystal growth to occur

at such high supersaturation values that the crystals do not grow regularly

but form polycrystalline aggregates.

∘ Macroabrasion can become important during intense stirring of suspensions.

In the case of the attrition mechanism of macroabrasion, the rate of nucle-

ation does not depend markedly on the supersaturation (Asselbergs and De

Jong, 1972). According to Nyvlt (1981a), the rate of this type of nucleation

is dependent on the number of nuclei formed by macroabrasion, the mean

retention time of the solution and the rate constant of macroabrasion; the

latter is largely determined by the hardness of the crystals and the quality

of the crystal surface.

2 True secondary nucleation. It is difficult to distinguish between the various

mechanisms of true secondary nucleation (see following text), but in some

instances it is possible:

∘ Formation of nuclei from the solid phase, that is, from a seed crystal

∘ Formation of nuclei from a dissolved substance in solution

∘ Formation of nuclei from a transition phase at the crystal surface

The kinetics of true secondary nucleation can be described by a modification

of the Becker–Döring equation in the form (Nyvlt, 1981b)

dNN

dt= k′ exp

[− C

ln2(w∕weq)

](10.19a)

where dNN/dt (s−1) is the number of nuclei coming into existence by true

secondary nucleation per unit time, k′ (s−1) is the rate constant of true sec-

ondary nucleation, C is a constant, ln denotes the natural logarithm, w is

the concentration of the solution, weq is the solubility and W is a refer-

ence concentration close to the saturation point. An approximate form of

Eqn (10.19a) was given by Nyvlt (1972):

dNN

dt= kN(Δw)n (10.19b)

where kN is the rate constant, Δw=W−weq, W is a reference concentration

close to the saturation point, n= (Δw/W)N′ is an exponent and N′ is the

number of particles forming a crystal nucleus. This is the power law that

is widely used for describing the kinetics of nucleation in addition to Eqns

(10.12) and (10.13).

3 Contact nucleation. This mechanism predominates in stirred crystallizers. It

occurs when a crystal is contacted with a glass rod or various other materials,

and even this contact induces nucleation. In contrast to simple abrasion,

which can also occur in undersaturated solutions, this mechanism is always

connected with growth of the seed crystal, where visible crystal damage need

not occur.

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346 Confectionery and chocolate engineering: principles and applications

10.2.8 Crystal growthWith the development of industrial crystallization, ever greater attention has

been devoted to questions connected with the growth rate of crystals.

The rate of growth can be characterized in several ways, the most obvious

way being the linear growth rate dL/dt, which expresses the rate of change of

a characteristic crystal dimension L with time. Other characteristic parameters

concern the surface area and the volume of the crystals: in the case of regular

(model) geometric bodies, the relationships between these parameters can easily

be expressed (Nyvlt, 1981a). The most marked and obvious property of crystals

is their shape, which differs for different substances. Explanations for this vari-

ability have been sought in the energy conditions in the crystal lattice, leading

to different rates of growth for different individual planes.

10.2.8.1 𝚫L Law: Constant growth of crystalsConstant growth was described by McCabe (1929), who postulated a ΔL law,

whereby crystallographically equivalent faces of similar crystals would grow at

the same rate, that is, dL/dt= constant:

L(t) = L0 +(

dLdt

)Δt = L0 + ΔL (10.20)

where L0 (m) is the original size of the crystal; dL/dt (m/s) is a constant, equal to

the linear rate of growth of the size; Δt (s) is the duration of crystal growth; and

ΔL (m) is the increment of crystal size during a time interval Δt. The implicit

meaning of the relationship described by Eqn (10.20) is that dL/dt is independent

of L0.

Moreover, since the weight of a crystal is proportional to the cube of its size,

if the ΔL law holds, then the mass distribution does not change during crystal-

lization. Consequently, the weight ratio R for bulk crystal growth can be calcu-

lated from

R =

∑wi(L0,i + ΔL)

3

∑wi(L0,i)3

(10.21)

where wi is the mass ratio of the ith crystal fraction, L0,i is the original size of the

ith crystal fraction and ΔL is the increment during Δt.

McCabe’s ΔL law is important also because, in a sense, all other theories of

crystal growth treat it as a starting point, the deviations from which are to be

explained. Example 10.3 shows how the ΔL law works in practice.

Example 10.3In Table 10.1, w(i) is the mass ratio (unchanged after t1 and t2 minutes);

i=1, 2, 3, 4, 5 labels the various fractions; L(0), L(1) and L(2) are the sizes of

the crystals at times t0, t1 and t2, respectively; S(0) is the denominator of Eqn

(10.21); S(1) and S(2) are the numerator of Eqn (10.21); R(1)= S(1)/S(0); and

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Crystallization 347

Table 10.1 Data for demonstration of the ΔL law in Example 10.3.

w(i)L(0)

(mm) L(1) L(2) S(0) S(1) S(2)

0.1 0.248 0.36 0.383 0.001525 0.004666 0.005618

0.27 0.183 0.295 0.318 0.001655 0.006932 0.008683

0.43 0.119 0.231 0.254 0.000725 0.0053 0.007046

0.15 0.078 0.19 0.213 7.12×10−5 0.001029 0.00145

0.05 0.059 0.171 0.194 1.03×10−5 0.00025 0.000365

1 0.003986 0.018176 0.023162R(1)=4.559978 R(2)=5.810684

R(2)= S(2)/S(0). For every fraction,

ΔL(t1) = L(1) − L(0) = 0.112mm

ΔL(t2) = L(2) − L(0) = 0.135mm.

The constant linear rate of crystal growth means that

[L(1) − L(0)]t1 = [L(2) − L(0)]t2 = [L(2) − L(1)](t1 − t2)

.

The actual values of t2 and t1 are uninteresting from our point of view. How-

ever, we can calculate the constant linear growth rate of the crystals using, for

example, the values t1 =100.00 min and t2 = 120.54 min. Then,

0.112100

= 0.135120.54

= 0.135 − 0.112120.54 − 100.00

≈ 0.00112mm∕min = dLdt

.

The original bulk weight of the crystals has grown by a factor of R(1)= 4.56

times after t1 minutes and R(2)= 5.81 times after t2 minutes.

Procedure of the aforementioned calculation, see Table 10.1

The ratios of the various fractions remain unchanged during the crystallization.

The differences between the values in columns L(1) and L(0) are equal to

0.112 mm (e.g. 0.36− 0.248= 0.171− 0.059= 0.112). The differences between

the values in columns L(2) and L(0) are equal to 0.135 mm (e.g. 0.318− 0.183=0.213−0.078=0.135). These equal differences correspond to ΔL.

Let us now calculate the values of S(0), S(1) and S(2) for fraction 3, with

w(i)= 0.43, according to Eqn (10.21):

S(0) = 0.43 × 0.1193 = 0.000725

S(1) = 0.43 × 0.2313 = 0.0053

S(2) = 0.43 × 0.2543 = 0.007046∑

S(0) = 0.003986,∑

S(1) = 0.018176,∑

S(2) = 0.023162

R(1) = S(1)S(0)

= 0.0181760.003986

= 4.559978

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348 Confectionery and chocolate engineering: principles and applications

and

R(2) = S(2)S(0)

= 0.0231620.003986

= 5.810684.

In Eqn (10.21), it is supposed that the weight of a crystal is proportional to the

cube of its size; the proportionality factor is simplified by the formation of a ratio.

For further details, see Nordeng and Silbey (1996), Kile et al. (2000) and Kile

and Eberl (2003).

10.2.8.2 Deviations from the 𝚫L Law: Size-proportionate growthof crystals

However, it has been found in a number of experimental studies that substan-

tial deviations from the ΔL law occur in some systems; for example, in a stirred

suspension of crystals, large crystals mostly grow faster than small crystals. The

deviations may be consequences of Ostwald ripening (the solubility of crystals

is dependent on crystal size), differences in diffusion rate for crystals of different

size and dependence of the surface integration mechanism on the crystal size.

Proportionate (size-dependent) growth, evidenced in both natural and synthetic

crystal systems, appears to account better for observed crystal size distributions

(CSDs). Simple mathematical arguments that favour proportionate rather than

constant growth for most natural systems have been presented by Eberl et al.

(2002). Proportionate growth can be approximated by (Kile and Eberl, 2003)

Xj+1 = Xj + kjXj

√b2 − 4ac. (10.22)

Proportionate growth has also been approximated, contrary to Eqn (10.20), as

drdt

= kr (10.23)

and ascribed (where k is constant) to:

• An accelerated solution velocity around larger crystals

• A greater density of dislocation defects on the surfaces of larger crystals

• Effects of lattice strain as a function of crystal size

In both Eqns (10.21) and (10.22), kj may contain inherent randomness.

According to the law of proportionate effect, kj is replaced by a random number

𝜀j in an equation similar to Eqn (10.22), where 𝜀j usually varies between 0 and

1. Such randomness is required to produce a log-normal CSD, which is one of

the most commonly observed CSD shapes. Constant growth can be distinguished

from proportionate growth by the effects that the growth mechanisms have on

the shapes of CSDs.

Constant growth maintains the absolute size differences between crystals as

the mean size increases because such growth can be described by adding the

same layer thickness to each crystal per unit time. For example, if one crystal is

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Crystallization 349

2 mm smaller than another at the beginning of growth, this 2 mm size difference

will be maintained throughout the growth process. Proportionate growth,

however, maintains the relative size differences between crystals because growth

is modelled by multiplying each size by a constant. In other words, if one crystal

is twice the size of another at the beginning of proportionate growth, it will

remain twice the size as growth proceeds.

There is some dispute as to whether only proportionate growth can generate

and maintain a log-normal CSD and whether only proportionate growth can

maintain the theoretical shape of the universal steady-state curve expected from

Ostwald ripening (see later text) after ripening has ceased.

10.2.9 Theories of crystal growthThe theories of crystal growth can, in principle, be divided into two broad

categories: theories dealing with crystal growth from a purely thermodynamic

point of view and theories dealing with the actual kinetics of crystal growth that

attempt to describe the effects of external parameters (such as concentration,

temperature and pressure) on the final crystal shape and also determine the

effect of these parameters on the rate of growth of the individual crystal faces.

Since we are dealing in this book with industrial crystallization processes and

are focusing on the technological questions of confectionery production, only

the boundary layer theory and the diffusion layer model are discussed here.

10.2.9.1 Boundary layer theoryVolmer (1939) determined experimentally the existence of a boundary layer

between the mother phase and the crystal, which adheres strongly to the crys-

tal surface and in which the structural species (molecules, atoms or ions) move.

A complicated potential surface can be assigned to the crystal surface, where

the valleys correspond to possible resting positions of adsorbed particles and the

peaks are a measure of the potential energy that the adsorbed species must over-

come to change their position. This energy is lower than that necessary to leave

the Volmer layer and for a transition into the mother phase.

The coefficient D of surface self-diffusion of an adsorbed species was given by

Taylor and Langmuir (1933) by the equation

D = d2

4tp(10.24)

where d is the average distance between adsorbed species in the boundary layer

and tp is the mean period of time spent by a particle in a position corresponding

to a potential valley. Volmer’s discovery of the existence of the boundary layer

and of surface diffusion of species within this layer was especially important for

the development of all modern theories of crystal growth and from the point of

view of practical applications.

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350 Confectionery and chocolate engineering: principles and applications

10.2.9.2 Diffusion layer modelThe diffusion theory of crystal growth is one of the oldest theories in this field.

According to this model, the crystallization process is separated into the following

steps:

1 Transfer of the substance to the diffusion layer

2 Diffusion of the substance through the diffusion layer

3 Incorporation of particles of the substance into the crystal lattice

4 Removal of heat released during crystal growth from the crystal into the

mother phase

The diffusion rate can generally be described by Fick’s first law in the form

dmdt

=DA(c − ck)

𝛿(10.25)

where dm/dt is the amount of substance diffusing per unit time through an area

A; D is the diffusion coefficient; c is the concentration of the substance in the

mother phase (c> ck > ceq); ck > ceq is the concentration of the substance at the

crystal surface, inside the Volmer layer; and 𝛿 is the thickness of the Volmer

layer. According to the investigations of Nyvlt and Václavu (1972) and Garside

and Mullin (1968), Eqn (10.25) can be written in the form

dmdt

= kGA(c − ceq)g (10.26)

where kG includes the ratio D/𝛿 and is a formal rate constant and g is an exponent

(=1–2).

10.2.10 Effect of temperature on growth rateIt is known that a rise in temperature promotes diffusion. For a broad interval of

temperature, the usual form of the diffusion coefficient D is

D = ATn exp(−B

T

)(10.27)

where n, A and B are positive constants and T is the temperature (K) (Liszi, 1975,

p. 286). It can be shown from Eqn (10.27) that

𝜕D𝜕T

= [nATn−1 + ABTn−2] exp(−B

T

)> 0,

that is, if the temperature is raised, D is increased. For a smaller interval of tem-

perature, a linear approximation holds:

D = D0(T0 + aΔT) (10.28)

where a (>1) is a constant.

The expression for the growth rate in Eqn (10.26) contains the concentration

difference c− ceq, which is also a function of temperature, and this usually

decreases under the effect of a temperature rise. But this decrease is com-

pensated by the increase in the diffusion coefficient D. Consequently, a rise in

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Crystallization 351

temperature speeds up the growth rate. This effect is important from the point of

view of confectionery technology as well: in the production of grained sweets,

the pulling operation starts a slow crystallization process, which must not be

completed during shaping but must be completed during storage before the

product leaves the plant. Therefore, before packaging, an overnight relaxation

is needed in a warm room at about 45–50 ∘C to complete the crystallization.

10.2.11 Dependence of growth rate on the hydrodynamicconditions

McCabe and Stevens (1951) demonstrated that the mean linear rate of crystal

growth depends on the relative velocity u of the liquid and solid phases according

to the relationship (dLdt

)−1

=(

1kd

+ 1ki

)𝜌c

Δc(10.29)

where L is the linear size of the crystal, kd (kg/m2 s) is the rate constant of diffu-

sion, ki (kg/m2 s) is the rate constant of incorporation of particles into the crystal

lattice, 𝜌c is the density of a solution of concentration c and Δc is the concentra-

tion difference, which serves as the driving force. If u→∞ (i.e. for very intense

stirring) and ki ≪ kd →∞, then

(dLdt

)−1

=(

1ki

)𝜌c

Δc. (10.30)

If u→0 (the rate of crystal growth is diffusion controlled) and kd ≪ ki, then

(dLdt

)−1

=(

1kd

)𝜌c

Δc. (10.31)

According to Karpinski (1980), the rate of crystal growth can be expressed as

a function of dimensionless criteria in the usual form of a Fröessling correlation

(see the discussion of the Colburn–Chilton analogy in Section 1.4.2):

Sh = a + bRecScd (10.32)

where a is a constant (a=2 for a sphere, 2√

6 for a tetrahedron and 2√

2 for an

octahedron; if Sh> 30, then a= 0 can be used), b is a constant (0.33–0.79), c is a

constant (0.5–0.6) and d= 1/3. The most commonly used form of Eqn (10.32) is

Sh = 2 + bRecSc1∕3 (10.33)

The Sherwood number is defined as

Sh =kdL

𝜌sD(10.34)

where 𝜌s is the density of the solution.

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352 Confectionery and chocolate engineering: principles and applications

It should be mentioned that in this case an equivalent rate constant ke would

be more correct than kd, where

1ke

= 1kd

+ 1ki

(10.35)

because no distinction can be made between kd and ki during intense stirring.

The Reynolds number is defined as follows:

For a single crystal:

Re =uL𝜌s

𝜂(10.36)

where 𝜂 is the dynamic viscosity of the supersaturated solution.

For crystals growing in a fluidized bed:

Re =uL𝜌s

𝜂𝜀(10.37)

where 𝜀 is the porosity of the fluidized bed.

For a rotating disc:

Re =𝜔d2𝜌s

𝜂(10.38)

where d is the diameter of the rotating disc and 𝜔 is the frequency of rotation.

For growth in a stirred suspension:

Re =L4∕3M′1∕3

𝜌s

𝜂(10.39)

where M′ is the energy dissipated by the stirrer per unit amount of suspension,

that is,

M′ (m2∕s3) = Wmsusp

.

The Schmidt number is defined as

Sc = 𝜂

𝜌sD. (10.40)

10.2.12 Modelling of fondant manufacture based on thediffusion theory

We illustrate the calculation of the growth rate constant ke with an example.

Example 10.4Fondant mass is produced with a continuous crystallizer (fondant gun), which is

a typical mixed suspension, mixed product removal (MSMPR) crystallizer. It has

a capacity of 360 kg/h, and the power consumption W of its motor that produces

dissipation energy is 3 kW. The characteristic size L of the (sugar) crystals in the

fondant is 20× 10−6 m. The density 𝜌s of the supersaturated sugar/glucose syrup

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Crystallization 353

solution used is 1.4×103 kg/m3. The (mean) dynamic viscosity 𝜂 of the solution

is 30 Pa s. The diffusion coefficient D of the sugar crystals is 2.5× 10−10 m2/s. Let

us calculate the growth rate constant ke by using the equation

Sh = 2 + 0.6Re1∕2Sc1∕3.

During 1 s, 360 kg/3600= 0.1 kg of fondant solution is produced with con-

sumption of 3 kJ of energy; consequently, M′ = 3 kW/0.1 kg= 3×104 W/kg:

Re =L4∕3M′1∕3

𝜌s

𝜂= (20 × 10−6)4∕3(3 × 104)1∕3 × 1.4 × 103

30= 7.7 × 10−4

Sc = 𝜂

𝜌sD= 30

1.4 × 103 × 2.5 × 10−10= 8.57 × 107.

Since Sc> 30, the Sherwood number can be calculated:

Sh = 0.6Re1∕2Sc1∕3 = 0.6 × (7.7 × 10−4)1∕2(8.57 × 107)1∕3

= 0.6 × (2.77 × 10−2)(4.34 × 102) = 7.21

Sh =keL

𝜌sD= 7.21 =

ke(20 × 10−6)(1.4 × 103)(2.5 × 10−10)

ke = 7.21 × 1.4 × 103 × 2.5 × 10−10

20 × 10−6= 0.126kg∕m2 s.

Calculation of growth rate of the sugar crystals

The recipe for the fondant mass is as follows:

Sugar, 80 kg

Glucose syrup, 13 kg (80% dry content= 10.4 kg, dextrose=40%)

Yield, 100 kg fondant; water content, 9.6 kg (%)

The boiling point of the sugar solution is 120 ∘C; at the end of cooling and

crystallization, the temperature is 30 ∘C.

The concentrations at the end of cooking are as follows:

Sugar, 80 kg

Glucose syrup dry content, 10.4 kg, which is distributed into two parts:

∘ Dextrose, 10.4 kg× 0.40= 4.16 kg

∘ Dextrins, 6.24 kg

The molar concentration of sugar is

80∕342

80∕342 + 4.16∕180 + 9.6∕18 + 6.24∕2000= 0.2951.

(The molar mass of the dextrins has been calculated with M= 2000; however,

their molar ratio can actually be neglected.)

At 30 ∘C, the solubility of sugar is 218.14 kg/100 kg water; therefore, the total

amount of dissolved substance (sugar+ glucose syrup) can be calculated from

225 kg/100 kg water (exact values are not at our disposal).

The amount y (kg) of the dissolved phase at 30 ∘C can be calculated as

225 + 100100

=y

9.6, that is, y = 31.2kg.

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354 Confectionery and chocolate engineering: principles and applications

Temperature (°C)

Boundary of

supersaturation B3

B3

B1

A

Saturation

0.2951

0.0557 C

30 120

Su

cro

se

mo

lar

co

nce

ntr

atio

n, X

Figure 10.2 The work curve of fondant crystallization.

Consequently, the amount of dissolved phase is 31.2 kg, and the amount of crys-

tallized sugar is (100−31.2) kg= 68.8 kg.

The concentrations in the dissolved phase are as follows:

Sugar, (80− 68.8) kg=11.2 kg;

Dextrose (assuming that it is not crystallized), 4.16 kg

Dextrins, 6.24 kg

Water, 9.6 kg

The molar concentration of sugar in the equilibrium phase is

xe =11.2∕342

11.2∕342 + 4.16∕180 + 9.6∕18 + 6.24∕2000= 0.0557

and

Δc = x − xe = 0.2951 − 0.0557 = 0.2394.

From Eqn (10.29),(

dLdt

)−1

=(

1kd

+ 1ki

)𝜌c

Δcor

(dLdt

)−1

=(

1ke

)𝜌c

Δc

or, with the substitution 1/kd + 1/ki =1/ke,

dLdt

=keΔc

𝜌c

= 0.126 × 0.2394

1.4 × 103= 2.15 × 10−5[m∕s] = 0.215μm∕s.

The mean crystal size develops during (20/0.215) s=93.02 s.

Work curve of the fondant crystallizer and calculation of retention time of the sugar

crystals

Figure 10.2 shows the A–B–C work curve; if the amount of cooling at the begin-

ning of the process is small, the appropriate work curve is A–B1–C and the point

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Crystallization 355

B1 is in the metastable region above the dotted line, where spontaneous crystal-

lization is possible. The points B2 and B3 are located in the region where strong

crystallization starts.

Let us calculate the retention time tr of a crystal particle in the crystallizer,

which has a length H= 2.5 m and an inner diameter d= 0.15 m, with a free open-

ing of 50%. The free volume of the fondant gun is 0.152 ×3.14×0.5×2.5 m3

= 0.0221 m3. The volume flow rate of the fondant mass is (0.1 kg/s)/(1.4×103 kg/m3)= 0.71× 10−4 m3/s.

The retention time is defined as

tr =volume of crystallizer

volume flow rate. (10.41)

In this case tr = 0.0221 m3/0.71×10−4 m3/s≈311 s.

This calculation illustrates a process in which, as a result of strong cooling at

the gun wall, the sugar content is crystallized but is then redissolved because

the stirrer mixes the developed sugar crystals with supersaturated, insufficiently

cooled solution from the axle of the stirrer. This crystallization–solution process

is repeated ca. 3–4 times (311/93.02≈3.34) before the ready fondant mass has

left the fondant gun.

10.3 Crystallization from melts

10.3.1 Polymer crystallizationPolymer crystallization controls the macroscopic structure of polymer materials

and thereby determines the properties of the final product. The morphology of

polymer crystals is different from that of crystals consisting of small molecules,

mainly because of the difference between the connectivity of the chains in a

polymer and the absence of such connectivity in assemblies of simple molecules.

This affects not only the equilibrium crystal structures but also the kinetics of

crystal growth.

In this context, fats and oils can be regarded as polymers. The essential fatty

acids of cocoa butter, which are typical of the kinds of fat used by the chocolate

industry, are as follows:

• Palmitic acid (P), CH3—(CH2)14—COOH, molecular mass 256

• Stearic acid (St), CH3—(CH2)16—COOH, molecular mass 284

• Oleic acid (O), CH3—(CH2)7—CH—CH—(CH2)7—COOH, molecular mass 282

The molecular mass of glycerol (C3H8O3) is 92. The molecular mass of the

triacylglycerol (TAG) P—O—St is

P + O + St + glycerol − 3H2O = 860.

(In the following, if a TAG is given as, for example, P—O—St, O means oleic acid,

not oxygen.) The TAGs of cocoa butter and other special confectionery vegetable

fats can be regarded as medium-to-large molecules.

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356 Confectionery and chocolate engineering: principles and applications

When a system is cooled from the equilibrium melting temperature Tm to a

lower crystallization temperature, polymer crystals can form two-dimensional

(2D) lamellar structures in both the melt and the solution via the stages of

nucleation, growth of lamellae and aggregative growth of spherulites. The

formation of a three-dimensional (3D) crystal structure from a disordered state

begins with nucleation and involves the creation of a stable nucleus from a

disordered polymer melt or solution. Depending on whether any second phase,

such as foreign particles or the surface of another polymer, is present in the

system, nucleation is classified as either homogeneous (primary nucleation) or

heterogeneous (secondary nucleation).

In primary nucleation, the creation of a stable nucleus by intermolecular forces

orders the chains into a parallel array. As the temperature falls below the melting

temperature Tm, the molecules tend to move towards their lowest-energy con-

formation, with stiffer chain segments, and this favours the formation of ordered

chains and thus nuclei.

Since it facilitates the formation of stable nuclei, secondary nucleation is also

involved at the beginning of crystallization through heterogeneous nucleation

agents, such as dust particles.

Following nucleation, crystals grow by the deposition of chain segments on the

surface of the nuclei. This growth is controlled by a small diffusion coefficient

at low temperatures and by thermal redispersion of chains at the crystal–melt

interface at high temperatures. Thus crystallization can occur only in a range of

temperatures between the glass transition temperature Tg and the melting point

Tm, which is always higher than Tg.

As a consequence of their long-chain nature, subsequent entanglements and

their particular crystal structure, polymers crystallized in the bulk state are never

totally crystalline, and a certain fraction of the polymer is amorphous. Polymers

fail to achieve complete crystallinity because polymer chains cannot completely

disentangle and align properly during a finite period of cooling. Lamellar struc-

tures can be formed, but a single polymer chain can pass through several lamel-

lae, with the result that some segments of the polymer chains are crystallized

Cluster

Particle

Crystallite

Figure 10.3 Fat crystal network.

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Crystallization 357

into lamellae and some other parts of the polymer chains are in an amorphous

state between adjacent lamellae.

Fat crystal networks are composed of branched, interlinked particles that form

a 3D network, the voids of which are filled by liquid fat. The particles, which are

aggregates of crystallites, form clusters. The clusters pack in a regular, homo-

geneous manner and represent the largest structural building block of the fat

crystal network. Figure 10.3 shows the hierarchical structure of the concepts of

crystallite< particle< cluster.

10.3.2 Spherulite nucleation, spherulite growth and crystalthickening

In this section, the 3D formation of spherulites is described, based on random

nucleation. The derivation of formulae for other cases, for example, needle-like

growth, is similar. The kinetics of crystallization depend on both diffusion of

the polymer and nucleation. The stages of spherulite nucleation and growth are

nucleation, growth of spherulites and crystal thickening.

Nucleation can occur at any temperature T below the melting temperature Tm

when the chemical potential of a monomer in the amorphous state (ga) and in

the crystalline state (gc) is the same, that is, ga(Tm)= gc(Tm). The main driving

force for nucleation (Δgm) upon cooling is the difference between the chemical

potentials of a monomer in the crystalline state and in the amorphous state:

Δgm = ga − gc. (10.42)

For slight cooling,

Δgm ≈ ΔSm(Tm − T) =(ΔHm

Tm

)(Tm − T) (10.43)

where ΔSm is the entropy of fusion (per unit volume) per monomer and ΔHm is

the enthalpy (heat) of fusion (per unit volume) per monomer.

The formation of an interface between the amorphous and crystalline phases

changes the Gibbs free enthalpy:

ΔG = ΔgV +∑

i

Ai𝜎i (10.44)

where V is the (total) volume of the nucleus, Ai is the ith part of the surface area

of the nucleus and 𝜎i is the free enthalpy associated with Ai. In the case of a

spherical nucleus of radius r,

ΔG =(4𝜋

3

)r3Δg + 4𝜋r2𝜎. (10.45)

Minimizing the free enthalpy with respect to r, we obtain

𝜕(ΔG)𝜕r

= 0 → r∘ = −2𝜎Δg

(10.46)

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358 Confectionery and chocolate engineering: principles and applications

where r is the critical nucleus size. Taking Eqn (10.43) into account, we obtain

r∘ = −2𝜎Tm

ΔHm(Tm − T). (10.47)

Since ΔHm is negative, the critical radius increases with a decrease of the degree

of cooling Tm − T.

The free enthalpy barrier for nucleation is obtained by substituting the value

of the critical radius into Eqn (10.44):

ΔG∘ =(4𝜋

3

)(r∘)3Δg + 4𝜋(r∘)2𝜎 = 4𝜋(r∘)2

(−2𝜎

3+ 𝜎

)= 4𝜋(r∘)2 𝜎

3

=16𝜋𝜎3T2

m

3(ΔHm)2(Tm − T)2. (10.48)

It can be seen that ΔG∘ is proportional to Tm2/(Tm − T)2. The Arrhenius equation

can be used in this case:

N = exp

(−ΔG∘

kT

)= C exp

[ −𝜎3T2m

3(ΔHm)2(Tm − T)2

](10.49)

where N is the nucleation constant per unit volume and time [in units of

nuclei/(m3 s)=1/(m3 s)], k is the Boltzmann constant, T is the temperature to

which the system is overcooled and C= ln(16𝜋).

Two types of nucleation can be observed: homogeneous and heterogeneous.

The characteristics of homogeneous nucleation are as follows:

• Polymer chains can aggregate spontaneously below the melting point.

• The distribution of the nuclei is random.

• The generation of nuclei is usually a first-order function of time:

ΔP = NΔt (10.50)

where ΔP is the number of nuclei generated during a time Δt.

• The size of the growing units is given by

Φ =(K

N

)3∕4

(10.51)

where Φ is the final average volume of the crystallized units (m3), N is as

mentioned earlier and K is the rate constant for the growth of the radius (m/s).

For homogeneous nucleation, the relationship between the nucleation rate

and temperature is, according to Turnbull and Fischer,

N = N0 exp

(−

Ed

kT− ΔG∘

kT

)(10.52)

where N0 is a material constant [nuclei/(m3 s)] and Ed is the activation energy

at the surface of the nucleus. Because ΔG∘ is proportional to Tm2/(Tm − T)2, the

nucleation rate increases with increasing overcooling (i.e. with decreasing tem-

perature); see Eqn (10.52). However, at low temperatures Ed/kT becomes domi-

nant, and since the activation energy Ed decreases in proportion to temperature,

nucleation slows down (Fig. 10.4).

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Crystallization 359

(Overcooling)

Nu

cle

atio

n c

on

sta

nt,

N

ΔGlkT dominantEdlkT dominant

Melting

point Tm

Temperature, T

Figure 10.4 Homogeneous nucleation: increasing overcooling (with decreasing temperatures)

first the term ΔG∘/kT becomes dominant which increases the nucleation rate, later the term

Ed/kT becomes dominant, and as a result, the nucleation rate will be decreased.

The characteristics of heterogeneous nucleation are as follows:

• Heterogeneous nuclei start from impurities.

• Nuclei form simultaneously as soon as the sample reaches the crystallization

temperature.

• The time dependence of nucleation is a zero-order function of time (i.e. inde-

pendent of time).

• The size of the growing units is given by

Φ =V∞

N′V0

≈ 1N′ (10.53)

where V∞ is the volume of the system when t→∞, V0 is the volume of the

system when t=0 and N′ is the number of nuclei per unit volume.

The crystal growth of low-molecular-mass materials is described by

N = exp

[−A

T− B

T(Tm − T)m

](10.54)

where m= 1 if the formation of nuclei is 2D. For a spiral-form crystal where

growth occurs with the help of a screw dislocation,

N = C(Tm − T)2 (10.55)

where A, B and C are material constants. For details, see Bodor (1991, p. 214).

After the spherulites start to touch each other, a further decrease in the Gibbs

free enthalpy can be achieved only by crystal thickening, which is very slow;

typically,dfcdt

∼ log( t

K

)(10.56)

where fc is the crystallinity ratio, t is the time (s) and K (s) is a constant.

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360 Confectionery and chocolate engineering: principles and applications

10.3.3 Melting of polymersHigh-molecular-mass crystalline materials do not melt at a single, well-defined

temperature but over a fairly wide temperature interval. The Thomson equation

is valid for the melting point of these materials:

Tm = T0.m

[1 −

2𝜎e

ΔHmD

](10.57)

where Tm is the melting point for lamellae of thickness D; T0.m is the melting

point for an infinite crystal; 𝜎e is the surface energy of the basal plane, involving

chain folding; and ΔHm is the melting enthalpy per unit volume.

Since fats are mixtures of different triglycerides, and every triglyceride has its

own typical melting point, the melting process means the successive melting of

fractions of different melting point as the temperature increases.

From a morphological point of view, melting is not simply the inverse process of

crystallization. Crystallization means nucleation and growth, while melting occurs

simultaneously at all crystallized parts of spherulites. At interfaces, where incom-

patible impurities are concentrated, melting proceeds faster.

10.3.4 Isothermal crystallization10.3.4.1 Kolmogorov–Avrami heuristic phase transition theoryKolmogorov (1937) and Avrami (1939, 1940, 1941) developed a description

of the overall kinetics of phase transitions known as the Kolmogorov–Avrami

equation. This equation can be applied to several types of phase transition, from

crystallization to cosmological problems. From the point of view of crystalliza-

tion, the Kolmogorov–Avrami equation can be demonstrated as follows.

10.3.4.1.1 Early stages of crystallization: Primary crystallizationIf spherulite nucleation and growth proceed for x minutes, during a given time

interval dx,Nm0dx

𝜌L

, (10.58)

nuclei are formed, where N is the formation (rate) constant for nucleation, that

is, the number of nuclei per unit volume and time [nuclei/(m3 s)]; m0 is the mass

(kg) of the crystallizing material at t= 0; and 𝜌L is the density of the liquid phase

(kg/m3). The nucleation rate is then

w =Nm0

𝜌L

(10.59)

where w is the growth rate of the number of spherulites (nuclei/s). Moreover,

if 𝜌S is the density of the crystallizing solid phase (kg/m3), r is the radius of a

crystallizing spherulite (m) and K is the rate constant for the growth of the radius

(m/s), then

r = Kx (10.60)

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Crystallization 361

expresses the size of a spherulite formed after time t, and

mS =(4

3

)r3𝜋𝜌S =

(43

)(Kx)3𝜋𝜌S (10.61)

expresses the total mass of a solid spherulite formed after time t. The mass growth

rate of a spherulite is

dmS

dt= wmS =

(Nm0

𝜌L

)(43

)(Kx)3𝜋𝜌S (10.62)

or

dmS =(

Nm0

𝜌L

)(43

)(Kx)3𝜋𝜌Sdt. (10.63)

After integration of Eqn (10.63) from x= 0 to x= t, the following is obtained:

mS

m0

=NK3t4𝜋𝜌S

3𝜌L

. (10.64)

If mL is the mass of the liquid phase, then

m0 = mS + mL (10.65)

andmL

m0

= 1 −mS

m0

= 1 −NK3t4𝜋𝜌S

3𝜌L

(10.66)

wheremL

m0

= 1 −mS

m0

(10.67)

is the proportionality ratio that shows the relative amount of liquid phase com-

pared with the initial mass of the crystallizing material.

10.3.4.1.2 Description of the overall crystallization process, includingcollisions

During the crystallization process, the proportionality ratio changes from one

(at the beginning of crystallization) to zero (at the end of crystallization). The

Kolmogorov–Avrami theory takes the probability of collisions into account by a

modification of Eqn (10.63) with the proportionality ratio:

dm′S =

dmS

1 − mS∕m0

=(

Nm0

𝜌L

)(43

)(Kt)3𝜋𝜌S dt (10.68)

ordmS

1 − mS∕m0

=(

Nm0

𝜌L

)(43

)(Kt)3𝜋𝜌S dt. (10.69)

After integration of Eqn (10.69) from t= 0 to t= t, the Kolmogorov–Avrami

equation is obtained:

ln

(m0 − mS

m0

)= −

NK3t4𝜋𝜌S

3𝜌L

(10.70)

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362 Confectionery and chocolate engineering: principles and applications

Equilibrium solid

Induction time

Cry

sta

lliza

tio

n (

%)

Maximum growth rate

Time (s)

7060504030201000

20

40

60

80

100

Figure 10.5 Shape of the Kolmogorov–Avrami equation.

ormL

m0

= exp(−zt4) (10.71)

where

z =NK3𝜋𝜌S

3𝜌L

. (10.72)

From Eqn (10.70), the so-called crystallinity ratio f is given by

f (t) =mS

m0

= 1 − exp(−zt4) (10.73)

which is a better-known form of the Kolmogorov–Avrami equation. In the

general case,

f (t) =mS

m0

= 1 − exp(−ztn) (10.74)

where n is the Avrami exponent.

Figure 10.5 shows the typical sigmoid shape of the Kolmogorov–Avrami

equation, which starts with an induction period (or induction time), then

continues with a quasilinear segment corresponding to the maximum growth

rate and finally ends with equilibrium. The induction period is defined by the

time at which mS/m0 (as given in Eqn (10.74)) differs appreciably from unity.

The half-time, which is also characteristic of crystallization, is defined by

f (t1∕2) = 0.5 = 1– exp{−z(t1∕2)n} → t1∕2 = (ln 2∕z)1∕n. (10.75)

The value of the exponent n in the Avrami equation (the Avrami exponent) can

vary between 1 and 4 depending on the nucleation and growth mechanisms, as

shown in Table 10.2.

In reality, 100% crystallization is never achieved. Therefore, a correction to

Eqn (10.74) is needed:

1 −f (t)fmax

= exp(−ztn) (10.76)

where fmax is the maximum crystalline fraction that can be achieved.

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Crystallization 363

Table 10.2 Avrami exponent n for different growth

and nucleation mechanisms.

Nucleation mechanism

Growthmechanism

Randomaddition, n=1

Instantaneousaddition, n=0

Spherulitic, n= 3 3+ 1=4 3+0=3

Disc-like, n=2 2+ 1=3 2+0=2

Rod-like, n=1 1+ 1=2 1+0=1

For isothermal crystallization, data obtained from differential scanning calorime-

try (DSC) can be evaluated by use of the relation

f (t)T =( 1ΔH

) ∫

t

0(dHC∕dt)dt

t∞

0(dHC∕dt)dt

. (10.77)

For the sake of completeness, we also give here the corresponding relation for

evaluating DSC data for non-isothermal crystallization, in which the variable is the

temperature T instead of the time t:

f (T) =( 1ΔH

) ∫

T

T0

(dHC∕dT)dT

T∞

T0

(dHC∕dT)dT

(10.78)

where HC is the enthalpy of crystallization and ΔH is the total enthalpy of crys-

tallization (i.e. for 100% crystallization).

In the case of mL/m0 = 0.5, t1/2 = ln 2/z can easily be determined from a plot of

f(t) versus t; see Eqn (10.77).

The reasons for deviations from the Avrami equation can be as follows:

• Simultaneous appearance of different growth mechanisms (see Table 10.2).

• The influence of impurities on crystal growth.

• The density of the growing phase is not uniform (it is higher in the internal

region), so thatmL

m0

= exp(−zt4At−m) (10.79)

where the factor At−m takes the time dependence of 𝜌S into account.

• The molecular mass distribution can influence the kinetics of crystallization.

10.3.4.1.3 Analysis of dilatometry data using the Avrami equationLet the volume of the (total) crystallizing mass m0 be Vt at a given instant of time,

and let the final volume be V∞ =m0/𝜌S when crystallization has ended. Then

Vt =mL

𝜌L

+mS

𝜌S

. (10.80)

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364 Confectionery and chocolate engineering: principles and applications

Since

m0 = mS + mL, (10.81)

therefore

Vt =mL

𝜌L

+m0 − mL

𝜌S

=m0

𝜌S

+ mL

(1𝜌L

− 1𝜌S

). (10.82)

Taking into consideration that

V∞ =m0

𝜌S

, 𝜌L =V0

m0

, 𝜌S =V∞

m0

, (10.83)

Eqn (10.82) becomes

Vt = V∞ +(

mL

m0

)(V0 − V∞) (10.84)

ormL

m0

=Vt − V∞

V0 − V∞= exp(−ztn) ≈

ht − h∞

h0 − h∞(10.85)

where htD=Vt is the volume of the crystallizing material (at t= 0 and at t→∞),

D is the diameter of the tube of the dilatometer (considered as constant) and ht is

the height of the surface of the crystallizing material at time t. From Eqn (10.85),

exp(−ztn) ≈ht − h∞

h0 − h∞= 1 − Xt (10.86)

where Xt is the relative crystallinity.

The evaluation of dilatometry data according to the Avrami equation can be

done using the double logarithm of Eqn (10.85):

ln

{− ln

[ht − h∞

h0 − h∞

]}= ln{−[(1 − Xt)]} = ln z + n ln t (10.87)

or by using Eqn (10.76):

ln

{− ln

(1 −

f

fmax

)}= ln z + n ln t (10.88)

The linearity of Eqn (10.88) forms the basis of the evaluation.

Kerti (2000) applied the Kolmogorov–Avrami equation in the form

log{− ln(1 − x)} = log k + n log t (10.89)

to distinguish between various special vegetable fats. Her results are shown in

Table 10.3, where tX is the time for which

log{− ln(1 − x)} = log z + n log tX = 0, (10.90)

that is,

− ln(1 − x) = 1 → x = e − 1e

≈ 63%. (10.91)

(The base of the logarithm log is 10.)

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Crystallization 365

Table 10.3 Distinction between various confectionery vegetable fats using

the Kolmogorov–Avrami equation (rounded values).

ParameterCocoabutter

Cocoa butterequivalent

Cocoa butterreplacer

Cocoa buttersubstitute

N 6.42 4.572 2.282 2.979

log k −22.725 −17.478 −5.52 −8.127

tX 3.54 3.823 2.419 2.728

Source: Kerti (2000). Reproduced with permission from Kerti.

At the time tX defined by Kerti using Eqn (10.89), the crystallinity (the value

of x) is about 63%. This characteristic time can be used to distinguish the group of

cocoa butter and cocoa butter equivalents (CBEs) from the group of cocoa butter

replacers (CBRs) and cocoa butter substitutes (CBSs) (Kerti, 2000).

Unfortunately, the application of the Kolmogorov–Avrami equation in the

lipid crystallization literature is inconsistent. Three different fits of the Avrami

model have produced significantly different values for the Avrami exponent and

constant (Narine et al., 2006). Some researchers suggest that only a portion of the

crystallization curve should be fitted with the model, thereby ignoring important

information about the entire crystallization process. It has also been suggested

that there are a number of line segments within a typical data set that can each

be fitted with the Kolmogorov–Avrami model, and researchers have arbitrarily

chosen one segment to fit with the model, without any justification. In fact, the

crystallization kinetics of most lipid systems are not characterized by the condi-

tions that are assumed to be valid in the Kolmogorov–Avrami model.

In order to solve this problem, a modification of the original Kolmogorov–

Avrami model was developed by Narine et al. (2006), the essence of which is the

application of the Kolmogorov–Avrami equation to consecutive segments of the

curve of solid fat content (SFC) versus time:

F1(t)F1∞

= 1 − exp(−A1tm(1)) (10.92)

where F1(t) is the absolute crystallinity at time t, F1∞ is the crystallinity at some

time when either the growth rate or the nucleation conditions change and A1 and

m(1) are the Avrami constant and exponent applicable to the nucleation, growth

and dimensionality of the crystallizing lipid over the segment of time where such

conditions are constant. In this manner, the Kolmogorov–Avrami equation for

step i is given byFi(t)F1∞

= 1 − exp[−Ai(t − 𝜏i)m(i)]. (10.93)

The total absolute crystallinity is the sum of the individual absolute crystallinities.

Marangoni (1998) emphasized that a modification which uses the form

F(t)F∞

= 1 − exp[−(At)m] (10.94)

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366 Confectionery and chocolate engineering: principles and applications

does not solve the problem of fitting but exacerbates it, since such a modification

as Eqn (10.94) would transform the Avrami constant from a complex constant

for a kth-order process to a first-order rate constant with units of t−1. However,

crystallization of fats from the melt is not a kinetically first-order process.

Several experimental techniques can be used to follow the isothermal crys-

tallization of fats as a function of time. In an isothermal DSC experiment, the

relative amount of material crystallized as a function of time is calculated by

integration of the isothermal DSC curve. The area enclosed by the baseline and

the exothermic peak corresponds to the heat of crystallization ΔH. The relative

amount of crystallized material is given by Eqn (10.77) or (10.78). In the pulsed

nuclear magnetic resonance (pNMR) technique, the SFC is measured directly.

The samples are first melted to destroy any memory effect and then transferred

to a thermostatted water bath at the crystallization temperature. SFC readings are

taken at appropriate time intervals. Wright et al. (2001) compared several differ-

ent techniques used in lipid crystallization studies and concluded that pNMR was

the best method to characterize the overall crystallization process. For further

details of these techniques, see Foubert et al. (2003).

10.3.4.2 Gompertz modelThe Gompertz model was used by Kloek et al. (2000), who claimed that there

were several analogies between crystallization of fats and bacterial growth: the

reproduction of bacteria is comparable to the nucleation and growth of crystals,

and the consumption of nutrients is comparable to the decrease in supersatura-

tion. Kloek et al. (2000) and Vanhoutte (2002) fitted their crystallization curves

to a reparametrized Gompertz equation as deduced by Zwietering et al. (1990):

S(t) = a exp[− exp

{(𝜇e

a

)(𝜆 − t) + 1

}](10.95)

where S(t) (%) is the SFC curve as a function of time t, a (%) is the value of

S(t) when t approaches infinity, 𝜇 (%/s) is the maximum crystallization rate,

e (=2.7182818) is the base of natural logarithms and 𝜆 (s) is a parameter propor-

tional to the induction time.

10.3.4.3 Aggregation and flocculation modelsBerg and Brimberg (1983) noted that the course of fat crystallization is similar to

that of aggregation and flocculation of colloids: solid fat is formed by aggregation

of dispersed particles, and fat crystals also grow by aggregation.

Prior to the main phase, an induction period exists, where the following

equations apply:

Aggregation: C − C0 = −k1(t − t0)2 (10.96)

Flocculation: ln

(CC0

)= −k3(t − t0)2 (10.97)

where C is the concentration of particles in the liquid phase at time t; C0 and t0 are

the initial values of C and t, respectively; the ki are rate constants; and C−C0 = S(t)

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Crystallization 367

is the amount of solid fat. For the main phase, the following equations were used:

Aggregation: C − C0 = −k2

√t − t0 (10.98)

Flocculation: ln

(CC0

)= −k4

√t − t0 (10.99)

10.3.4.4 Foubert modelThe model of Foubert et al. (2002) was, in contrast to the aforementioned models,

originally written in the form of a differential equation; however, an algebraic

solution assuming isothermal conditions was also developed.

The variable chosen is h, which is the amount of remaining crystallizable fat:

h(t) =a − f (t)

a(10.100)

where f(t) is the amount of crystallization at time t and a is the maximum amount

of crystallization. The variable h(t) is related to the remaining supersaturation and

thus decreases – in contrast to f(t) – in a sigmoidal way with time.

In this model, crystallization is represented as if it were a combination of a

first-order forward reaction and a reverse reaction of order n with rate constants

Ki for each of the reactions:

dhdt

= Knhn − K1h. (10.101)

Extensive parameter estimation studies revealed that the approximation Kn =K1

is acceptable, and therefore the model can be simplified to

dhdt

= K(hn − h) (10.102)

and

h(0) =a − f (0)

a. (10.103)

Since the physical interpretation of a parameter called the induction time is

more straightforward than that of the parameter h(0) and since the induction

time can be more easily extracted from a crystallization curve, the function 𝜏(x)

is introduced instead of h(0); this is defined as the time needed to obtain x%

crystallization. Thus the integrated form of Eqns (10.102) and (10.103) is

h = [1 + {(1 − x)(1−n) − 1} exp{−(1 − n)K(t − 𝜏)}]1∕(1−n). (10.104)

Figure 10.6(a) shows a visual comparison of the fit between the Avrami, Gom-

pertz and Foubert models. It can be seen that the Foubert model shows a better

fit than the two other models. The adequacy of the various models for describ-

ing isothermal fat crystallization was tested statistically by Foubert et al. (2002).

This study revealed that the Gompertz and Foubert models always perform bet-

ter than the Avrami model and that the Foubert model performs better than the

Gompertz model in the majority of cases.

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368 Confectionery and chocolate engineering: principles and applications

10.3.4.4.1 Modelling of two-step isothermal crystallizationSince fats are complex mixtures of triglycerides, their crystallization can lead to

the formation of many crystal types, owing either to polymorphism or to con-

comitant growth of several crystal types (Foubert et al. 2006a). This may lead to

crystallization curves in which two steps can be identified [Fig. 10.6(b)].

The assumptions used to build a model of crystallization were based on

the presence of an isosbestic point [Fig. 10.6(b)], indicating that the first step

involves crystallization from the melt to the 𝛼 phase and the second step involves

70

60

50

Re

lea

se

d c

rysta

lliza

tio

n h

ea

t (J

/g)

40

30

20

10

0

0.18

0.16

Isosbestic point

α

βʹ

1.66 h

0.56 h0.67 h0.78 h0.89 h1.00 h1.11 h1.22 h1.33 h1.44 h1.55 h1.66 h

1.55 h1.44 h1.33 h1.22 h1.11 h1.00 h0.89 h0.78 h0.67 h0.56 h

0.14

0.12

0.1

0.08

Pe

ak in

ten

sity

0.06

0.04

0.02

0

0.016 0.016 0.02 0.022 0.024

(b)

s (Å–1)

0.026 0.028 0.03

0 0.2 0.4

Date Avrami Gompertz Foubert

0.6 0.8 1Time (h)

(a)

1.2 1.4 1.6 1.8 2

Figure 10.6 (a) Visual comparison of fit between the Avrami, Gompertz and Foubert models

(isothermal crystallization of cocoa butter as measured by means of DSC). (b) Isothermal

crystallization of cocoa butter at 20 ∘C: SAXS diffraction patterns as a function of time. Time

span 2, from 0.56 h onwards; s (horizontal axis) is the wavenumber of the X-rays. In time span

1 (0–10.56 h), the formation of the 𝛼 modification is practically entirely completed, but the

formation of 𝛽′ is still at an early stage. In time span 2, the formation of the 𝛽′ modification

takes place. (c) Example of a two-step process and a fit obtained by combining two Foubert

equations. (d) Example of crystallization curves obtained with a fractional model using the

following parameter values: K𝛼 = 6/h, K𝛽′ =3/h, n𝛼 = 100, n𝛽′ = 4, 𝜏𝛼 = 0.01 h and 𝜏𝛽′ =0.5 h.

Source: Foubert et al. (2003). Reproduced with permission from Elsevier.

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Crystallization 369

70

60

50

40

30

20

10

0

1.2

1

0.8

0.6

0.4

0.2

0

0 1 2 3 4

0 0.5 1 1.5 2 2.5

Time (h)

(c)

(d)

Time (h)

Cry

sta

llize

d f

ractio

nR

ele

ase

d c

rysta

llize

d h

ea

t (J

/g)

Data Combination of two foubert equations

3 3.5

frβʹ

frα

Figure 10.6 (Continued)

a polymorphic transformation from 𝛼 to 𝛽′ without direct crystallization from

the melt into 𝛽′. The data sets shown in Fig. 10.6(b) were acquired by means

of time-resolved X-ray diffraction (tr-XRD). The small-angle X-ray scattering

(SAXS) represent the long spacings.

To develop the two-step model, the Foubert model was reformulated (Foubert

et al., 2006a) (see Eqn 10.100) as

dtdt

= K(a − f ) − aK

[a − f

a

]n

, (10.105)

and this equation formed the basis of the proposed two-step model.

The change in the fractions of 𝛼 and 𝛽′ crystals, fr𝛼 and fr𝛽′ , as a function of

time can be written as a function of the rate r𝛼 of formation of 𝛼 crystals from

the melt and the rate r𝛽′ of transformation of 𝛼 to 𝛽′ crystals; see Eqn (10.105),

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370 Confectionery and chocolate engineering: principles and applications

where a=1:

rα = Kα[1 − (f rα + f rβ′ )] − Kα[1 − (f rα + f rβ′ )]n(α) (10.106)

rβ′ = Kβ′ (1 − f rβ′ ) − Kβ′ [1 − (1 − f rβ′ )]n(β′). (10.107)

In addition, the following equations hold:

df rαdr

= rα − rβ′ (10.108)

drβ′

dr= rβ′ . (10.109)

The initial values of fr𝛼 + fr𝛽′ were calculated for x= 0.01.

Figure 10.6(c) shows the crystallization curves of the 𝛼 and 𝛽′ modifications as

a function of time. Figure 10.6(d) shows several crystallization curves obtained

with a fractional model by Foubert et al. (2006a).

For further details of kinetic formulae, see Smith (2005). On microstructural

properties of isothermal palm oil crystallization, see Veerle De Graef (2009).

10.3.5 Non-isothermal crystallizationIn the study of non-isothermal crystallization, the energy released during the

crystallization process is measured as a function of the temperature T by means

of the DSC technique. This method was developed by Jeziorny (1978).

The relative crystallinity, X(t), is given by

X(t) =ΔHT

ΔHC

(10.110)

where ΔHT (J) is the enthalpy of crystallization released during a temperature

change T−T0 and ΔHC is the overall enthalpy of crystallization, which is equal

to the area enclosed by the crystallization peak in a plot of H versus T obtained

from the DSC data. The crystallization time t can be calculated from the relation

t =( 1Φ

)|T − T0| (10.111)

where Φ is the heating or cooling rate (K/s), T is an arbitrary temperature (K)

and T0 is the onset temperature (K).

The basis of data evaluation may be the Avrami equation:

f (t) =mS

m0

= 1 − exp(−zt4) (10.73)

where mS/m0 =X(t); see Eqns (10.109) and (10.110). Another approach was pro-

posed by Ozawa (1971), who used a modified Avrami equation of the form

1 − X(t) = exp

[−K(T)

Φm

](10.112)

where K(T) (K/min) is a cooling/heating function, Φ is the heating or cooling rate

(K/s) and m is the Ozawa exponent, which depends on the dimensionality of the

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Crystallization 371

crystal growth (Ziru, 1997). K(T) and m can be determined after linearization

of Eqn (10.112) in the usual way (Yuxian, 1998). Jooson et al. (2003) studied

both of these approaches, and the Avrami equation in the original form provided

better fitting.

Non-isothermal crystallization needs further study. The modelling approaches

used for isothermal crystallization (e.g. the Avrami equation) may provide

starting points; however, the variables and parameters of the equations describ-

ing the isothermal case cannot be used unchanged. It should be emphasized

that from the engineering point of view, it seems essential to consider the

non-isothermal case.

10.3.6 Secondary crystallizationCrystallization does not always end as predicted by the Kolmogorov–Avrami

equation, which can be applied to primary crystallization only. A secondary stage

of crystallization can proceed after the first stage, and this process can last for a

considerable period of time.

The crystallinity versus time relationship in the case of secondary crystalliza-

tion can be given by the formula

x(t) = C + D ln

[t − t0

E

](10.113)

where x(t) (<100%) is the crystalline mass fraction at time t; C, D and E (s) are

constants; and t0 is the time point at the beginning of the secondary crystallization

process.

10.4 Crystal size distributions

10.4.1 Normal distributionIn the study of crystallization processes, a great deal of attention is devoted to

the size distribution of the particles of the product formed. It has been found

that the sieve spectrum may be a useful diagnostic indicator of the operation of

a crystallizer and that the data from a sieve analysis can be used to evaluate a

number of fundamental kinetic parameters that characterize the crystallization

process and can be used to guide the design of machinery.

The best-known distribution function (Randolph and Larson, 1971) is the

normal distribution, defined as follows:

f (L) = 1𝜎(2𝜏)1∕2

exp

[−(L − L50)2

2𝜎2

](10.114)

where 𝜎 is the scatter and L50 is the crystal size corresponding to an oversize

fraction of 50%. The normal distribution is frequently used, especially to express

the distribution of particle sizes of poorly soluble substances.

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372 Confectionery and chocolate engineering: principles and applications

10.4.2 Log-normal distributionCSDs in the larger size region are mostly better expressed by an empirical

log-normal distribution (Randolph and Larson, 1971; Nyvlt and Cipová, 1979):

f (L) = 1log 𝜎(2𝜏)1∕2

exp

[−

log2(L∕L50)2log2

𝜎

]. (10.115)

For both the normal and the log-normal distribution functions, the distribution

of the number of particles is expressed by the relationship

N(L) = 0.5 + 0.5erf(x) (10.116)

where, for the normal distribution,

x =L − L50

21∕2𝜎(10.117)

and, for the log-normal distribution,

x =log(L∕L50)21∕2 log 𝜎

. (10.118)

As has been demonstrated by Nyvlt and Cipová (1979), even the log-normal

distribution cannot express the experimental data in corresponding coordinates

as a straight line; the plot is curved, especially in the region below oversize frac-

tions of 10% and above 90%.

10.4.3 Gamma distributionThe gamma distribution function

f (L) =La′ exp(a′L∕b)

Γ(a′ + 1)(b∕a′)(a′+1) (10.119)

is very useful for expressing the CSDs of crystallization products, as, for a per-

fectly stirred continuous crystallizer, its form can be derived theoretically and the

values of the parameters a′ and b are related directly to the crystallization process:

a′ = 3 (10.120)

b = 3tr

(dLdt

). (10.121)

See Randolph and Larson (1971).

The Rosin–Rammler–Sperling distribution is less useful for describing CSDs (Nyvlt

and Cipová, 1979).

10.4.4 Histograms and population balanceHistograms of N versus L are important if prepared for equidistant values of the

sieve aperture.

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Crystallization 373

If the population density of the crystals n(L) can be expressed as a function of

their sizes, then a complete description of the CSD can be obtained by integration

from L= 0 to L=∞ to obtain the following expressions:

N =∫

n(L)dL (10.122)

where N is the number of crystals;

L =∫

n(L)LdL (10.123)

where L is a summary of the crystal size, or the visible crystal size;

A = 𝛽∫

n(L)L2 dL (10.124)

where A is the surface area of the crystals and is 𝛽 a surface shape factor; and

m = 𝛼𝜌c∫n(L)L3 dL (10.125)

where m is the concentration of the crystal mass in a suspension, 𝛽 is the surface

shape factor and 𝜌c is the density of a solution of concentration c.

These integrals (Eqns 10.122–10.125) represent the zeroth, first, second

and third moments of the distribution. In order to describe a distribution

function n(L) for a given model of a crystallizer, the population density must be

introduced.

10.4.4.1 Population balanceThe balance of the number of particles has the general form

Accumulation = input − output.

To describe this balance, the following assumptions are made:

• Perfect mixing of the suspension in the crystallizer.

• Steady state (constant crystal population density at all times).

• Samples of the suspension correspond to the suspension in the crystallizer.

• The feed is constant and does not contain any crystals.

• The volume of the suspension is constant.

Under these conditions, the balance simplifies to the form

dndt

= 𝜕

𝜕L

[n

(dLdt

)]+

n(dV∕dt)V

= 0. (10.126)

If the crystal growth is controlled by the McCabe ΔL law,

𝜕

𝜕L

(dLdt

)= 0 (10.127)

and, at steady state (dn/dt= 0),

dndt

=(

dndL

)(dLdt

)+ n

tr= 0 (10.128)

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374 Confectionery and chocolate engineering: principles and applications

Continuous

(a)

L L

(b)

log

n

log

n

crystallizer

Batchcrystallizer

3ʹ3

2ʹ2

1ʹ1

Figure 10.7 Plots of log n versus L for (a) a continuous and (b) a batch crystallizer. Source:

Nyvlt et al. (1985). Reproduced with permission from Elsevier.

where tr =V/(dV/dt). From Eqn (10.128), we obtain

dndL

+ n(dL∕dt)tr

= 0 (10.129)

dnn

=∫

dL(dL∕dt)tr

. (10.130)

After integration of these two equations between the limits n and n0, and 0 and

L, respectively, we obtain

n = n0 exp

{− L(dL∕dt)tr

}. (10.131)

For an MSMPR crystallizer, that is, a continuous crystallizer, a plot of log n

versus L theoretically gives a straight line [Fig. 10.7(a)]. The following reasons

can be given for deviations from linearity (Canning, 1971; Nyvlt, 1973a):

• Unintentional dissolution of small crystals

• Separate dissolution of small crystals

• Deviation from the McCabe ΔL law

• Internal classification

• Sampling of a classified product

• Splitting of the crystals into particles with comparable sizes

10.5 Batch crystallization

An unseeded batch crystallizer has no input or output. The crystal population

density balance (Eqn 10.126) is thus reduced to the form (Randolph and

Larson, 1971)𝜕

𝜕L

[n

(dLdt

)V

]+ 𝜕

𝜕t(nV ) = 0. (10.132)

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Crystallization 375

If the population density n is related to the overall working volume V, then

𝜕w𝜕t

+ 𝜕

𝜕L

[w

(dLdt

)]= 0 (10.133)

where w= nV. The integration of this partial differential equation is easy if the

initial distribution w=w(0; L) is known; however, this assumption is not fulfilled

in most cases. For details, see Baliga (1970), Mucsai (1971), Randolph and Larson

(1971), Wey and Estrin (1973), Blickle and Halász (1973, 1977) and Nyvlt et al.

(1985, p. 228).

Figure 10.7(b) shows a plot of log n versus L for a batch crystallizer. The curves

1→1′ mean the primary distribution, the curves 2→2′ the secondary distribu-

tion and the curves 3→3′ the resultant distribution, which is the sum of the

previous two. The symbol → here represents a time shift of the curves. The pri-

mary curve (1) has a maximum, which causes a maximum in the resultant curve

(3) also.

10.6 Isothermal and non-isothermal recrystallization

Recrystallization is a process involving a change in the size and/or shape of

crystals by a mechanism of surface diffusion of the solid or mass transport

through the liquid phase. Isothermal recrystallization (or Ostwald ripen-

ing) and non-isothermal recrystallization can be distinguished depending on

the conditions.

10.6.1 Ostwald ripeningThe reasons for the change in the CSD of crystals in contact with the mother

liquor follow from the expression for the change in the overall Gibbs free

enthalpy of the system:

dG = −SdT − V dP +∑

𝜇i dni + 𝜎sl dA. (10.134)

For a system at equilibrium, G is a minimum, and if dT= 0, dP= 0 and dni =0, then

the surface area A of the interface must be as small as possible (i.e. a minimum).

It can thus be expected that spontaneous processes leading to a decrease in the

surface area of the solid phase will occur in the heterogeneous system considered

here. A decrease in the surface area of the solid phase means dissolution of the

small particles. The use of modern experimental techniques has justified Gibbs’s

original ideas.

According to the Gibbs–Thomson equation, the activity a(r) of a solid sub-

stance in a solution and the concentration a0 of the solution in equilibrium with

the solid particle are a function of the particle size r:

ln

(a(r)a0

)=𝛽v𝜎sl

rkT(10.135)

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376 Confectionery and chocolate engineering: principles and applications

where 𝛽 is the surface shape factor, v is the particle volume, 𝜎sl is the solid–liquid

interfacial tension, k is the Boltzmann constant and T (K) is the temperature.

From the Gibbs–Thomson equation, it can be seen that if r1 < r2 < r3, then

a(r1)> a(r2)> a(r3), that is, the smaller the particles are, the greater is the

corresponding equilibrium concentration and vice versa. Moreover, the greater

the degree of polydispersity in the system, the more readily and rapidly ripening

occurs (Glasner, 1975). Evidently, the Ostwald–Freundlich equation (Eqn 10.11)

and the Gibbs–Thomson equation (Eqn 10.135) are equivalent; both can be

derived from the fact that the Gibbs free enthalpy is a minimum in equilibrium.

For more details, see Section 16.4.1.

10.6.2 Recrystallization under the effect of temperature orconcentration fluctuations

A special case of recrystallization is involved in systems containing medium-size

particles. These particles are too large for Ostwald ripening, that is, their changes in

solubility as a result of the differences between crystal sizes are negligible accord-

ing to the Gibbs–Thomson equation. The consequence is that recrystallization

of these particles occurs because of the effect of fluctuations in temperature or

concentration.

10.6.3 AgeingTwo mechanisms are classified into this category:

1 Recrystallization of primary particles in forms such as needles, dendrites and

thin plates into more compact shapes by surface diffusion or mass transport

through the liquid phase.

2 Transformation of metastable crystal modifications into stable modifications by dis-

solving and recrystallization. This process is essential to fat crystallization.

10.7 Methods for studying the supermolecularstructure of fat melts

10.7.1 Cooling/solidification curveFor the correct moulding of chocolate, it is essential that the crystallization

behaviour of the cocoa butter used should be critically examined before the

cocoa butter is added to the chocolate mixture. In this respect, the cool-

ing/solidification curve may give valuable information. Since phase transitions

are accompanied by thermal effects, these may be indicated by changes in the

slope of the cooling/solidification curve. Various fats, in particular cocoa butter,

and mixtures of fats give characteristic cooling/solidification curves.

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Crystallization 377

Prime stay point

t(min)

Cooling time (min)

T(min)

Soybean oil

T(max)

Tem

pera

ture

(°C

)

t(max)

Cocoa butter

or other special fat for confectionery

Figure 10.8 Cooling curves of fats, determined with a Shukoff flask. The crystallization is

characterized by [T(max)−T(min)]/[t(max)− t(min)].

The cooling/solidification curve is a time–temperature curve measured dur-

ing the cooling of cocoa butter or other fats until crystallization occurs under

the specified conditions of the test. The steps of the method are immersion of a

Shukoff flask filled with a given quantity of molten cocoa butter at a specified

depth in an ice–water mixture at 0 ∘C and recording, during cooling of the cocoa

butter under precisely specified conditions, the temperature of the fat at regular

time intervals. A plot of temperature versus time is then constructed. The method

is illustrated in Fig. 10.8.

In Fig. 10.8, the cooling curves of soybean oil and of cocoa butter and other

special confectionery fats are presented together, schematically. The first point

(temperature value) at which the curves start to diverge is the prime stay point,

then the curve of cocoa butter or other special fat passes through a tempera-

ture minimum and a temperature maximum, and finally the temperature starts

to decrease again. A ratio formed from the temperature and time values at the

extremities gives a measure of crystallization.

The reason for the increase in the temperature of cocoa butter during the cool-

ing is that crystallization processes have taken place in the cocoa butter and the

latent heat of these processes is negative, that is, they are exothermic (heat pro-

ducing) (IOCCC Analytical Method 31, 1988; IUPAC, 1986).

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378 Confectionery and chocolate engineering: principles and applications

100

Hardness

Heat

resistance

Waxiness

Temperature (°C)

So

lid fat

co

nte

nt

(%)

80

60

40

20

020 25 30 35 40

Figure 10.9 Solid-fat-content curve of cocoa butter.

10.7.2 Solid fat contentThe cooling curve indicates an exothermic process but does not give information

about the proportion in the solid state in cocoa butter or fats as a function of

temperature. Fats are a mixture of different triglycerides, and therefore there is

a characteristic temperature region in which the various triglyceride fractions

become solid. In this region, the proportion of solid phase increases from 0% to

100% as a function of temperature. A curve of the SFC curve of cocoa butter is

presented in Fig. 10.9. A characteristic feature of this curve is a certain hardness

in the temperature interval 25–30 ∘C; however, at the temperature of the human

body (36.5 ∘C) the SFC is practically zero (total melting).

There are several techniques for determination of the SFC. NMR (pulsed or

continuous-wave) is the only one that makes a direct measurement of SFC;

other techniques, such as dilatation and thermal analysis, utilize related prop-

erties (changes in specific volume and changes in enthalpy, respectively). Pulsed

NMR is the preferred technique and the predominant one in use.

10.7.3 Dilatation: Solid fat indexDilatation is a classic, simple technique (Fig. 10.10). The change in specific volume

(dilatation) gives a guide to the relative proportions of solid fats and liquid oils

in a semi-solid sample. The results should be stated as a solid fat index (SFI),

which is expressed in mm3/25 g or ml/kg. The SFI is merely an empirical index and

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Crystallization 379

Figure 10.10 Interpretation of solid-fat-index curve

(dilatation curve). Temperature

X

Specifi

c v

olu

me

Solid line

Liquid line

an arbitrary approximation of an absolute value, which should never be used to

state the percentage of solids.

10.7.4 Differential scanning calorimetry, differential thermalanalysis and low-resolution NMR methods

Thermal analysis methods such as DSC and differential thermal analysis (DTA)

are used to determine the melting properties of a fat and are based on changes in

enthalpy during a temperature–time programme (Fig. 10.11). A plot of enthalpy

(H) versus temperature (T) shows a steep fall and then a rise at the temperature

of a first-order phase transition (melting) (see Section 3.4.2).

This type of determination also relates to merely a function of the percentage

of solids, since the melting enthalpy differs from triglyceride to triglyceride and

varies considerably between different polymorphs. Integration of the melting peak

always gives results between 0% and 100% liquid fat and should preferably be

stated in the form of an SFI. For further details, see Lund (1983).

Low-resolution NMR (pulsed or continuous-wave) is the only technique yet

devised that gives a direct measurement of SFC. A charge in motion generates a

magnetic field. Protons have spin and thus act as tiny bar magnets that tend to

align themselves in the direction of a powerful, steady magnetic field in the NMR

Figure 10.11 The melting peak – the change

of enthalpy during the melting of fats.

Enthalpy ΔH

Temperature

Temperature

Liquid fat

(%)

(a)

(b)

100

50

0

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380 Confectionery and chocolate engineering: principles and applications

90° pulse

Instrument ‘dead time’

Liquid decay

Time (μs)

Sig

na

l

L

S'

L

S

70100 105

Solid decay

Figure 10.12 Principle of solid-fat-content determination by NMR.

instrument and precess at a specific angular frequency. After energy is introduced

by means of a strong radio-frequency pulse, the angle of precession is changed by

90∘. This induces a signal in the receiver coil of the instrument, proportional to

the number of protons in the solid or liquid phase. When the energy input ceases,

certain relaxation processes start, and the system returns to its initial state. In SFC

determination, the so-called spin–spin relaxation is significant. In this case, the

energy is distributed among protons in the same molecule, and different relax-

ation times occur in different nuclear environments. On this basis, protons in

the solid phase relax much faster than those in the liquid phase, because of the

denser and more rigid distribution net in the solid. A schematic magnetization

decay obtained from a fat sample is shown in Fig. 10.12.

The SFC can be calculated by either a direct or an indirect method. In the

(simpler) direct method, the calculation employs signals from both the solid fat

(S′) and the liquid fat (L) using the formula

Solids (%) = 100 ×f × S′

f × S′ + L= 100 × S

S + L(10.136)

where f= S′/S is a factor that takes into account the dead time of the instrument.

(The indirect method, by which the f-factor is excluded, is recommended where

the accuracy of the results is very important.)

The concept of the SFC plays an important role in understanding the crystal-

lization of the fats used in cocoa, chocolate and confectionery manufacture. A

conclusion of the mentioned studies is that the temperature region of 25–40 ∘Cneeds particular attention from the point of view of determining the specific heat

capacity and enthalpy of substances that contain cocoa butter or special fats.

For details of the methods used, see Wunderlich (1990), Dean (1995) and

Pungor (1995). For further details, see Bodor (1991, Chapter V), Karlshamns Oils

and Fats Academy (1991), Minifie (1999, pp. 848–855) and McGauley (2001).

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Crystallization 381

10.8 Crystallization of glycerol esters: Polymorphism

To study the behaviour of cocoa butter, let us look at the crystallization charac-

teristics of glycerol esters.

The TAG composition of a fat is one of its most important parameters because

it governs the physical properties and the polymorphic behaviour of the fat.

Polymorphism is defined as the ability of a TAG molecule to crystallize in differ-

ent molecular packing arrangements (polymorphs or polymorphic forms), cor-

responding to different unit cell structures, which are typically characterized by

X-ray diffraction spectroscopy. Two types of polymorphism exist: enantiotropy and

monotropy. Enantiotropic polymorphism is characterized by a greater number of

stable crystal forms in a given temperature range, that is, the transformations

between crystal forms are reversible. In monotropic polymorphism, which is char-

acteristic of cocoa butter as well, only one stable crystal form exists, and the

transformation of other crystal forms to the stable form is irreversible.

The Gay-Lussac–Ostwald step rule states that if more than one modification can

occur, then the most stable modification, which has the lowest free enthalpy,

never comes into existence first; instead, the spontaneous decrease of free

enthalpy always takes place step by step. Although the Gay-Lussac–Ostwald

step rule is not a strict natural law – there are exceptions – it mostly provides

good guidance about the direction of transitions between modifications.

Since Chapman’s study (Chapman, 1971), fat polymorphs have been delin-

eated into three main forms, denoted by 𝛼, 𝛽′ and 𝛽, and variations within these

main types. The main crystal characteristics of the various polymorphs are sum-

marized in Table 10.4.

Schenk and Peschar (2004) discussed the structure of chocolate and the poly-

morphism of cocoa butter. For further details, see also Larsson (1997).

When a melt of a simple TAG is cooled quickly, it solidifies in its lowest-melting

form (𝛼), with perpendicular alkyl chains in its unit cell (the angle of tilt is 90∘).When heated slowly, this melts, but, if held just above this melting point, it will

resolidify in the 𝛽′ crystalline form. In the same way, a more stable 𝛽 form can

be obtained from the 𝛽′ form. The 𝛽 form has the highest melting point and

can be obtained directly by crystallization from solvent. The 𝛽′ and 𝛽 forms have

tilted alkyl chains, which permit more efficient packing of the TAGs in the crystal

lattice. Glycerol esters with only one type of acyl chain are easy to make and

have been thoroughly studied. The results have provided useful guidance, but

Table 10.4 Crystal polymorphs.

Polymorph Unit cell Short spacing(s) (Å)

𝛼 Hexagonal 4.15

𝛽′ Orthorhombic 3.8 and 4.2 (both strong)

𝛽 Triclinic Multiple peaks+one strong (4.6)

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382 Confectionery and chocolate engineering: principles and applications

H2C P

O

PH2C

HC

H2C P

O

StH2C

HC

H2C St

O

O

St

P or St

P or St

Double bond

(cis–trans rotation)

Typical

‘chair ’ shape of TAGs

StOSt

26%

POSt

40%

POP

16%

H2C

HC

Figure 10.13 Average composition of cocoa butter and the chair shape of triacylglycerols

(TAGs).

such molecules are not generally significant components of natural fats (except

perhaps after complete hydrogenation). With mixed saturated TAGs such as PStP

(P= palmitic acid and St= stearic acid), the 𝛽 form is only obtained with difficulty,

and such compounds usually exist in their 𝛽′ form.

Among TAGs with saturated (S) and unsaturated (U) acyl chains, symmetri-

cal compounds (SUS and USU) have higher-melting (more stable) 𝛽 forms – this

applies to cocoa butter as well as for other fats. The main TAG components of

cocoa butter according to Jovanovic et al. (1995) are POSt, 16.5–41.2%; StOSt,

22.6–28.8%; and POP, 12.0–18.4%. However, the unsymmetrical compounds

(USS and UUS) have stable 𝛽′ forms. A schematic picture of the chair shape of

the TAGs and the average composition of cocoa butter are presented in Fig. 10.13.

A pecular property of the cocoa butter is that in the 2-position of glycerides exlu-

sively oleic acid (O) is located.

For the determination of mono-oleo disaturated symmetrical triglycerides

(SOS) in the oils and fats used in chocolate and in sugar confectionery products,

see IOCCC Analytical Method 35 (1990a). For the determination of the com-

position of the fatty acids in the 2-position of glycerides in the oils and fats used

in chocolate and in sugar confectionery products, see IOCCC Analytical Method

41 (1990b).

It should be mentioned that oleic acid and elaidic acid are cis–trans isomers

of each other; their schematic geometries are represented in Fig. 10.14. There

are important differences between their physical characteristics; for example,

the melting point of oleic acid is 16 ∘C, and that of elaidic acid is 51–52 ∘C. In

practice, the olefin carboxylic acids that occur as natural components of fats are

always of cis structure (Bruckner, 1961, p. 564). However, as a consequence of

hydrogenation, a certain degree of cis→ trans transition takes place, and this is

disadvantageous from the point of view of nutrition. Cocoa butter contains oleic

acid (the cis isomer).

Figure 10.15 shows the double-chain-length (DCL) and triple-chain-length

(TCL) arrangements and the short and long spacings of tilted dimers of

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Crystallization 383

Elaidic acid (trans)

Oleic acid (cis)

(Rotation)

HO

HO

O

O

Figure 10.14 Oleic and elaidic acids – cis–trans isomers.

Double-chain-length Triple-chain-length

Short

spacing

Short

spacing

Long

spacing

Long

spacing

Tilt

Figure 10.15 Double- and triple-chain-length arrangements and short and long spacings of

tilted dimers of triglycerides.

triglycerides provided by X-ray diffraction. The stable 𝛽 form generally

crystallizes in a DCL arrangement (𝛽2), but if one acyl group is very different

from the others in either chain length or degree of unsaturation, the crystals

assume a TCL arrangement (𝛽3), since this allows more efficient packing of the

alkyl chains and head groups. The crystals of this form have the short spacing

expected of a 𝛽 crystalline form, but the long spacing is about 50% longer than

usual. In the DCL arrangement, the molecules align themselves (like tuning

forks) with two chains in an extended line (to give the double chain length) and a

third chain parallel to these (see Fig. 10.15 and Table 10.4). Some mixed glycerol

esters, which have a TCL form when crystallized on their own, give high-melting

(well-packed) mixed crystals with an appropriate second glycerol ester.

The methyl groups at the top and bottom of each TAG layer do not usually lie

in a straight line, but form a boundary with a structure depending on the lengths

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384 Confectionery and chocolate engineering: principles and applications

Transition point

Fre

e e

nth

alp

y, G

TT0

G1

G2

G1

G2

U2,0

U1,0

Figure 10.16 Change of free enthalpy of fat crystal modifications as a function of temperature.

of the various acyl groups. This is called the methyl terrace. The molecules tilt with

respect to their methyl end planes to give the best fit of the upper methyl terrace

of one row of glycerol esters with the lower methyl terrace of the next row of

esters. There may be several 𝛽2 modifications, differing in the slope of the methyl

terrace and in the angle of tilt.

Crystallization occurs in two stages: nucleation and growth/thickening. A crys-

tal nucleus is the smallest crystal that can exist in a solution and is dependent on

concentration and temperature. Spontaneous (homogeneous) nucleation rarely

occurs in fats. Instead, heterogeneous nucleation occurs on solid particles (e.g.

dust) or on the walls of the container. Once crystals are formed, fragments may

drop off and either redissolve or act as nuclei for further crystals. The nucleation

rates for the various polymorphs are in the order 𝛼 > 𝛽′ >𝛽 so that 𝛼 and 𝛽′ crys-

tals are more readily formed in the first instance, even though the 𝛽 polymorph

is the most stable and is favoured thermodynamically. Crystal nuclei grow by

incorporation of other molecules from the adjacent liquid layer at a rate depend-

ing on the amount of supercooling and the viscosity of the melt. Figure 10.16

shows the change of the free enthalpy G of several modifications as a function of

the temperature T.

The free enthalpies of two modifications labelled 1 and 2 are

G1 = U1,0 − kT lnΩ1 and G2 = U2,0 − kT lnΩ2 (10.137)

where U1,0 and U2,0 are the internal energies of the modifications 1 and 2 at

absolute zero temperature, k is the Boltzmann constant and lnΩ1 and lnΩ2 are

the partition functions of the modifications 1 and 2. ΔU0 is the latent heat of the

transition at absolute zero temperature and is defined by

U2,0 − U1,0 = ΔU0 > 0. (10.138)

Since the bonding relationships between the lattice elements of the various

modifications are different, the partition functions are also different, and, conse-

quently, the curves of G1 and G2 are not parallel to each other. Generally, if the

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Crystallization 385

bonding energy is lower, then the vibration frequencies are also lower and the

series of energy levels is denser; therefore, Ω2 increases more quickly with tem-

perature than Ω1 does, and G1 and G2 intersect at a transition point T0. Since U1,0

has been chosen as the zero energy level in Fig. 10.16, the stable modification is

represented at temperatures less than T0 by the curve G1 and by the curve G2 at

temperatures higher than T0.

The change between the modifications takes place through transformation of

the crystal network. The condition for such a transformation is the existence of

sufficient mobility of the crystals, which is rather limited in general; however, the

mobility increases quickly with any temperature rise. This fact explains how the

origin of unstable modifications and their existence for a long time are possible.

Moreover, it points towards the importance of temperature conditions in storage.

10.9 Crystallization of cocoa butter

10.9.1 Polymorphism of cocoa butterIn the confectionery industry, crystallization of cocoa butter (alone or in choco-

late) is carried out in two steps:

1 Pre-crystallization, or tempering

2 Crystallization by cooling (e.g. moulding) and in storage

Since cocoa butter has six crystal modifications, the purpose of pre-

crystallization is to produce the necessary amount of crystal seeds of the least

unstable modification, 𝛽(V) (see following text). Here, least unstable means that

this modification remains unchanged over several months.

To produce the stable modification 𝛽(VI) directly needs sophisticated technol-

ogy, and such technology is not yet in everyday use, but investigations aimed

at solving this problem are in progress. If the correct technology is used, the

proportion of the 𝛽(V) modification generated by tempering is about 1–5%, and

the proportion generated by cooling is about 45–60%. Crystallization is finished

in storage, when the proportion of crystals of the 𝛽(V) modification increases

to 60–80%.

Several authors have discussed the crystalline forms of cocoa butter poly-

morphs (Duck, 1964; Wille and Lutton, 1966; Huyghebeart and Hendrickx,

1971; Lovegren et al., 1976; Dimick and Davis, 1986; Jovanovic et al., 1995). For

the determination of the melting points of cocoa butter, see IOCCC Analytical

Method 4 (1961).

The data on the melting points are rather different for the various crystal mod-

ifications. In the confectionery industry, the data provided by Wille and Lutton

(1966) are perhaps the most often used, although in a mixed form (Greek let-

ter+numbering):

𝛾 = I, 17.3 ∘C𝛼1= II, 23.3 ∘C𝛼2= III, 25.5 ∘C

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386 Confectionery and chocolate engineering: principles and applications

β'(IV)

β'(IV), orthorhombic

Carbon atoms

β(V), triclinic

Shearing

H

H

H

HH

HH

H

HHH

HHHH

HH

H H H

HHHH

H

H

H

H

H

H H

HH

HH

H

Figure 10.17 Polymorphic transformation of cocoa butter modifications 𝛽′(IV)→ 𝛽(V) on

shearing.

𝛽′ = IV, 27.3 ∘C𝛽(V), 33.8 ∘C𝛽(VI), 36.3 ∘C

The idea of polymorphic crystalline forms of cocoa butter – as well as of other

fats – refers not to the external microscopic or macroscopic geometrical appear-

ance of the fat crystals but to the internal structure of the crystals at a molecular

level, that is, the packing of the triglycerides in the molecular crystal lattice.

Figure 10.17 represents the transition 𝛽′(IV) → 𝛽(V) of the crystal modifica-

tions of cocoa butter. The transition 𝛽′ → 𝛽 is stimulated by shearing, which is

caused by strong mixing of chocolate mass. The characteristic feature of the 𝛼(II

and III) modifications is that the TAGs start to align along the axis of the fatty

acids and a chair-type arrangement is formed. (The modification I is designated

by 𝛾 in the literature.) The 𝛽′(IV) modification is more compact, its consistency

is harder, and two chairs form one bond (DCL arrangement). The characteris-

tic feature of the 𝛽(V) modification is a compact structure in which three chairs

form one bond (TCL arrangement).

In the modification 𝛽(VI), which is the stable one and evolves over weeks or

months, the consistency becomes more compact through the development of a

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Crystallization 387

curved tuning-fork shape of the parts of the TAGs where the oleic acid groups

are located.

The chemical composition and physical properties of cocoa butter show more

or less differences according to its origin (Far East, Africa, South and Middle

America). Ribeiroa et al. (2010) compared the chemical and technological prop-

erties of Brazilian cocoa butter and industrial blends from the point of view

of crystallization kinetics and polymorphic behaviour. The percentages for the

SFCmax varied between 78.4% and 89.5% for all samples. In particular, the values

of t1/2 (SFCmax) and the Avrami parameters differentiated the industrial blends

and the Brazilian samples on the crystallization rate. The standardized blends

were characterized by higher crystallization rates and more uniform structur-

ing, suitable for use in tropical areas. All evaluated samples exhibit the poly-

morphic form 𝛽V, desirable for the production of chocolates, in the conditions

of analysis.

10.9.2 Tempering of cocoa butter and chocolate massThe crystallization of cocoa butter or chocolate mass, usually containing about

28–38% cocoa butter, means the solidification of the material in such a way that

the cocoa butter is crystallized in the form of the 𝛽(V) modification. The series of

operations starts with tempering, the next operation is the shaping of the cocoa

butter or chocolate mass, and, finally, the operation of cooling finishes this series.

In the following descriptions, the tempering of cocoa butter and of chocolate

mass is presented together. However, there is an important difference: since the

contraction of cocoa butter in a chocolate mass is proportional to the volume

ratio of cocoa butter, the contraction of a cocoa butter bar is about three times

higher than that of a chocolate bar, assuming that they are of the same volume.

Therefore, the moulding of cocoa butter bars, which is a relatively rare task, needs

more cautious cooling because the bars can crack. The risk of such a phenomenon

is less in the case of the moulding of chocolate mass.

10.9.2.1 TemperingFrom the point of view of the technology, the control of the transitions

𝛼(III)→ 𝛽′(IV)→ 𝛽(V) plays an essential role. This is the tempering operation.

At the end of tempering, all of the 𝛽′(IV) modification has to be melted, and, at

the same time, tempering must provide a seed concentration of the 𝛽(V) mod-

ification of 0.1–1.15% of the cocoa butter mass according to Loisel et al. (1997).

Jewell (1972), however, reported that larger amounts of seeds, 2–5% of the

cocoa butter, were needed for good temper. According to Lonchampt and Hartel

(2004), this difference may be due to differences in seed size, which affects the

number of seed crystals. Von Drachenfels et al. (1962) specified the importance

of crystal size. The smaller and more regular the size of the seed crystals, the

glossier the chocolate and the greater its bloom resistance. On the other hand,

if the crystal size is too large, the crystals tend to recrystallize during storage.

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388 Confectionery and chocolate engineering: principles and applications

Molten

chocolate

(–50 °C)

γ(I)

α1(I)

α2(III)

β'(IV) + β(V)

β(V)

crystallized

β(V) seeds

remain

β'(IV) molten

Cooling

Quick transformation

Quick transformation

Coolin

g

Quick transformation

Inte

nsive

shearin

gWarming

Figure 10.18 Monotropic (one-way) changes of cocoa butter modifications during tempering

and cooling.

It was mentioned earlier that the transitions from modification I to modifica-

tion VI are increasingly slow. At the beginning of the cooling of cocoa butter, the

𝛾(I) and 𝛼(II and III) modifications occur, but they change rapidly to the 𝛽′(IV)

and 𝛽(V) modifications. For details, see Ziegleder (1988).

Since the crystallization of cocoa butter follows monotropic polymorphism,

the direction of the changes is exclusively 𝛾(I)→ 𝛼(II)→ 𝛼(III)→ 𝛽′(IV)→ 𝛽(V)→

𝛽(VI). Moreover, under the usual conditions all the modifications can be crystallized

directly from molten cocoa butter except for 𝛽(VI), which crystallizes slowly from

the 𝛽(V) modification (Fig. 10.18).

The stable form 𝛽(VI) cannot be produced directly from melted chocolate

except by the addition of 𝛽(VI) cocoa butter seeds and under very well-controlled

conditions (Giddey and Clerc, 1961; van Langevelde et al., 2001). It should be

emphasized that the target of tempering is to bring about the 𝛽(V) modification,

which is unstable, although its transition to the stable 𝛽(VI) modification is

very slow: it needs weeks or months. During these monotropic changes, the

Gibbs free enthalpy decreases continuously; its minimum is reached in the

𝛽(VI) modification.

However, if the tempering results in a majority of crystals of the 𝛽′(IV)

modification, the transition 𝛽′(IV)→ 𝛽(V) will take place in the chocolate

product within hours or days, and the consequence of such a transition will be

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Crystallization 389

–50

–32

30–31

–27

20

Warming Cooling

Tem

pera

ture

(°C

)

Warming

Time

Cooling

β'(IV)

+

β(V)

β(V)

crystallization

β'(IV)

molten

+

β(V)

Figure 10.19 Temperature profile in the chocolate tempering process.

the appearance of fat bloom on the surface of the chocolate product. This is a

severe quality defect, called blooming.

Taking into account all the considerations mentioned earlier, the principle of

the tempering process is to produce the 𝛽′(IV) and 𝛽(V) modifications and then

to melt the 𝛽′(IV) modification while the 𝛽(V) modification is retained. Although

the 𝛽(V) modification can be produced directly from a molten chocolate mass,

such a direct method cannot exclude the development of crystals of the 𝛽′(IV)

modification. A warming period is necessary in the tempering operation which

destroys the crystals of the 𝛽′(IV) modification – this is the way to avoid fat bloom.

Figure 10.19 shows the temperature profile of a correct tempering operation

for chocolate mass, which consists of three steps: two steps of cooling and one

step of warming between them. The traditional tempering machine is similarly

partitioned in the direction of advance of the chocolate mass. It is evident

that a simple conical double-jacketed chocolate tank with a mixer is hardly

suitable for performing tempering correctly, because it is difficult to carry out

the warming phase.

Strong mixing of the chocolate mass during tempering promotes the develop-

ment of crystals of the 𝛽(V) modification by the shearing effect.

The measurement of tempering, for which the temperimeter is a practical instru-

ment, provides important technological parameters. This instrument includes

a small vessel, which the tempered chocolate mass is poured into. The vessel

is placed in an ice–water bath, and the temperature of the chocolate mass is

measured as a function of time. The resulting temperature versus time plots are

represented in Fig. 10.20.

The curve for a well-tempered chocolate mass is characterized by a horizontal

line: the amount of crystals of the 𝛽(V) modification is sufficient, and in the time

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390 Confectionery and chocolate engineering: principles and applications

Under-tempered

Well-tempered

Over-tempered

Time

Te

mp

era

ture

(°C

)

Figure 10.20 Typical temperimeter curves.

interval represented by this line, the latent heat generated by crystallization (an

exothermic effect) and the cooling effect of the bath (an endothermic effect) are

in balance. Consequently, the temperature does not change in this interval.

When the chocolate mass is under-tempered, too many crystals of the 𝛽′(IV)

modification develop, which rapidly transform to the 𝛽(V) modification. Con-

sequently, the latent heat dissipated by their crystallization exceeds the cooling

effect of the bath. Therefore, an increase in temperature occurs. When the choco-

late mass is over-tempered, too many crystals of the 𝛽(V) modification develop,

which melt too slowly to compensate the cooling effect of the bath. Conse-

quently, the temperature decreases continuously.

Afoakwa et al. (2008) determined that particle size was inversely related with

texture and colour, with the greatest effects noted in hardness, stickiness and

lightness at all temper regimes. Moreover, over-tempering caused significant

increases in product hardness, stickiness with reduced gloss and darkening

of product surfaces. Under-tempering induced fat bloom in products with

consequential quality defects on texture, colour and surface gloss. Micrographs

revealed variations in surface and internal crystal network structure and

interparticle interactions among tempered, over-tempered and under-tempered

(bloomed) samples. Under-tempering caused whitening of both surface and

internal periphery of products with effects on texture and appearance. Thus,

attainment of optimal temper regime during pre-crystallization of dark chocolate

was central to the desired texture and appearance as both over-tempering and

under-tempering resulted in quality defects affecting mechanical properties and

appearance of products.

In many publications, bloom in chocolate is often described as a process

involving the migration by capillary action of a liquid fat to the surface

(Kleinert, 1962). Loisel et al. (1997) considered chocolate as a porous material

and were able to determine, by mercury porosimetry, the porosity volume of

well-tempered dark chocolate [𝛽(V)], under-tempered chocolate [𝛽(IV)] and

over-tempered chocolate [a mixture of 𝛽(V) and 𝛽(VI)]. The volume of air

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Crystallization 391

bubbles due to the process was determined by X-ray radiography to be less

than 0.1% of the sample volume. The porosity of normal chocolate was about

1% of the total volume, and this increased to 2% for the under-tempered

chocolate and 4% for the over-tempered chocolate. The results did not allow

determination of the precise pore diameter, but suggested that the chocolate

did not have open, interconnected pores with a mean diameter larger than

0.1 μm at the surface. Moreover, it seems that the pores were filled by the

liquid fraction of cocoa butter at room temperature. As a result, it is better to

talk about empty cavities rather than pores. Khan et al. (2003) highlighted the

presence of pores at the surface of milk chocolate by scanning the surface with

an atomic force microscope. These authors estimated the concentration of pores

to be thousands/cm2; the pores, 1–2.5 μm in depth, were randomly distributed

on the surface.

As mentioned previously, a preferable method of crystallization from melts is

to add crystal seeds of the stable modification to the molten substance, which

start an overall crystallization in the stable modification. This is the principle of

the Seedmaster tempering machine manufactured by Bindler, in which crystals

of the stable 𝛽(VI) modification are produced by intensive shearing (Seedmaster

cryst) and the pre-tempered chocolate mass is seeded by these stable crystals in

the Seedmaster mix.

Besides cocoa butter, several types of chocolate may contain milk fat (milk

chocolate) and/or oils derived from added almonds or hazelnuts (dark and milk choco-

late) if these nuts are refined together with the chocolate mass. Since the prop-

erties of these fats/oils are essentially different from those of cocoa butter, they

can exert an important effect on the crystallization of cocoa butter in chocolate.

As a rule, it can be stated that in the case of milk fat, almond oil or /hazelnut

oil, the end point of cooling will be ∼26 ∘C instead of 27 ∘C, and the end point of

warming will be 29–31 ∘C instead of 30–32 ∘C. The decrease in temperature that

is to be used is dependent on the amount of these fats/oils. For further details,

see Kniel (2000) and McGauley (2001).

10.9.3 Shaping (moulding) and cooling of cocoa butterand chocolate

Tempering is followed by shaping and cooling. In order to avoid sudden

cooling of the well-tempered chocolate mass, the moulds (metal or plastic) are

pre-tempered, that is, pre-warmed to a temperature of about 30 ∘C. Figure 10.21

shows the usual method of moulding; the various kinds of moulding machines,

which are not discussed here, are a subject of confectionery technology. On

entering the cooling machine, the temperature of the chocolate mass is a little

lower than at the dosing stage because there is some cooling in the vibration

section as well.

Figure 10.22 shows three stages in the cooling tunnel, although the tunnel

is not actually divided into three stages: each stage means about one third of

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392 Confectionery and chocolate engineering: principles and applications

Warm side

Dosing

Vibration

Cooling tunnel

Demoulding

Cool side

Wall

Pre-warming

of moulds

Figure 10.21 Moulding of chocolate.

the length of the tunnel. The values of the temperature of the chocolate mass

and cooling air are for information only; the unit mass and the shape of the

moulded product are crucial factors in determining these values. In Fig. 10.22,

the temperature profiles of the cooling in the case of cocoa butter/CBE fats and

in the case of CBR/CBS fats are represented in parallel in order to stress the

differences between these two types of fats.

30°C

40°C

16°C

8°C 8°C 16°C

12°C 16°C

Cooling of cocoa butter and CBE

Cooling of CBR and CBS

Air flow Product flow

Figure 10.22 Temperature profile of cooling process. CBE= cocoa butter equivalent,

CBR= cocoa butter replacer, CBS cocoa butter substitute.

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Crystallization 393

In the first stage, a moderate cooling is recommended in order to avoid the

development of a solid crust on the surface of the chocolate that could hinder

heat transfer and the correct crystallization into the 𝛽(V) modification. In any

case, the second stage of cooling is essential from the point of view of crystal-

lization because the majority of the crystal seeds are formed in this stage. The

latent heat of crystallization of cocoa butter, which is on average −1.88 kJ/kg, is

released mainly in this stage and as a result of the temperature of the chocolate

is slightly increased. This stage is characterized by the growth of crystal seeds. If

the tempering is not correct, few crystal seeds develop on slow cooling. However,

if the cooling is too fast, unstable seeds develop, and the surface of the product

acquires a reddish tint, which is soon followed by fat bloom.

As a result of crystallization of the majority of the cocoa butter in chocolate, a

contraction takes place, equal to about 9.3% (V/V%) relative to the cocoa butter

and about 3% (V/V%) relative to the chocolate product if we take into account

the fact that the proportion of cocoa butter in chocolate is about 30 m/m%.

This contraction makes demoulding possible. If the tempering is not correct, the

consequence is a smaller contraction. In extreme cases, the demoulding is not

perfect: the surface of the product is not bright, the consistency (Brucheigenschaft)

is not cracking.

10.9.4 Sugar blooming and dew point temperatureIn the third stage, the chocolate leaves the cooling tunnel, the temperature of

which increases continuously. On leaving the cooling machine, the moulded

chocolate has a temperature of about 16 ∘C, which must not be lower than the

dew point of the external air in the room; otherwise water from the air will con-

dense as dew on the surface of the chocolate and dissolve the sugar content of

the chocolate surface. Later, this sugar solution will dry and its solid content will

remain as sugar bloom. The two types (sugar and fat) of blooming can be easily

differentiated either microscopically or by fingering (in the case of sugar bloom,

the surface is coarse).

Barenbrug (1974) used the Magnus–Tetens formula for the saturated vapour

pressure of water pw.s:

pw.s = 0.6105 exp

(aTd

b + Td

)(kPa) (10.139)

where Td is the dew point temperature (∘C), a= 17.27 and b= 237.7 ∘C. It is

known that if T> Td, then pw.s(T)> pw.s(Td). Moreover, if the vapour at the tem-

perature T is not saturated, then the relative humidity (RH) can be defined by

the relationship

pw.s(Td) = RHpw.s(T). (10.140)

From Eqn (10.139),

0.6105 exp

(aTd

b + Td

)= RH × 0.6105 exp

( aTb + T

)(10.141)

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394 Confectionery and chocolate engineering: principles and applications

aTd

b + Td

= aTb + T

+ ln(RH)(= 𝛼). (10.142)

From Eqn (10.142), the dew point temperature can be calculated:

Td = b𝛼a − 𝛼

(10.143)

where

𝛼 = aTb + T

+ ln(RH). (10.144)

𝛼 is a function of T and RH is the relative humidity of the air at temperature T;

see Eqn (10.140).

If 0 ∘C< T< 60 ∘C, 0.01<RH<1.0 and 0 ∘C< Td < 50 ∘C, then the uncertainty

in the calculated dew point temperature is ±0.4 ∘C. For more details, see Konin-

klijk Nederlands Meterologisch Instituut (KNMI) (2000).

Example 10.5Assume that the temperature at the end of the cooling tunnel is 16 ∘C. Let us cal-

culate the dew point temperatures for the cases RH= 0.4, RH= 0.6 and RH= 0.7.

From Eqn (10.144),

𝛼(0.4) = 17.27 × 16237.7 + 16

+ ln 0.4 = 0.173

𝛼(0.6) = 17.27 × 16237.7 + 16

+ ln 0.6 = 0.578

𝛼(0.7) = 17.27 × 16237.7 + 16

+ ln 0.7 = 0.732.

From Eqn (10.143),

Td(0.4) = 237.7 × 0.17317.27 − 0.173

= 2.4∘C

Td(0.6) = 237.7 × 0.57817.27 − 0.578

= 8.23∘C

Td(0.7) = 237.7 × 0.73217.27 − 0.732

= 10.52∘C.

Table 10.5 summarizes the values of dew point of air at 16 ∘C.

This means that, for example, if a chocolate bar leaves the cooling machine at

10 ∘C and the external air parameters are 16 ∘C and 70% RH, then vapour will

condense on its surface (10 ∘C<10.52 ∘C).

10.9.5 Crystallization during storage of chocolate productsThe crystallization of cocoa butter finishes during the storage of chocolate prod-

ucts. This after-crystallization is dependent on the previous steps of crystallization,

the conditions of storage and the behaviour of the chocolate product.

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Crystallization 395

Table 10.5 Dew point of air of 16 ∘C as a function of the relative humidity of air (RH)

calculated according to Barenbrug (1974) by using the Magnus–Tetens formula.

RH → 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

T(∘C) ↓ Dew point of air of 16 ∘C6 −23.3 −15.3 −10.3 −6.6 −3.6 −1.2 0.9 2.8

8 −21.8 −13.6 −8.5 −4.8 −1.8 0.7 2.9 4.8

10 −20.2 −11.9 −6.8 −3 0.1 2.6 4.8 6.7

12 −18.7 −10.3 −5 −1.2 1.9 4.5 6.7 8.7

14 −17.1 −8.6 −3.3 0.8 3.7 6.4 8.6 10.6

16 15.6 −7 −1.6 2.4 5.6 8.2 10.5 12.6

18 −14.1 −5.3 −0.2 4.2 7.4 10.1 12.4 14.5

Source: Data from Barenbrug (1974).

The problem of formation of fat bloom during storage originates mainly from:

• Too high a ratio of after-crystallization. According to Kniel (2000), post-

crystallization means that there is still formation of crystals after the cooling

process. In optimal cases, approximately 20% of the cocoa butter crystallizes

during the cooling step, and the fraction of crystallized cocoa butter reaches

about 45–60% in the first few hours after cooling. Then this fraction slowly

increases to 56–80% during storage, that is, the fraction of post-crystallization

is about 20%. However, if the residence time of the chocolate in the cooler is

too short or the temperature of the cooler is too low, the post-crystallization

can reach 40% (i.e. after cooling, the crystallized fraction is too low, less than

45% instead of 45–60%). In this case the post-crystallization occurs slowly

under uncontrolled conditions. The consequence is an uneven structure with

large crystals and a high fat bloom risk.

• Tempering was not correct. During tempering, the 𝛽(IV) modification might not

be melted, and the remaining seeds of it may cause fat bloom.

• Fractionation of triglycerides. In addition to symmetric triglycerides, cocoa but-

ter also contains the asymmetric triglycerides POO and StOO. If crystallization

is too quick, the symmetric triglycerides migrate to the solid crystals, and the

asymmetric ones to the melt. Consequently, the random distribution of triglyc-

erides in the melted cocoa butter will no longer exist: the crystals will be

enriched in symmetric triglycerides (and the melt will contain more asymmet-

ric triglycerides), and this promotes fat blooming. Fat bloom contains mainly

symmetric triglycerides.

• Fat migration. It is important to remember that even a seemingly solid product

such as chocolate at room temperature contains considerable amounts of liquid

oil. The SFC of cocoa butter at 25 ∘C is approximately 80–85%, the remainder

of the fat consisting of low-melting triglycerides that do not crystallize at this

temperature. These liquid triglycerides are trapped in a matrix consisting of

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396 Confectionery and chocolate engineering: principles and applications

solid fats and normally move only by slow diffusion processes. However, if the

temperature is raised to 30 ∘C, the amount of liquid increases to approximately

50% and the solid matrix becomes much less efficient as a migration barrier. At

this concentration of solid material, the distance between particles is so large

that continuous liquid channels may form and the movement of liquid triglyc-

erides becomes rapid. The liquid also dissolves some of the more high-melting

triglycerides in the cocoa butter such as POP (a symmetric triglyceride) and

transports them to the chocolate surface, where they can recrystallize on exist-

ing POP-rich crystals. When the crystals have increased sufficiently in size,

they can be observed as fat bloom and even before that as a visible dulling of

the surface.

The problem is of course accentuated in a composite product such as a filled

praline. The filling is normally quite fluid owing to the desired sensory char-

acteristics, and the oil content of the filling may be as high as 50%. When in

contact with a chocolate shell, the oil gradually enters the solid chocolate and

dissolves some of the high-melting cocoa butter. The triglycerides of the soft

fat contained in a filling or in pieces of nuts (hazelnut, almond, etc.) migrate

much more quickly than the triglycerides of cocoa butter do (e.g. OOO migrates

four times quicker than POSt). Therefore, these fast-moving triglycerides push

out cocoa butter to the surface of the product, and the consequence of this phe-

nomenon is fat blooming.

The aforementioned problems of fat bloom can develop separately and

together as well. However, fat blooming may be delayed for years by correct use

of technology and correct storage conditions.

The transition 𝛽(V)→ 𝛽(VI) is relatively quick in dark chocolate but can be

slowed down by adding 1–2% of milk fat because milk fat consists of many dif-

ferent triglycerides, and this seems to hinder fat blooming. For details of the prop-

erties and polymorphism of milk fat, see Timms (1984), Campbell and Pavlasek

(1987), Breitschuh and Windhab (1998) and ten Grotenhuis et al. (1999).

When we study the rates of various phenomena as a function of storage tem-

perature, which plays an essential role in after-crystallization, it is surprising that

for chocolate containing soft fats, the temperature interval of 20–22 ∘C is not ben-

eficial, because crystallization has not yet ceased in this interval but migration

is speeded up. The combination of these two effects results in a maximum in the

rate of fat blooming. (The fat-blooming curve is a sum of the curves due to these

two effects.)

10.9.6 Bloom inhibitionLonchampt and Hartel (2004) have divided the factors having an effect on fat

blooming into two groups: compositional factors and factors associated with the

processing method.

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Crystallization 397

10.9.6.1 Compositional factorsIn general, the higher the solid content and the lower the liquid fraction,

the more resistant a chocolate is to bloom. However, because of organoleptic

consequences, it is possible to increase the melting point of chocolate by only

1 ∘C (Arishima and Mc Brayer, 2002). Several different ways have been used

to increase the SFC, including the use of a stearine (high-melting) fraction

of cocoa butter (after fractionation) and adding specific TAGs to chocolate,

namely, StOSt, POP or asymmetric TAGs such as StStO or PPO, to impede the

𝛽(V)→ 𝛽(VI) transition.

Milk fat has long been known to have an anti-bloom effect when blended with

cocoa butter in chocolate. (However, it is also known to enhance bloom when

used with compound coatings; see following text.) The anti-bloom effect of milk

fat and emulsifiers was discussed by Lonchampt and Hartel (2004) in detail. It

should be mentioned that the effect of emulsifiers on the improvement of bloom

resistance is strongly dependent on the type of emulsifier.

10.9.6.2 Processing factorsThe key processing factor is tempering, which must be different for dark and milk

chocolate, as previously mentioned. As already discussed, cooling that is either

too slow or too quick can induce bloom. Rapid cooling produces small cracks and

pores on the chocolate surface, enhancing bloom (Kleinert, 1962). Rapid cooling

may also promote the formation of unstable polymorphs in regions that have

cooled too quickly. Proper cooling of both types of chocolate (and compound

coatings) is needed to protect against early bloom formation.

10.9.6.2.1 Warm treatment prior to storageIt has been found that a brief period of warming to 32–35 ∘C protects chocolate

against bloom formation. Following his earlier work, Kleinert (1962) investi-

gated the possibility of exposing chocolate to a brief warm-temperature hold to

prevent bloom formation. A minimum treatment time of 80 min at 32–35 ∘C was

sufficient to protect the chocolate against bloom for more than 1 year, although

a similar hold at temperatures from 28 to 31 ∘C did not prevent the chocolate

from blooming. Minifie (1989a,b) also noted a similar treatment (32.2 ∘C for 2 h);

however, he described also a second treatment using a lower temperature for a

longer period of time. Treatment for 2 days at 26.7–29.4 ∘C for dark chocolate

and 22.8–25 ∘C for milk chocolate also inhibited bloom formation. However, this

later method decreased the final gloss. After warm treatment, the chocolate was

in the 𝛽(VI) form. For details, see Lonchampt and Hartel (2004, p. 264).

10.9.6.2.2 Storage conditionsThe inhibition of storage bloom is maximum when the chocolate is stored at

18 ∘C or below, without any temperature fluctuations. Chocolate can be stored

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398 Confectionery and chocolate engineering: principles and applications

frozen for a very long time. However, even though the ideal storage conditions

that prevent bloom are well known, it is impossible to control the temperature

after the chocolate leaves the plant.

10.9.7 Tempering of cocoa powderBecause cocoa powder contains 8–24% of cocoa butter – the usual values of

cocoa butter content are 8–10% or 10–12% if produced for industrial purposes

and 16–24% if produced for household use, this fraction of cocoa butter is tem-

pered as well in order to hinder fat blooming. Fat blooming in cocoa powder

has been studied less than in chocolate, although modern powder-cooling and

stabilizing systems can solve this problem.

The colour of cocoa powder is an essential quality property: a deep red/brown

colour is preferred. According to Fincke (1965), two types of colour can be dis-

tinguished. The inherent colour derives from the flavonoid substances of fat-free

cocoa cells, which can be enhanced by alkalization; see Section 16.3. The inher-

ent colour plays an important role in cocoa drinks because the flavonoids are

dissolved and provide the colour of the drink. The outer colour is a result of the

correct tempering of the cocoa butter content. Alkalization and tempering have

a synergistic effect from the point of view of the outer colour, which is regarded

by customers as essential.

A simple experiment shows how the outer colour depends on tempering. If

we warm some cocoa powder up to about 45 ∘C while mixing it and then cool it

below about 20 ∘C, the result is a deep red/brown outer colour, which is likely

to become greyish in a short time. This phenomenon is more evident when the

cocoa butter content is higher: this gives both a deeper red/brown colour and

faster blooming.

The tempering of cocoa powder has two steps:

1 In pre-tempering, before grinding, the cakes of cocoa powder are tempered at

43–45 ∘C in order to melt the total cocoa butter content.

2 In the grinding machine, the cocoa powder is pulverized in a fluidized bed,

which ensures uniform, gradual cooling first down to 20–24 ∘C and then

down to 16–18 ∘C.

The DSC curve of a well-tempered cocoa powder shows that the highest peak

of heat absorption is at 34 ∘C, which is related to the 𝛽(V) and 𝛽(VI) modifications.

A peak at 28–29 ∘C is evidence of poor tempering, that is, the existence of the

very unstable 𝛽(IV) modification.

10.10 Crystallization of fat masses

10.10.1 Fat masses and their applicationsIn the following discussion, the expression fat mass relates to products and

semi-products of the confectionery industry which consist of about 28–38 m/m%

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Crystallization 399

of non-cocoa-butter vegetable fats. These fats form the continuous dispersion

phase of these products. The usual names for such products are compounds

(or surrogates), which are similar to chocolate; coatings, which substitute for

couverture chocolate in cheap products; and creams/fillings, which have a soft

consistency relative to compounds and coatings, the consistency of which is

similar to that of chocolate.

In the following vegetable fat always means non-cocoa butter vegetable fats.

Briefly, the crystallization of fat masses is determined by the properties of the

vegetable fat that they contain. Since compounds and coatings have, if possible,

a similar consistency to chocolate, the vegetable fat contained in them also has a

similar consistency to chocolate. Namely, the consistency of the product and the

consistency of the vegetable fat are in the closest possible relationship allowed

by the properties of the crystallization.

As a consequence of the aforementioned reasoning, on the one hand, the veg-

etable fats used for producing compounds and coatings imitate the crystallization

(consistency) properties of cocoa butter; on the other hand, the vegetable fats

used for producing creams and fillings imitate the crystallization (consistency)

properties of milk fat, milk butter or milk cream. Although this is a simplifica-

tion, and there are differences of greater or lesser extent between this picture

and the true situation, it essentially expresses the fact that fat masses provide a

cheaper solution than products made with cocoa butter or milk cream.

The vegetable fats other than cocoa butter that are used in the confectionery

industry are discussed in the following sections.

10.10.2 Cocoa butter equivalents and improversCBEs and cocoa butter improvers (CBIs) are designed to be completely miscible

with cocoa butter. The range comprises in part not only products that are nearly

identical to cocoa butter but also products that can be used to alter the properties

of chocolate to make it more heat resistant or slightly softer, to mention just a

few examples.

CBEs are composed of the triglycerides POP, POS and SOS in order to mimic

the properties of cocoa butter. POP is obtained from palm oil by fractionation and

is then blended with fats rich in POS and SOS. A typical source of SOS is shea nut

oil, while illipe fat contains POS and SOS. The typical triglyceride compositions

of the components used in CBEs are shown in Table 10.6. Other sources of oils

and fats used in CBEs are sal, mango and kokum. Today, CBE-like products can

also be manufactured through enzymatic interesterification of more abundant

raw materials; however, these products are not approved for use in chocolate in

the European Union (EU) (see later text).

The melting points of the 𝛽 polymorphs of POP, POS and SOS are 37, 37 and

43 ∘C, respectively. This implies that the higher the SOS content of the fat, the

harder it will be, although an excessively high content may increase the viscos-

ity of the tempered chocolate mass. If POP is the main component, the fat will

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400 Confectionery and chocolate engineering: principles and applications

Table 10.6 Typical triglyceride compositions (average in m/m%) of

components used in CBEs.

CBE raw material POP POSt StOSt Others

Palm mid-fraction 65 13 2 20

Illipe butter 10 36 42 12

Shea stearine 1 8 69 22

Cocoa butter (as reference) 17 39 26 18

temper slowly and be soft. Since POP is normally the cheapest component, there

must be an optimum cost/benefit, depending on the application of the fat.

There is another dimension to fat quality: the purity of the fractions or the

concentration of the required symmetric triglycerides that are used in the final

CBE. This will also be reflected in the performance, as well as the price of the fat.

Generally, CBEs show the same properties in chocolate as cocoa butter does with

regard to crystallization, texture and eating properties. The shelf life can be pro-

longed and the bloom stability improved by the addition of a good-quality CBE

to the chocolate formula. With a normal CBE, no modification of the manufac-

turing process is necessary, although slight adjustments of temperature during

tempering may be required in the case of the softer and harder CBEs.

A good-quality CBE can be mixed with cocoa butter in any proportion without

changing the melting sequence. A CBE will react in the same way as cocoa butter

when milk fat or other softening fats such as nut oils are mixed in.

Owing to their homogeneous triglyceride composition, both CBEs and cocoa

butter crystallize in a highly ordered structure, and they do so more easily than

does a fat with a large number of different fatty acids. This fact is responsible for

the hardness and uniquely well-defined melting behaviour of CBEs.

A CBE based mainly on POP results in a softer chocolate product than does

an SOS-rich CBE. CBEs rich in POP are also more difficult to temper, requiring

tempering temperatures some degrees lower than for cocoa butter. The properties

and the tempering temperatures for chocolate based on these POP-rich CBEs are

very dependent on the level of CBEs used. Softer CBEs are normally used at a

lower level or may also replace part of the milk fat if that is used. The entire

chocolate formula must be considered in order to find the desired properties and

the most cost-efficient product.

In products with a very high milk fat content, the softening effect of the milk

fat can be compensated for by using a hard CBE. A soft cocoa butter can be

hardened with a hard CBE as well. These hard CBEs, sometimes called CBIs,

make it possible to improve the shelf life of cocoa butter-based chocolate in hot

climates. The production process for chocolates containing hard CBEs requires a

slightly higher tempering temperature.

There is a special group of vegetable fats called cocoa butter equivalents defined by

the EU Directive 2000/36/EC relating to cocoa and chocolate products. According

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Crystallization 401

Table 10.7 Vegetable fats that may be used in chocolate to a

maximum of 5% according to the European Union Directive

2000/36/EC.

Common name ofvegetable fat

Scientific name of plant fromwhich the listed fat is obtained

Illipe, Borneo tallow or

Tengkawang

Shorea spp.

Palm oil Elaeis guineensis, Elaeis oleifera

Sal Shorea robusta

Shea Butyrospermum parkii

Kokum gurgi Garcinia indica

Mango kernel fat Mangifera indica

to the Preamble, ‘(5) The addition to chocolate products of vegetable fats other

than cocoa butter, up to a maximum of 5%, is permitted in certain Member

States’. Moreover (Annex II), ‘In conformity with the criteria laid down by this

directive, the following vegetable fats, obtained from the plants listed below, may

be used (Table 10.7). Furthermore, as an exception to the above, Member States

may allow the use of coconut oil for the following purpose: in chocolate used for

the manufacture of ice cream and similar frozen products’.

10.10.3 Fats for compounds and coatingsCocoa butter, CBEs and other fats in the tempering group are based mainly on

speciality raw materials. This places them in a high price range compared with

fats based on the major vegetable oils. By means of fat modification techniques

such as hydrogenation, fractionation and interesterification, it is possible to pro-

duce fats with melting profiles similar to cocoa butter at significantly lower cost.

These fats have a completely different composition and crystallization pattern,

but the sensory properties of the end product still resemble those of chocolate.

There are two types of so-called non-tempering fats: CBRs (non-lauric) and

CBSs (lauric).

10.10.3.1 Crystallization properties of non-tempering confectionery fatsIn contrast to cocoa butter and other fats based on triglycerides with an unsatu-

rated fatty acid in the mid-position on the glycerol backbone, hydrogenated and

lauric fats do not require tempering in the same way as cocoa butter does to reach

a stable crystalline form. It should be emphasized that these non-tempering veg-

etable fats also require controlled cooling conditions, but these are different from

the tempering process used for cocoa butter and chocolate.

In this type of fat, the triglycerides tend to crystallize in a double-layer struc-

ture, since the saturated and trans-unsaturated fatty acids have a higher degree

of molecular similarity. The formation of a double-layer (DCL) structure is rapid

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402 Confectionery and chocolate engineering: principles and applications

compared with the triple-layer (TCL) formation characteristic of cocoa butter.

Most hydrogenated and lauric fats are reasonably stable in the 𝛽′ form, although

the thermodynamically favoured state is the 𝛽 form.

10.10.3.2 Crystallization dynamics of non-tempering fatsHydrogenated fats comprise mixtures of saturated (palmitic and stearic),

cis-unsaturated (oleic) and trans-unsaturated (elaidic) fatty acids. The molecular

structures of elaidic and stearic acid are quite similar (they are cis–trans isomers),

and these fatty acids are very compatible with each other. Elaidic acid has a

melting point that is intermediate between those of stearic and oleic acids, and

this fact also determines the melting points of the triglycerides where elaidic

acid is present. The mixtures of longer-chain (C-16 to C-18) and medium-chain

(C-12 and C-14) saturated fatty acids (SAFAs) in combination with oleic acid

that occur in lauric fats (coconut oil and palm kernel oil) are also very compatible

with each other (but not with cocoa butter!), especially when the unsaturated

fatty acid is present in one of the outer glycerol positions.

The crystallization process proceeds via nucleation and crystal growth. Hydro-

genated fats based on long-chain fatty acids nucleate readily, whereas lauric fats

may need a higher degree of supercooling to start crystallization. Once nucleated,

however, the lower molecular weight of the lauric fats tends to give a higher

crystal growth rate compared with the larger palmitic/stearic/elaidic-based

systems. The exact composition of the fat determines the overall crystallization

kinetics. In general, the higher the SFC, the more rapid is the crystallization

(nucleation+ growth). The shape of the melting curve (flat or steep) is also a

good indication of the crystallization rate: the steeper the melting curve, the

faster the setting.

10.10.3.2.1 Effect of additives and matrix on crystallization dynamicsThe product matrix and the presence of additives strongly affect the overall crys-

tallization rates of non-tempering fats. Nucleation rates are strongly influenced

by the presence of particles such as those of sugars, cocoa and milk solids.

Surface-active components, either naturally present in the system or added

as functional additives, influence the crystallization rate. It is well known that

diglycerides, lecithin and sorbitan esters influence the crystallization kinetics.

Diglycerides and sorbitan triesters slow down the overall crystallization by reduc-

ing either the nucleation rate or the crystal growth. On the other hand, sorbitan

monoesters, as well as monoglycerides and other more polar emulsifiers, may

act as nucleating agents and thus increase the overall crystallization rate.

The non-tempering systems are sensitive to differences in cooling conditions. If

a non-tempering fat is cooled rapidly to very low temperatures, it can crystallize

in an unstable 𝛼 form, especially if the fat has a high melting point and a steep

melting profile. To avoid subsequent fat bloom, such systems should be either

crystallized or annealed at higher temperatures to obtain a controlled transfor-

mation to the desired 𝛽′ form before packing and storage.

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Crystallization 403

10.10.3.2.2 Fat bloom and fat bloom inhibition in non-temperingsystems

The desired crystal form in non-tempering systems is normally the 𝛽′

(beta-prime) form. The 𝛽 forms can be used on the condition that the pro-

cessing conditions and the composition are optimized to meet melting-profile

and crystallization-rate criteria. Generally, 𝛽′ crystals are thermodynamically

unstable, although some individual triglycerides exist that do not show any

𝛽 form. Similarly to the case of cocoa butter and the Sat–Unsat–Sat type of

triglycerides, 𝛽′ crystals may exist in at least two modifications, with different

melting points and structural features. The 𝛽′ forms are numbered in order of

decreasing stability: 𝛽′-1, 𝛽′-2 and so on.

In a confectionery fat based on hydrogenated fats, the conversion of 𝛽′-2 to

either 𝛽′-1 or 𝛽 crystals may constitute a driving force for fat bloom formation.

It can also be argued, by analogy with the cocoa butter case, that these crys-

tal form transformations are not the cause of but rather a consequence of fat

bloom formation. In general, fat bloom is a crystal growth process that requires

the triglycerides in the bloom to be mobile at the time of formation, either by a

melting process or by solubilization in a liquid phase. These crystal growth pro-

cesses may be associated with a phase transformation process, but not necessarily

so (Liedefelt, 2002, p. 129).

With this in mind, any measure taken to minimize the solubilization and

transport of solubilized triglycerides will enhance the bloom stability in non-

tempering systems. By optimizing the triglyceride composition so that only

co-crystallizing triglyceride species are present in the system, the solubilization

of unstable compositions can be inhibited. Similarly, adding components that

slow down the crystal growth process, such as diglycerides, will also slow down

bloom formation. The presence of non-co-crystallizing fractions, for example,

low-melting trisaturated triglycerides such as trilaurin, is sometimes the cause

of fat bloom, especially in lauric fats.

The transport of solubilized triglycerides may of course be minimized by lower-

ing the amount of liquid phase in the system. This will also bring about an unde-

sired increase in the melting point of the fat, however. The use of lower-melting

triglyceride fractions to bind the liquid phase is sometimes possible.

10.10.4 Cocoa butter replacersCompounds and coatings based on CBRs do not need tempering like cocoa but-

ter. Upon cooling they crystallize in the 𝛽′ form, which in practice is the stable

modification for these fats. CBRs can be produced from a number of different

raw materials, such as soybean oil, rapeseed oil, palm oil, cottonseed oil and

sunflower oil. The production of this type of fat involves special hydrogenation

and fractionation techniques.

The main fatty acids are the saturated palmitic and stearic acids, together with

the monounsaturated oleic acid and its trans isomer. Thus, the fatty acid chain

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404 Confectionery and chocolate engineering: principles and applications

Fats for ice creamS

olid

fa

t co

nte

nt

(%)

Filling fatsFats for toppings

37353025201510

0

10

20

30

40

50

60

70

80

Temperature (°C)

Figure 10.23 Solid-fat-content curves for filling fats and fats for coating of ice cream.

lengths are C-16 and C-18. The use of different raw materials or combinations of

them, in conjunction with the flexibility of the processes, allows a considerable

range of compositions and provides a means of customizing a wide range of fats.

CBRs may contain small amounts of additives such as sorbitan tristearate to

help stabilize the 𝛽′ form. This improves both the gloss retention and the initial

gloss of compound coatings.

There are two main reasons for using CBRs instead of cocoa butter: the price is

lower, and production is simplified since the tempering step (in the sophisticated

form that is necessary for cocoa butter and chocolate) can be omitted.

Setting times are adequate for modern high-speed equipment, even though

they are somewhat longer than for CBS compounds. The recommended cooling

conditions are represented in Fig. 10.23. The melting properties of CBR com-

pounds do not quite match the standards of chocolate or CBS compounds in

moulded products. For coating applications, they offer several advantages, such

as good heat stability and simplified manufacturing procedures. In general, CBR

coatings have very good initial gloss and gloss retention.

In some applications, the fact that they are non-lauric and hence cannot

develop a soapy flavour makes a CBRs a preferred choice over CBSs.

Finally, the possibility to use some cocoa liquor together with a CBR (see fol-

lowing text) is a way to improve the flavour.

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Crystallization 405

10.10.4.1 Compatibility with cocoa butterIt is obvious that the triglycerides of cocoa butter are different from those of

CBRs. Since the fatty acids of both of these alternatives are C-16 and C-18, how-

ever, there is a certain degree of compatibility, and up to 20% cocoa butter (20%

of the fat phase) can be tolerated before eutectic effects become too severe for

practical use. Blends of cocoa butter and CBRs show typical eutectic behaviour.

Within limits, this can be used to improve the melting and sensory properties of

CBR-based compounds. In the 10–20% range, the addition of cocoa butter has a

controlled softening effect that is more pronounced at higher temperatures. This

good miscibility enables manufacturers to use all types of cocoa powder or a cer-

tain amount of cocoa liquor, which ensures that the final product can be given a

rich chocolate flavour and good flavour release. The drawback of including cocoa

liquor is that the setting time is prolonged and gloss retention reduced to some

extent. The use of higher levels of cocoa butter than 20% is not recommended,

since the eutectic effects will be too severe.

As a final remark, it should be mentioned that accidental admixtures, such as

might occur when a manufacturer switches from chocolate to compound pro-

duction on a line, will not have severe negative effects on product quality.

10.10.4.2 Milk fat and CBR blendsCBRs work well with milk fat. Milk fat/CBR blends exhibit no eutectic effects,

resulting in a predictable linear decrease in SFC with increasing content of milk

fat. The practical limit may be 20%, since the product may be too soft at higher

levels. Nut oils such as peanut, hazelnut and almond oils act in a manner analo-

gous to milk fat in this respect. The presence of milk fat extends setting time but

may improve gloss stability.

CBRs may not only be used in solid and filled moulded items but are also

excellent for all kinds of coating applications. Since CBRs tolerate relatively high

amounts of cocoa butter (20%), cocoa liquor may be used in the formulation

to give a good, full cocoa flavour to the product. CBRs, being non-tempering

systems, have low viscosity, fast crystallization and some elasticity, which make

them suitable for coating. The high gloss and good gloss retention give the prod-

uct an appealing appearance.

Within the CBR range there are also products with a high solids content, well

suited for use in warmer climates.

10.10.4.3 Moulding and coatingIt is important to use appropriate cooling conditions for all CBRs used for mould-

ing. To achieve good contraction, as well as good gloss and shelf life, CBRs benefit

from so-called shock cooling. When a CBR is crystallized in a cooling tunnel, the

temperature should be around 6–8 ∘C. The temperature should be increased to

around 16 ∘C at the end of the tunnel to match the ambient temperature without

risk of condensation.

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406 Confectionery and chocolate engineering: principles and applications

When CBRs are used in coating applications, the cooling parameters are of

importance for achieving the best gloss and shelf life. A low initial temperature

in the cooling tunnel is recommended, similarly to the requirements for the crys-

tallization of moulded items.

10.10.5 Cocoa butter substitutesCompounds and coatings based on CBSs are widely used in both the chocolate

and the bakery industries. Like CBRs, CBSs do not need tempering like cocoa

butter, since they crystallize spontaneously in the 𝛽′ form, which is stable in

practice.

CBSs are based on lauric fats, that is, fats that contain a high percentage of

lauric acid in their fatty acid composition. The main raw materials in this group

are coconut and palm kernel oil, with palm kernel oil being the preference for

CBS manufacture. The production of CBSs involves special hydrogenation and

fractionation techniques. Lauric acid (C-12) makes up approximately 50% of the

fatty acid composition, with myristic acid (C-14) as the second most abundant.

In addition, smaller amounts of the longer-chain palmitic and stearic acids are

present. Sorbitan tristearate has sometimes been added to CBSs to help improve

the stability of the 𝛽′ crystals. Such addition of sorbitan tristearate improves both

initial gloss and gloss retention.

To a large extent, the use of CBSs in compounds is driven by the same motives

as the use of CBRs: lower costs and simplified production procedures. A CBS sim-

ilarly needs no tempering, and high crystallization rates allow a high throughput

in the cooling tunnel. For recommended cooling conditions, see Fig. 10.22.

CBS-based compounds generally have better melting properties than CBRs,

almost on a par with chocolate. As can be seen in the following, however, CBSs

are less compatible with cocoa butter.

In some applications, when the water content of a product is more than ca. 3%

or when there is an effect of lipase originating from moulds, the fact that lauric

fats may develop a soapy flavour makes CBRs a preferred choice over CBSs.

Fats with a high content of short-chain fatty acids have a lower viscosity than

fats based on longer-chain fatty acids. This means that for a given fat content and

a fixed set of emulsifiers, CBS coatings and compounds have a lower viscosity

than CBR coatings and compounds.

CBSs and cocoa butter have completely different fatty acid and triglyceride

profiles. Hence, eutectics are apparent even at low levels of cocoa butter.

In contrast to cocoa butter/CBR blends, the strongest effects are seen at inter-

mediate temperatures, from 20 to 30 ∘C. At higher temperatures (>33–35 ∘C),

only small effects are observed. This means that cocoa liquor cannot be used in

CBS-based compounds and coatings. Cocoa powders typically contain 10–12%

cocoa butter. A typical content of cocoa powder in compounds is 15%, which

gives a CBS/cocoa butter ratio of approximately 95/5, as a short calculation

shows. Let the cocoa butter content of a product be 15%×0.11= 1.65%. If the

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Crystallization 407

total fat content in the product is 33.3%, which is a commonly used value,

then the amount of CBS is 31.65% (=33.3%−1.65%), and the CBS/cocoa

butter ratio is 31.65/1.65= 94.95/4.95≈95/5. Going beyond this will result in

excessive softening of the product.

In a recipe for a compound such as milk chocolate, a cocoa powder content

of at least 4–5% is needed; however, in a recipe for a compound such as dark

chocolate, 15% of cocoa powder, as an upper value, is sufficient for the appro-

priate taste. Consequently, this limited compatibility of CBSs with cocoa butter

does not tighten the field of applications.

CBS fats are excellent for both tablet and shell moulding, especially the types

based on fractionated and hydrogenated components. Products containing frac-

tionated CBSs display very fast crystallization and excellent contraction properties.

The resulting tablet has a good snap and melts very quickly.

CBS fats are highly suitable for a wide range of coating purposes and are often

used for this purpose in the bakery industry to coat various pastry products. They

are appreciated for their convenience in that they do not need tempering and set

very quickly on the coated item. It is easy to produce a thin, even layer of coating.

CBS fats also leave a good gloss on the surface.

Thanks to their low viscosity and good flow properties, coatings based on CBSs

are very good to use for hollow-figure moulding. In addition, CBS-based coatings

give a good contraction that facilitates demoulding. Other suitable application

areas for CBS fats are pan-coated products and lentils.

10.10.6 Filling fatsAlthough there are many differences between the various types of fillings, the

essential similarity is that the suspension phase is fat, and the crystallization prop-

erties of this fat determine the consistency of the filling. It is not only the filling fat

itself that affects the final properties of the filling. Besides adding to the flavour

sensation, other components will contribute to building up the fat phase, for

example, cocoa powder or liquor, milk powder, nuts and possibly others as well.

Fat bloom is often the main factor that limits the shelf life of moulded or coated

products. Bloom may occur as a result of migration of fat from the filling to the

surrounding chocolate layer. The migration process is very difficult to avoid, since

it is driven by the fact that the filling contains more liquid fat than the coating.

In an attempt to reach equilibrium, this liquid fat will migrate into the coating

and recrystallize on the surface of the product, with fat bloom formation as a

consequence. Instead of trying to hinder this migration, more recent product

developments in filling fats have focused on gaining control over the effects of

the migration (Liedefelt, 2002, p. 137).

10.10.6.1 Fat-based confectionery fillingsThe fat-based confectionery fillings include various praline fillings, such as

nougat, truffles, yogurt fillings and chocolate spreads. The filling can also be a

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408 Confectionery and chocolate engineering: principles and applications

centre for a coated product or a filling in a bakery product. In these products, fat

is the continuous phase, constituting some 30–40% of the product. The other

ingredients are sugar, milk powder, cocoa products and, often, some kind of

nuts. Depending on the choice of fat for the filling, almost any kind of eating

sensation from very hard and cool-melting to soft and creamy can be achieved.

Figure 10.22 shows curves of the SFC versus temperature for filling fats and

fats for ice cream. The region covered by the SFC curves of filling fats is peculiarly

broad, which shows the great variety of demands to be met.

10.10.6.2 Firm fillingsThe firm fillings include praline and nougat fillings.

The fats used in these products consist of fractionated non-lauric components

with very steep melting curves. They are rather similar to cocoa butter in their com-

position and are therefore highly suitable for use in fillings with high amounts of

chocolate in the recipe. The similarity to cocoa butter also means that these filling

fats are stable in the 𝛽 crystal form and, as such, normally require tempering.

If tempering is not possible, good melting properties can be achieved in other

ways. There are hydrogenated and fractionated non-lauric fats that are stable in

the 𝛽′ form. With these types of fats, good melting can be achieved in combina-

tion with simple production steps, since tempering can be excluded.

Lauric fats can also give a cool-melting sensation to a filled product. However,

lauric fats are not suitable for mixing with cocoa butter; therefore, the cocoa

powder that provides the cocoa flavour of a filling must be of low cocoa butter

content (8–12%) when lauric fats are employed.

Hydrogenated non-lauric fats have widespread use in the confectionery indus-

try. They are suitable for praline fillings, as well as for wafer fillings and sugar

confectionery. They generally show a fast crystallization pattern and are thus

convenient to use in most production units. In addition, they are stable in the 𝛽′

form and give products with high migration stability.

10.10.6.3 Soft fillings and chocolate spreadsFor soft, creamy fillings, very soft fats are needed. Oil migration is even more

difficult to control in such cases.

The same type of fats is suitable for chocolate spreads. In this application as

well, a soft and creamy product is required. The product must also be spreadable

over a wide temperature range, from refrigerator to room temperature, and have

a good shelf life. It should have a shiny and attractive appearance and, above all,

should not separate so that liquid oil shows on the surface of the product.

10.10.6.4 Aerated fillingsGenerally, all kinds of fat-based fillings may be aerated. There are two ways of

aerating a filling: either by melting the fat and aerating during crystallization or

by starting from a solid pre-crystallized fat and aerating it. A fat suitable for whip-

ping must be able to retain air bubbles during aeration. This result is obtained

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Crystallization 409

through small 𝛽′ fat crystals that create a network around the air bubbles. To

stabilize the air bubbles, a certain amount of solid fat is necessary, and thus it is

not possible to aerate fats that are completely liquid. The method of starting from

a pre-crystallized fat is often used for manufacturing wafer and biscuit fillings.

These normally consist of fat, sugar and a flavouring. First the fat is tempered

to room temperature, after which it is mixed with the other ingredients and

whipped. It is also possible to use a continuous aeration process. In this case the

filling is melted and subsequently aerated during crystallization. It is thus impor-

tant to have good control over the temperature gradient during the process to

obtain optimal aeration, as well as pumpability of the cream.

10.10.6.5 Sugar-based confectionery fillingsThe fat content of sugar-based fillings is normally less than 20%, and the contin-

uous phase is a sugar and water solution emulsified with fat. The most important

types of sugar-based fillings for confectionery are toffee/fudge and fondant.

10.10.6.5.1 Toffee/fudge

Toffee and fudge consist of oil, sugar, water and milk ingredients. The heating

of sugar and milk proteins results in a Maillard reaction (see Section 16.2.1), a

process that gives the toffee its characteristic flavour and colour.

The hardness and texture of the final toffee/fudge are mainly determined by

the water content, which in turn is controlled by the boiling temperature. The

higher the temperature, the lower the water content and the harder the final

product. In toffee/fudge applications, the fat works as a smoothing and shorten-

ing agent, making the product less sticky. Another very important function of the

fat is as a flavour carrier, which means that it needs to have very good flavour

and flavour stability. Because of the processing conditions, the fat must also tol-

erate high temperatures and a high water content, without the risk of oxidation,

hydrolytic reactions or the formation of off flavours.

10.10.6.5.2 Fondant

When a sugar solution is cooled under constant agitation, small crystals are

formed, transforming the solution into a white, sticky dough or mass – a fondant.

Here as well, the water content is the main factor that determines the hardness

of the product. A low water content allows a fondant to be moulded in starch

moulds or formed into various shapes. With a higher water content, the fondant

is more liquid and can be used as a fondant cream filling.

The fat’s role in a fondant is similar to its role in toffee. It can smooth the

texture and give the fondant extra creaminess, but most of all it acts as a flavour

carrier. In this case the fat might be added to the sugar solution at more moderate

temperatures. It still needs to tolerate a high water content and be very stable

against oxidation, however, since air will be mixed into the fondant mass during

processing.

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410 Confectionery and chocolate engineering: principles and applications

10.10.7 Fats for ice cream coatings and ice dippings/toppings10.10.7.1 CoatingsBoth chocolate and compounds are used in the coating of ice cream. For choco-

late, the normal chocolate legislation is applicable, that is, if vegetable fat is

allowed, the same rules apply to its use in ice cream coatings. In the EU, coconut

oil is added to the list of permitted vegetable fats, as mentioned previously. Coat-

ings are in common use today in the production of ice cream. Since the fat

content of a coating varies between 55% and 70%, its properties are derived

mainly from the fat used. Besides economic considerations, vegetable fats have

an advantage over cocoa butter in ice cream coatings as they are better equipped

to meet the special demands made. In particular, fast crystallization is critical,

and non-transparent but thin layers are required.

Ice cream coatings should have a melting point below 30 ∘C; otherwise the

coating will not melt during eating, since the mouth temperature falls a few

degrees when ice cream is being eaten. A coating must have good snap and then

melt rapidly and totally to give a good mouthfeel. The SFC curve (Fig. 10.23) is

a good indicator in this respect.

With a view to simplifying the production process and ensuring that the prod-

uct is completely covered with a thin, non-transparent layer, ice cream coatings

should have a low viscosity. If this is not the case, bleeding will occur, with the

ice cream appearing in white spots on the coating. Not only is this unattractive,

but it may also cause wrappers to stick. Moreover, coatings must also have a

somewhat elastic structure to prevent them from breaking or chipping off the

ice cream during eating.

A coating should have a rapid rate of solidification, so that production output

can be kept at a high level. A fast flavour release is particularly essential in coat-

ings. Since the fat is the carrier of the flavour, it should be chosen with care to

guarantee fast flavour release.

The types of fats used in ice cream coatings are mainly lauric fats, such as

coconut oil. These fats have an advantage over cocoa butter in their high crystal-

lization rates – an important property in this field. To prevent the coating from

cracking, other softer vegetable fats are often added to the lauric fats to increase

the elasticity. There are also non-lauric fats available for ice cream coatings. These

are particularly suitable in cases where the same equipment is used for the pro-

duction of both chocolate and ice cream coatings. The risk of contamination

between a lauric and a non-lauric fat is then eliminated. Whenever a thicker

layer of coating on ice cream is desired, a non-lauric fat is also a good alternative.

10.10.7.2 ToppingsIce dippings and ice toppings are other types of ice cream coatings, applied at the

point of sale or at home. These should be liquid at room temperature and solidify

almost instantly when in contact with cold ice cream. As the product may be

kept at room temperature for a long period of time, stability against oxidation

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Crystallization 411

and rancidity is important. The quality of an ice dipping or ice topping is largely

determined by the properties of the fat system. The product should have a low

viscosity and be liquid at room temperature. Since cooling is only by contact

with the ice cream, a rapidly crystallizing fat is needed. The melting profile of the

fat should also be designed to ensure good flavour release.

10.11 Crystallization of confectionery fats with a hightrans-fat portion

There are health concerns about trans-fatty acids (TFAs) formed by hydrogena-

tion, related to the coating fats and filling fats used in confectionery.

10.11.1 Coating fats and coatingsFoubert et al. (2006b) investigated a trans-containing coating fat (TCF) with 36%

TFA content and a trans-free coating fat (TFCF) with 0.4% TFA content of lauric

type. (In both samples, the TFA was of C 18:1 type.)

The isothermal crystallization behaviour was as follows:

• TCF: modified 𝛽′ at 17 ∘C and direct 𝛽′ at 23 ∘C.

• TFCF: mediated 𝛽′ and direct 𝛽′ at 23 ∘C.

• The crystallization rate was higher for the TFCF.

The behaviour in storage was as follows:

• TFC: increasing hardness due to continued crystallization.

• TFCF: increasing hardness due to changes in microstructure and sintering.

• No significant difference in hardness.

• However, there were large differences in the hardness of coatings due to vari-

ous triglyceride interactions and other components in the coating matrix.

10.11.2 Filling fats and fillingsVereecken et al. (2007) investigated a trans-containing filling fat (TCFF) with 10%

TFA content of lauric type and a trans-free filling fat (TFFF) with 0.2% TFA con-

tent. (In both samples, the TFA was of C 18:1 type.)

The isothermal crystallization behaviour was as follows:

• TCFF: at 15–20 ∘C, limited post-crystallization, direct 𝛽′, no sandiness.

• TFFF: at 8–10 ∘C, direct 𝛼; at 12–17.5 ∘C, 𝛼-mediated 𝛽′; at 20 ∘C, direct 𝛽′.

• The crystallization rate was higher for the TCFF.

The behaviour in storage was as follows:

• TCFF: decreasing hardness.

• TFFF: decreasing hardness.

• Both TCFF and TFFF: decreasing hardness; no significant difference in hard-

ness after 1 week of storage; reduction in differences in crystal size and shape.

• The filling matrix had an important influence.

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412 Confectionery and chocolate engineering: principles and applications

Pajin et al. (2007) investigated the influence of filling fat type on praline prod-

ucts with nougat fillings. Of three samples, two (S1 and S2) were practically

lauric acid-free with a high TFA content (S1= 38.08%; S2=33.68%); the third

sample had a lauric acid content of 11.28% and a relatively low TFA content

(6.99%). The crystallization kinetics were observed by means of the change in

the SFC, under static conditions at a 20 ∘C crystallization temperature, using the

NMR technique and a modified Gompertz model (see Eqn 10.95). The results

showed that the amount of solid phase formed in S1 in the course of crystalliza-

tion was 2–2.5 times larger than that in S2 and S3. In addition, the maximum

rate of crystallization in S1 was about twice that in the two other samples. How-

ever, there were large differences in the induction periods: the induction period

for S2 was four times higher than that for S2, and the induction period of S3 was

practically negligible, that is, crystallization of S3 started promptly at 20 ∘C. The

investigation was complemented by a rheometric study. Measurement of SFC

and viscosity are two approaches to determining the suitability of a filling fat to

be used in a praline. Both methods provide valuable information, and, particu-

larly, viscosity build-up is very important from the point of view of production

on a factory scale.

10.11.3 Future trends in the manufacture of trans-free specialconfectionery fats

Karlovits et al. (2006) discussed the possibilities of manufacturing filling confec-

tionery fats of low TFA content. They cited the conclusions of the European Food

Safety Authority of 1 September 2004, which can be summarized as follows:

• Both TFAs and SAFAs are risk factors for high blood pressure and coronary

heart disease.

• At equivalent dietary levels, the effects of TFAs on the heart may be greater

than those of SAFAs; however, the intake of TFAs is ca. 10 times less than that

of SAFAs, taking into account the dietary recommendations in many European

countries.

• The relationship between TFA intake and cancer, type 2 diabetes and allergies

is weak and inconsistent.

• At present, TFAs from natural sources and those formed during food processing

cannot be distinguished analytically.

Karlovits et al. (2006) highlighted a contradiction: if two blends of the same

SFC are produced with a low-trans-fat content and a high-trans-fat content, the

following equation holds for the sum SAFA+ TRANS:

(SAFA + TRANS)low trans fat ≥ (SAFA + TRANS)high trans fat (10.145)

That is, it is easier to produce a blend with high-trans-fat components than with

low-trans-fat components if the sum SAFA+TRANS and the SFC are specified.

However, the traditional possibilities (an increase in the ratio of fully hardened

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Crystallization 413

vegetable oils, lauric oils, palm oil fractions, etc.) decrease the TRANS content

but increase the sum SAFA+TRANS.

According to Karlovits et al. (2006), a non-traditional possibility may be to

develop a new generation of confectionery fats which consist of liquid oil, fat

replacers, gelling/texture-building agents, emulsifiers and antioxidants. How-

ever, a series of new filling fats has already been presented (the Kruszwica range):

all-purpose fats, a medium-trans range and a low-trans range, the latter of which

is non-lauric and GMO-free.

Health concerns about TFAs formed by hydrogenation have led to the use

of interesterification, fractionation and blending of saturated and polyunsatu-

rated oils as an alternative method to hydrogenation. These alternatives are costly

and do not easily produce the desirable physical and chemical properties of oils

suitable for broad ranges of food products. Therefore, these alternative methods

cannot easily replace the hydrogenation of vegetable oils. Hydrogenation is still

a viable choice for food manufacture if TFAs can be substantially reduced dur-

ing the hydrogenation process (Jang et al., 2006). New hydrogenation processes

such as electrocatalytic hydrogenation, precious-metal catalyst hydrogenation

and supercritical-fluid-state hydrogenation have shown promising results for the

reduction of TFAs below the level of 8%. These hydrogenation techniques would

be viable alternatives for replacing the conventional Ni catalyst hydrogenation to

produce hydrogenated products with low TFAs. However, further research needs

to be done on the economic feasibility of new hydrogenation processes and the

reusability of precious-metal catalysts.

Manufacturers have to be aware that when replacing trans-containing fats

with their trans-free alternatives, differences in chemical composition between

these alternatives can have a tremendous effect on the final product quality. The

formulation of a suitable alternative is, therefore, not straightforward. In addi-

tion, some modification of processing conditions might be anticipated. A major

challenge will be to characterize the microstructural development of fat blends

in industrial manufacturing. To adapt an industrial process in such a way that

the desired product quality and functionality are guaranteed, more insight and

understanding into the fat crystal network is needed. Nowadays, the microstruc-

tural development on an industrial scale, starting with nucleation and crystal

growth and leading towards final macroscopic properties, remains mainly a black

box process (Veerle De Graef, 2009).

A possible way to produce trans fat-free blends which meet the consumers’

requirements in relations to taste and consistency is mixing (animal↔ vegetable)

fats. Soós (2014) studied the blending animal fats (lard, milk fat and goose fat)

with vegetable fats (cocoa butter, palm oil medium fraction, coconut oil) with

compositions 25; 50 and 75 m/m%, altogether in 3× 3×3= 27 combinations.

In this topic Gray (2014) discusses the tentative announcement made by the

Food and Drug Administration in 2013 on the presence of partially hydrogenated

oils (PHOs) and the referring analytical issues (e.g. determination of SFC).

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414 Confectionery and chocolate engineering: principles and applications

10.12 Modelling of chocolate cooling processesand tempering

10.12.1 Franke model for the cooling of chocolate coatingsFranke (1998) proposed a one-dimensional, unsteady-state heat transfer model

for the crystallization of chocolate coatings of coated products using a linear term

q′/cp to account for latent-heat evolution:

𝜕T𝜕t

= 𝛻∗(a𝛻T) +q′

cp

(10.146)

where 𝜕T/𝜕t (K/s) is the change of temperature T as a function of time t, a (m2/s)

is the thermal diffusivity of the chocolate mass, q′ (kJ/kg s) is the latent heat of

crystallization per unit time, cp (kJ/kg K) is the specific heat capacity of the choco-

late and 𝛻= 𝜕( )/𝜕xi is the gradient of the space coordinates, where i= 1, 2, 3. The

form of the function T is T= T(t, x), where the x direction is perpendicular to the

chocolate surface.

Obviously, Eqn (10.146) is Fourier’s second equation for thermal conduction

plus an external heat source originating from crystallization of cocoa butter.

This equation is combined with appropriate heat-transfer-coefficient boundary

conditions for convective heat transfer from the surrounding air (Newton’s law

of cooling):𝜕Q𝜕t

= 𝛼F(Tair − Tsurface) (10.147)

where 𝛼 (kJ/m2 K s) is the heat transfer coefficient and F (m2) is the surface area

of the cooling chocolate. The integral of Eqn (10.147) leads to a function T= T(t)

of the following form:

T(t) = T0 exp(−kt) (10.148)

where T0 and k are determined from the boundary conditions.

An essential part of the Franke model is the supposition that q′ can be decom-

posed into a product of two variables:

q′ = f1(Qm)f2(T) (10.149)

where f1(Qm) (kJ/kg s) is the dependence of the rate of crystallization on the

undercooling and Qm (kJ/kg) is the specific heat of crystallization per unit time

that has already been released during crystallization, and

f2(T) = fT(Tcryst − T) (10.150)

where fT is a coefficient (0.00043 K−1, experimentally determined) and Tcryst (∘C)

is the temperature of crystallization (=26.5 ∘C, experimentally determined for

plain chocolate). Consequently, one of the initial conditions is the following rela-

tionship derived from Eqn (10.150):

ifTcryst ≤ T , then q′ = 0 (10.151)

The function f2(T) is linear, as Eqn (10.150) shows.

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Crystallization 415

Figure 10.24 Modelling of heat flux as a

function of released crystallization heat

Qm. Source: Franke (1998). Reproduced

with permission from Elsevier.

m2

f1m

f1

m1

Qmax Qm Qend

The modelling of f1(Qm) is represented in Fig. 10.24. The released heat of crys-

tallization is proportional to f1. The evolution of the heat flux of crystallization

(q′ vs t) is presented in Fig. 10.26, which is a mapping of the f1 versus Qm plot

modified by the effect of f2. Calculated temperature plots for different layers were

obtained from the first term of Eqn (10.146), which describes the penetration of

the cooling effect with respect to both time t and depth x. On the surface, x= 0.

Equations (10.146)–(10.150) provide a complete description of the cooling

process of chocolate couverture; solutions can be obtained by numerical inte-

gration by computer.

The model is able to fit the general course of temperature variation, includ-

ing the plateau phase caused by the release of heat of crystallization. A plot of

T(t) is presented in Fig. 10.25 to illustrate this fact. Simulations of the cooling of

coated cookies under different cooling conditions using the model showed pos-

sibilities for optimizing the process with respect to the expected surface gloss and

hardness.

26

25

24

23

22

21

20

0 1 2 3 4 5 6

Calculated valuesMeasured values

Te

mp

era

ture

(°C

)

Cooling time (min)

Figure 10.25 Cooling curve T(t) for chocolate crystallization obtained from measured and

calculated values. Source: Franke (1998). Reproduced with permission from Elsevier.

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416 Confectionery and chocolate engineering: principles and applications

35

30

25

20

Specifi

c c

rysta

llization r

ate

(kJ/k

g/m

in)

15

10

5

00 60 120 180

Cooling time (s)

240 300

0.4 mm (Bottom)

1.2 mm (Middle)

2.0 mm (Surface)

Figure 10.26 Specific crystallization rate as a function of cooling time. Calculated temperature

plot in different layers of the chocolate coating during cooling by forced convection. Source:

Franke (1998). Reproduced with permission from Elsevier.

Figure 10.26 presents a plot of the specific crystallization rate versus cooling

time. Temperature plots for different layers of the chocolate coating during cool-

ing by forced convection were calculated.

10.12.2 Modelling the temperature distribution in coolingchocolate moulds

Tewkesbury et al. (2000) developed a computational model using the alternative

approach of the effective heat capacity, in which latent heat is included in the

specific heat term:

𝜌cp,eff𝜕T𝜕t

= 𝛻∗(𝜆𝛻T) (10.152)

where 𝜌 (kg/m3) is the density of the chocolate; cp eff (kJ/kg K) is the effective

heat capacity, which is a function of temperature and thermal history; and 𝜆 (kJ/m s)

is the coefficient of thermal conduction.

This approach takes as its starting point the fact that chocolate displays a

range of melting temperatures instead of a single melting point. In the classical

Maxwell–Stefan formulation of phase transition problems, solidification occurs

at a well-defined front that moves through the material (Taylor and Radha

Krishna, 1993; Viskanta et al., 1997). This is appropriate for simple materials

such as water and elemental metals but is inappropriate for chocolate, which is a

multicomponent mixture of triglycerides that display a spread of melting points.

The effective specific heat capacity of tempered chocolate can be obtained from

DSC experiments at various cooling rates. Crystallization is a kinetic process, so

the effective heat capacity of chocolate is dependent on the thermal history of

the sample and on the cooling rate (Stapley et al., 1999).

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Crystallization 417

Ø 60 mm

2 mm

4 mm

4 mmPolycarbonate

mould

Thermocouple

leads to data

logger

AChocolate

C3C2

C1

4 mm

4 mmB

Figure 10.27 Vertical cross section of a mould with thermocouple positions. Source:

Tewkesbury et al. (2000). Reproduced with permission from Elsevier.

35

30

25

Te

mp

era

ture

(°C

)

20

0 200 400

A

B C1

C3

C2

600 800

Time (s)

(a)

(b)

1000 1200 1400

15

10

30

28

26

24

22

20

18

16

14

12

Te

mp

era

ture

(°C

)

0 500

A

B

C1

C3

C2

1000

Time (s)

1500 200010

Figure 10.28 Cooling curves for (a) untempered and (b) tempered chocolate with a nominal

air-cooling rate of 2 ∘C/min. Source: Tewkesbury et al. (2000). Reproduced with permission

from Elsevier.

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418 Confectionery and chocolate engineering: principles and applications

A plan view of a mould with thermocouple positions used by Tewkesbury et al.

(2000) is shown in Fig. 10.27. Figure 10.28 presents several cooling curves for

(a) untempered and (b) tempered chocolate with a nominal air-cooling rate of

2 ∘C/min.

These experiments proved, as Stapley et al. (1999) showed, that the slower the

material is cooled, the higher the temperature at which latent heat is evolved and

also the greater the amount of latent heat. Two methods were used to model the

latent-heat release:

• Use of cp versus T data from a single data set corresponding to the nominal

cooling rate of the cooling tunnel, that is, working with a function cp = cp(T)w

(where w is the cooling rate)

• Use of a set of cp versus T curves over a range of cooling rates, that is, working

with a function cp = cp(T; w), which is a 3D surface plot

The effective specific heat capacity is high in the region of melting (20–30 ∘C),

as the peak in Fig. 10.29 shows.

To solve the differential equation (10.152) taking the effective heat capacity

functions cp = cp(T)w and cp = cp(T; w) into account, a simple moving-average tech-

nique was applied, which takes a window of N data points and finds the average

ordinate. Good agreement was found between the model and experiment for

cooling rates of 1 and 2 ∘C/min, but they diverged at higher and lower cooling

rates. Simulations that used a specific data set for a single cooling rate alone failed

to predict the temperature at which crystallization occurred. The programme was

thus altered to allow the specific-heat-capacity data for chocolate to be calculated

as a function of both temperature and cooling rate, and the resulting data sets

were used in the simulations. This fitted the experimentally measured mould

temperatures well within a cooling-rate window of 0.5–2 ∘C.

50 4030

20Temperature (°C) Coolin

g r

ate

(°C

/min

)E

ffective

heat capacity

(kJ/k

g K

)

100

–1010

8

6

4

20

2

3

4

5

6

7

8

Figure 10.29 Plot of effective heat capacity as a function of temperature and cooling rate.

Source: Tewkesbury et al. (2000). Reproduced with permission from Elsevier.

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Crystallization 419

10.12.3 Modelling of chocolate tempering processDebaste et al. (2008) developed a model that enhanced our understanding and

control of the chocolate tempering process and aimed to predict the temperature

field during melting and crystallization. The heat transfer problem was simplified

by using an effective thermal conductivity to model the mixing obtained with a

newly designed stirrer. The heat conduction equation was solved using Comsol.

The essential attributes of this model are as follows:

• A mechanical stirrer was designed to simulate manual mixing in a controlled

and reproducible manner.

• The convective terms in the heat balance equation were neglected, and an

effective thermal-conductivity approach was used to take into account the

enhancement of heat transport by the mixing process.

• A sink term was added to the heat balance equation to take into account the

additional cooling arising from the latent heat of melting of the solid pieces

used as crystallization seeds. This term was written in the form of a kinetic

equation, whose parameters were identified by DSC and by melting experi-

ments carried out under adiabatic conditions. One should note that the term

kinetic is used in a broad sense in thermal analysis: it covers the study and

modelling of the rate(s) of change of measured quantities (Várhegyi, 2007).

• The predicted transient temperature profiles were validated against the results

of tempering experiments, using the new stirring device.

The mathematical model consists of the following three equations. The first

equation is

𝜌cp𝜕T𝜕t

= 𝛻(𝜆eff𝛻T) + Q (10.153)

where 𝜌 and cp are the density and specific heat capacity, respectively, of choco-

late; 𝜆eff (kJ/m s) is a lumped thermal-conductivity parameter taking into account

the enhancement of heat transport by the mixing process of tempering; and Q

expresses the heat originating from crystallization.

The initial condition (the second equation) is expressed as

T(t = 0) = T0 (10.154)

where the temperature T0 is uniform within the whole tempering bowl.

The heat flux boundary condition (the third equation) at the wall of the bowl

and on the free surface is given as a sum of a convective flux and a radiative flux:

− k(𝜕T𝜕t

)

wall= htot(T − Text) + 𝜎𝜀(T4 − T4

ext) (10.155)

where the emissivity 𝜀 and the convective heat transfer coefficient htot depend

on the nature and positions of the surfaces considered; 𝜎 (W/m2 K4) is the

Stefan–Boltzmann constant. (The units of k are W s/m2 K.) Figure 10.30 shows a

comparison of the convective heat flux with the radiative heat flux as a function

of temperature in the case of a grey (𝜀= 0.93) body in ambient air at 20 ∘C.

Obviously, the radiative heat flux is too important to be neglected in the model.

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420 Confectionery and chocolate engineering: principles and applications

1.5

1.4

1.3

1.2

1.1

1.0

0.9

0.80 20 40

Temperature (°C)

Ra

tio

of

co

nve

ctive

to

ra

dia

tive

flu

x

60 80 100

Figure 10.30 Convective heat flux divided by radiative heat flux as a function of temperature;

𝜀=0.93, ambient air temperature=20 ∘C. Source: Debaste et al. (2008). Reproduced with

permission from Elsevier.

The appropriate relationship for calculating the global heat transfer coefficient

htot at the wall is1

htot

= 1hin

+dwall

𝜆wall

+ 1hout

(10.156)

where the corresponding heat transfer coefficients (W/m2 K) are hin (on the

inner wall) and hout (the resistance of the outer wall); dwall is the thickness of

the wall (m) and 𝜆wall is the conductivity of the wall (W/m K).

The heat resistance of the inner wall hin was calculated from a relationship of

the type Nu= f(Re; Pr) referred to the anchor stirrers used. When the bowl was

immersed in water, the resistance of the outer wall could be neglected, and when

the bowl was in air, this resistance was calculated from a relationship of the type

Nu= g(Ra; Pr), where Ra is the Rayleigh number. For details, see Debaste et al.

(2008).

If the total observed heat flow used for melting is F=F(t), then the degree of

conversion is given by the fraction of the heat flow that has been consumed by

the melting:

𝛼 =∫

F(t)dt(t ∶ 0 → t)

∫F(t)dt(t ∶ 0 → ∞)

. (10.157)

It was proposed in this model to describe the kinetic model of melting under

non-isothermal conditions by the following equation (Chen et al., 2007):

d𝛼dt

= A0 exp

(−

Ea

R(T − Tref)

)(1 − 𝛼)n (10.158)

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Crystallization 421

where Tref = 0 ∘C. The parameters A0, Ea and n were fitted to DSC results by

a non-linear multivariable least-squares technique (d𝛼/dt as a function of 𝛼

and T) (Wasan, 1970). The values of the kinetic parameters of Eqn (10.158)

were log A0 = 5.34, Ea = 1001.4 cal/mol and n= 2.8. The curves of 𝛼 = 𝛼(t) (see

Eqn 10.158) were of the usual S shape.

The model gives an accurate prediction of the cooling rate and the tempera-

ture field within a mass of melted chocolate seeded with small solid grains and

left at ambient temperature. It can be used to identify the criteria for good tem-

pering. It could be observed that the initial temperature of the seeds was not

a critical parameter, whereas the ambient temperature, not surprisingly, had a

large influence in the case of cooling in ambient air.

The opinion of Debaste et al. (2008) is that, in its present state of development,

this model is unable to correlate the prediction of the evolution of temperature

with time to the quality of tempering. These authors’ ongoing studies are focus-

ing on the development of a shrinking-core model to get a better description

of the kinetics of the melting of seeds, which is related to the value of Q (see

Eqn 10.153). In addition, to complete the model, the nucleation that takes place

later in the second stage of the tempering process will be studied.

10.13 EU programme ProPraline

In the framework of EU programme ‘Research for the benefit of small and

medium enterprises (SMEs)’, the Swedish Institute for Food and Biotechnology

(SIK) (Gothenburg) coordinated the project ProPraline – Structure and pro-

cessing for high quality chocolate pralines. The project focused on developing

a mechanistic understanding for bloom formation and cracking in chocolate

pralines and knowledge-based processing solutions for chocolate manufacture.

ProPraline is an EU-funded project with the objective to develop new routes

for prevention of fat bloom and crack formation in chocolate pralines by

understanding the role of chocolate microstructure at different length scales and

their time-dependent changes during processing.

The project consortium involves a balanced combination of six R&D groups,

three SME chocolate producers and two large companies supplying equipment

and ingredients.

Major results from ProPraline:

ProPraline Book of Methods

ProPraline Course Material

ProPraline Routes for Prevention of Fat Bloom and Cracking

ProPraline Handbook

Source: https://www.sp.se/en/units/fb/forskning/tidigare/ProPraline.pdf

(2013-05-14 10:35:28)

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422 Confectionery and chocolate engineering: principles and applications

This brief introduction can be merely confined to propose for studying the

ProPraline project with a thorough and detailed discussion of the matters con-

cerning fat bloom and crack formation in chocolate pralines.

Further reading

ADM Cocoa (2009) deZaan Cocoa & Chocolate Manual, ADM Cocoa International, Switzerland,

40th Anniversary Edition.

Afoakwa, E.O., Paterson, A., Fowler, M. and Vieira, J. (2008) Effects of tempering and fat

crystallisation behaviour on microstructure, mechanical properties and appearance in dark

chocolate systems. Journal of Food Engineering, 89, 128–136.

Alikonis, J.J. (1979) Candy Technology, AVI Publishing, Westport, CT.

Beckett, S.T. (ed.) (1988) Industrial Chocolate Manufacture and Use, Van Nostrand Reinhold, New

York.

Beckett, S.T. (2000) The Science of Chocolate, Royal Society of Chemistry, Cambridge.

da Silva Martins, P.M. (2006) Modelling crystal growth from pure and impure solutions: a case

study on sucrose. Doctoral thesis. University of Porto, Portugal.

De Graef, V., Van Puyvelde, P., Goderis, B. and Dewettinck, K. (2009) Influence of shear flow

on polymorphic behavior and microstructural development during palm oil crystallization.

European Journal of Lipid Science and Technology, 111, 290–302.

De Graef, V., Goderis, B., Van Puyvelde, P. et al. (2008) Development of a rheological method to

characterize palm oil crystallizing under shear. European Journal of Lipid Science and Technology,

110, 521–529.

De Graef, V., Foubert, I., Smith, K.W. et al. (2007) Crystallization behavior and texture of

trans-containing and trans-free palm oil based confectionery fats. Journal of Agricultural and

Food Chemistry, 55 (25), 10258–10265.

De Graef, V., Dewettinck, K., Verbeken, D. and Foubert, I. (2006) Rheological behavior of crys-

tallizing palm oil. European Journal of Lipid Science and Technology, 108, 864–870.

Friberg, S.E., Larsson, K. and Sjöblom, J. (2003) Food Emulsions, Marcel Dekker, New York.

Kempf, N.W. (1964) The Technology of Chocolate, The Manufacturing Confectioner Publishing Co.,

Glen Rock, NJ.

Lakatos, B.L. and Blickle, T. (1995) Nonlinear dynamics of isothermal CMSMPR crystallizers: a

simulation study. Computers & Chemical Engineering, 11 (Suppl 1), 501–506.

Lees, R. (1980) A Basic Course in Confectionery, Specialized Publications Ltd, Surbiton.

Marangoni, A.G. and Narine, S.S. (2004) Fat Crystal Networks, Marcel Dekker, New York.

Mazzobre, M.F., Aguilera, J.M. and Buera, M.P. (2003) Microscopy and calorimetry as comple-

mentary techniques to analyze sugar crystallization from amorphous systems. Carbohydrate

Research, 338, 541–548.

Meiners, A. and Joike, H. (1969) Handbook for the Sugar Confectionery Industry, Silesia Essenzen-

fabrik, Gerhard Hanke KG, Norf, West Germany.

Minifie, B.W. (1970) Chemical analysis and its application to candy technology. Confectionery

Production, 36 (7), 423–426, 449.

Minife, B.W. (1970) Chemical analysis and its application to candy technology – the analysis of

fats. Confectionery Production, 36 (9), 554–555.

Minife, B.W. (1970) Chemical analysis and its application to candy technology – the analysis of

fats. Confectionery Production, 36 (10), 615–616.

Minife, B.W. (1970) Chemical analysis and its application to candy technology – the analysis of

fats. Confectionery Production, 36 (12), 746–747, 770.

Minifie, B.W. (1999) Chocolate, Cocoa and Confectionery, Science and Technology, 3rd edn, Aspen Pub-

lications, Gaithersburg, MD.

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Crystallization 423

Narine, S.S. and Marangoni, A.G. (2002) Physical Properties of Lipids, Marcel Dekker, New York.

Peyronel, F. and Marangoni, A.G. (2014) In search of confectionary fat blends stable to heat:

hydrogenated palm kernel oil stearin with sorbitan monostearate. Food Research International,

55, 93–102.

Pratt, C.D. (ed.) (1970) Twenty Years of Confectionery and Chocolate Progress, AVI Publishing, West-

port, CT.

Rojkowski, Z. (1977) New empirical kinetic equation of size dependent crystal growth and its

use. Kristall und Technik, 12 (11), 1121–1128.

Rojkowski, Z.H. (1993) Crystal growth rate models and similarity of population balances for size

dependent growth rate and for constant growth rate dispersion. Chemical Engineering Science,

48 (8), 1475–1485.

da Silva Martins, P.M. (2006) Modelling crystal growth from pure and impure solutions – a case

study on sucrose. Doctorial Thesis. University of Porto, Portugal.

Sullivan, E.T. and Sullivan, M.C. (1983) The Complete Wilton Book of Candy, Wilton Enterprise,

Inc., Woodridge, IL.

Taylor, J.E., Van Damme, I., Johns, M.L. et al. (2009) Shear rheology of molten crumb chocolate.

Journal of Food Science, 74 (2), 55–61.

Widlak, N. (1999) Physical Properties of Fats, Oils, and Emulsifiers, American Oil Chemists Society.

Wieland, H. (1972) Cocoa and Chocolate Processing, Noyes Data Corp., Park Ridge, NJ.

Winter, H.H. and Mours, M. (1997) Rheology of polymers near liquid–solid transitions. Advances

in Polymer Science, 134, 165–234.

Wolf, B. (2011) Rheological properties of chocolate. New Food, 14 (2), 15–20.

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CHAPTER 11

Gelling, emulsifying, stabilizingand foam formation

11.1 Hydrocolloids used in confectionery

Jellies and foams (e.g. marshmallows) are popular types of confectionery. These

products are made from hydrocolloids. Consequently, gelling and foaming are

important operations. Emulsifying and stabilizing are essential from the point of

view of emulsions (see Section 5.8). The technological role of hydrocolloids in the

confectionery industry is very complex and can be difficult to categorize because

of the wide range of effects exerted. Relating to theories of gelation see Gelation

as a second order phase transition , moreover, Fractal structure of gels, Section 4.8.1.

In the following sections, the most characteristic properties of the hydrocol-

loids used in confectionery and their application for producing confectionery

jellies are discussed.

11.2 Agar

11.2.1 Isolation of agarAgar is a gelatinous product isolated from seaweed (red algae class,

Rhodophyceae, e.g. Gelidium spp., Pterocladia spp. and Gracilaria spp.) by a hot-

water extraction process. Purification is possible by congealing the gel.

Agar is a heterogeneous complex mixture of related polysaccharides having

the same backbone chain structure. The main components of the chain are

β-D-galactopyranose and 3.6-anhydro-α-L-galactopyranose, which alternate

through 1→4 and 1→3 linkages.

The chains are esterified to a low extent with sulphuric acid. The sulphate

content differentiates the agarose fraction (the main gelling component

of agar), in which close to every tenth galactose unit of the chain is

esterified, and the agaropectin fraction, which has a higher sulphate ester-

ification degree and, in addition, has pyruvic acid bound in ketal form [4.6-

(1-carboxyethylidene)-D-galactose]. The ratio of the two polymers can vary

greatly. Uronic acid, when present, does not exceed 1%.

Confectionery and Chocolate Engineering: Principles and Applications, Second Edition. Ferenc Á. Mohos.© 2017 John Wiley & Sons Ltd. Published 2017 by John Wiley & Sons Ltd.

424

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Gelling, emulsifying, stabilizing and foam formation 425

11.2.2 Types of agarBar-style agar. The weight of one piece is 7.5 g on average. Owing to its

honeycomb-like structure, the bulk density is about 0.030–0.036 g/cm3.

Stringy agar. The normal length of an agar string is 28–36 cm, although there are

no definite required dimensions.

Agar flakes and powdered agar. Flakes (or coarse powder) are normally produced

by a freezing process, while most of the powdered agar (or fine powder) is pro-

cessed by a pressing dehydration method.

The Japanese agricultural standard for powdered agar (officially, special type

agar) is given in Table 11.1.

11.2.3 Solution propertiesAgar is not soluble in cold water but is soluble in boiling water. Merely heating

the water, if it is kept at a temperature below boiling point, does not bring about

perfect dissolution. When bar-style agar, stringy agar or agar flakes are used,

soaking in cold water beforehand, preferably overnight, greatly assists in full dis-

solution. Even when so-called quickly dissolvable agar is used, at least 5–10 min

soaking is recommended.

Two ranges of viscosity of agar sols can be distinguished (see Matsuhashi,

1990a):

1 Low concentrations, c (%)= 0.06–0.2 and 𝜂rel = 1.2–3.5. For this region,

log 𝜂rel = Kc (11.1)

where K is a constant (0.9–1.22, depending on the type of agar).

2 High concentrations, c (%)=0.8–4.1.

Gel setting occurs upon cooling. Agar gels are typical dissolution gels because

gelation is started by the effect of cooling a solution of agar.

Agar is a most potent gelling agent, as gelation is perceptible even at 0.04%.

The setting and stability of the gel are affected by the agar concentration and its

Table 11.1 Grades specified by Japanese agricultural standard for powdered agar.

Superior 1st 2nd 3rd

Gel strength (g/cm3) ≥600 ≥350 ≥250 ≥150

Insoluble in hot water (%) <0.5 <2 <3 <4

Crude protein (%) <0.5 <1.5 <2 <3

Crude ash (%) <4 <4 <4 <4

Moisture (%) <22 <22 <22 <22

Source: Matsuhashi (1990a,b). Reproduced with permission from Elsevier.

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426 Confectionery and chocolate engineering: principles and applications

average molecular weight. A 1.5% solution sets to a gel at 32–39 ∘C, but does

not melt (transition from the gel state to the sol state) below 60–97 ∘C. The great

difference between the gelling and melting temperatures, due to hysteresis, is a

distinct and unique feature of agar.

11.2.4 Gel propertiesAgar can be regarded as a prototype and model for all gelling systems (Rees,

1969). Typically, a 1% concentration in water is good enough to make a rigid

gel suitable for most applications. Upon cooling to about 30–40 ∘C, the sol sets

to a firm gel that must be heated to about 85–95 ∘C before it will melt, that is,

soften. Thus, the hysteresis of the thermally reversible changes between the gel

and sol phases of agar is significant (Indovina et al., 1979), because the sol can

set at room temperature, and the resultant gel is stable even during the hottest

summer season.

For the preparation of a gel, it is essential to boil the agar at natural pH in order

to make a true gel; merely mixing the agar with water will make only a false gel.

11.2.4.1 Dynamic properties of agar gelsThe concept of gel strength varies between countries. Matsuhashi (1990a,b, p. 23)

recommended and briefly described the methods of determination of gel strength

used by Marine Colloids and by Meer Corporation. The gel strength (as used by

Marine Colloids) in the case of agarose is defined as that force, expressed in grams

per square centimetre, which must be applied to a 1% agarose gel to cause it to

fracture.

Apparent gel strength means a value at a non-defined concentration (Mat-

suhashi, 1970). Matsuhashi found a linear relationship between the apparent gel

strength Y and the concentration of the gel X over a wide range of concentration

for a number of agars:

Y = aX − b (11.2)

where a and b are constants. The value of X≥ b/a should theoretically correspond

to the minimum concentration (%) of agar that forms a gel (Y≥ 0).

The concept of gel strength was established by Tanii (1957), who measured the

rigidity coefficient T/𝜃 and the breaking (or cracking) load TC of agar gels using an

improved torsion dynamometer (by Sheppard), where T is the twisting moment

(in grams), 𝜃 is the angle of twist in degrees and TC is the breaking load (in grams)

that causes a crack of about 2 mm in a moulded gel.

By using numerical relationships between the physical properties and the con-

centration of a gel, the properties of any sampled gel can be expressed relative to

those of standard agar as follows:

Cr, related to the rigidity coefficient

Cc, related to the cracking load

Cr.s, related to the rigidity coefficient of a 1% gel

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Gelling, emulsifying, stabilizing and foam formation 427

The gel strength (or the gel properties in general) of agar is most stable at

about or a little above pH 7.0. Therefore, if any kind of acidic substance needs to

be added to a gel preparation, it should be added after the agar is dissolved and

at a temperature lower than the boiling point of water.

11.2.5 Setting point of sol and melting point of gelThe setting point (or gelling point) of a sol is the temperature of gelation

(=setting). The melting point is the temperature at which the gel→ sol change

takes place. It should be emphasized that melting of a gel is not the same as the melting of

a crystalline substance, although both types of melting are a solid→ liquid change.

For methods of measuring the melting point, see Matsuhashi (1990a,b, p. 28).

There is a relationship between gel strength and melting point. In general, as

the gel strength increases, the melting point also increases. However, there are

exceptions to the general rule, for example, Ceramium agars. At low concentra-

tions, the melting point of most agar gels is dependent on concentration; at high

concentrations, the melting point becomes independent of concentration. The

actual melting point of agar depends on the type and the seaweed source.

11.2.5.1 Mechanism of gelationIt is the agarose component of agar that is responsible for gelation. At elevated

temperatures, agarose exists as a disordered random coil, but on cooling it forms

strong gels at a low polymer concentration. The gelation process involves the

adoption of an ordered double-helix state (Ablett et al., 1978; Morris and Norton,

1983).

11.2.6 Syneresis of an agar gelAn agar gel in a closed vessel will eliminate a certain amount of water at its sur-

face as time passes. This phenomenon is called syneresis and results in volumetric

shrinkage of the gel. The basic factors that influence the syneresis of agar gels are:

Concentration of agar in gel. The amount of synerized water Δw(t) after a time

t is approximately inversely proportional (∼) to the square root of the agar

concentration X for most practical concentrations (Tanii, 1959):

Δw(t) ∼ 1√X

. (11.3)

Holding time of gel. At 30 ∘C, syneresis almost reaches an equilibrium state in 72 h;

144 h is recognized as the time to reach practical equilibrium. See Eqn (5.17):

m(t) = m∞ + (m0 − m∞) exp(−kt) (11.4)

where k is the rate constant of syneresis and m(t), m∞ and m0 are the weight

of gel at time t, after very long storage and at the beginning of storage, respec-

tively. The amount of synerized water is Δw(t)=m0 −m(t).

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428 Confectionery and chocolate engineering: principles and applications

Apparent gel strength. The higher the apparent gel strength, the lower the

syneresis:

Δw(t) ∼ 1y

. (11.5)

This relation is a consequence of the relation expressed by Eqn (11.2).

Rigidity coefficient. For a variety of agars, the amount of synerized water is propor-

tional to the rigidity coefficient Cr.s:

Δw(t) ∼ Cr.s. (11.6)

Pressurization. For most agar gels, the application of pressure increases syneresis;

however, exceptions have been reported as well:

Δw(t) ∼ Δp. (11.7)

Total sulphate content. The amount of synerized water is generally inversely pro-

portional to the total sulphate content:

Δw(t) ∼ 1(SO4)

. (11.8)

11.2.7 Technology of manufacturing agar gelsThe effect of added sucrose on the rheological properties of 1% agar gel was

investigated by Nakahama (1966) and Isozaki et al. (1976) using sugar solutions

in the range 0–75% and a concentration of agar of exactly 1%.

Agar is widely used, for example, in preparing nutritive media in microbiology.

Its application in the food industry is based on its main properties: it is essentially

indigestible, forms heat-resistant gels and has emulsifying and stabilizing activity.

Agar is added as a stabilizer to sherbets (frozen desserts of fruit juice, sugar,

water or milk) and ice creams (at about 0.1%), often in combination with gum

tragacanth or locust (carob) bean gum or gelatin. Agar has a role in vegetarian

diets (meat substitute products), desserts and pretreated instant cereal products.

An amount of 0.1–1% stabilizes yogurt, some cheeses, candies and bakery prod-

ucts (pastry fillings). Agar (or pectin) dissolved in water is added to the fondant

filling of pralines to hinder the separation of a thin aqueous sugar solution from

the fondant mass under gravity; otherwise, the separated thin solution easily

finds slits in the chocolate coating.

The manufacture starts with soaking of the agar, and then the agar is dissolved

in boiling water together with sugar. The solution is cooked to a boiling point of

about 106 ∘C, and then starch syrup (and possibly invert syrup) is added to this

solution, which is boiled to 106 ∘C again. After cooling to about 60 ∘C, flavouring

and colouring agents are added, and finally the resulting sol is cast in starch or

Teflon moulds and allowed to gel at room temperature overnight (Fig. 11.1). The

dry content of the cast gel is about 75%.

Agar is one of the most favoured gelling agents (besides pectin and gelatin)

by the confectionery industry for manufacturing jellies and jelly centres. The

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Gelling, emulsifying, stabilizing and foam formation 429

Agar

Water Water

Soaking Dissolution

Sugar

Evaporation,106 °C Mixing

Coolingto about60 °C

DosingColouring,flavouring

Starchsyrup

Figure 11.1 Schematic layout of agar jelly production.

jellies are covered either by couverture chocolate or sugar crystals in perforated

dragée kettle in a wetting process (This is called ‘panning’). The jelly centres are

semi-product for dragée production (All kinds of jellies are confectioned mostly

in these two methods).

11.3 Alginates

11.3.1 Isolation and structure of alginates11.3.1.1 IsolationAlginates occur in all brown algae (Phaeophyceae) as a skeletal component of

their cell walls. The major source of industrial production is the giant kelp, Macro-

cystis pyrifera. Some species of Laminaria, Ascophyllum and Sargassum are also used.

Algae are extracted with alkali. The polysaccharide is usually precipitated from

the extract with acid or calcium salts.

11.3.1.2 StructureThe building blocks of alginate are β-D-mannuronic and α-L-guluronic acid,

joined by 1→4 linkages. The ratio of the two sugars (mannuronic/guluronic

acids) is generally 1.5, with some deviations depending on the source. Alginates

extracted from Laminaria hyperborea have ratios of 0.4–1.0. Partial hydrolysis of

alginate yields chain fragments that consist predominantly of either mannuronic

or guluronic acid and also fragments where the two uronic acid residues alter-

nate in a 1 : 1 ratio. Owing to the differing monomer (mannuronic or guluronic

acid) ratios, alginates are commonly referred to as being either high-M or high-G

alginates.

The molecular weights M of alginates are in the range 32–200 kDa. This cor-

responds to a degree of polymerization n= 180–930. The pK values (the nega-

tive logarithm of the dissociation constant) of the carboxyl groups are 3.4–4.4.

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430 Confectionery and chocolate engineering: principles and applications

Alginates are water soluble in the form of alkali, magnesium, ammonium and

amine salts.

The viscosity of alginate solutions is influenced by the molecular weight and the

counter-ion of the salt. In the absence of divalent and trivalent cations or in the

presence of a chelating agent, the viscosity is low (long flow property). However,

with a rise in the levels of multivalent cations (e.g. calcium), there is a parallel

rise in viscosity (short flow). Thus, the viscosity can be adjusted as desired. As a

general rule of thumb, doubling the alginate concentration increases the viscosity of the

solution by a factor of 10.

Freezing and thawing of a sodium alginate solution containing Ca2+ ions can

result in a further rise in viscosity. A 1% solution, depending on the type of

alginate, can have a viscosity range of 20–20 000 cPa s. The viscosity is unaffected

in a pH range of 4.5–10. It rises at a pH below 4.5, reaching a maximum at pH

3–3.5.

Gels, fibres or films are formed by adding Ca2+ or acids to sodium alginate

solutions. A slow reaction is needed for uniform gel formation. This is achieved

by use of a mixture of sodium alginate, calcium phosphate and glucono-𝛿-lactone

or a mixture of sodium alginate and calcium sulphate.

Propylene glycol alginate is a derivative of economic importance. This ester

is obtained by the reaction of propylene oxide with partially neutralized alginic

acid. It is soluble down to pH 2 and, in the presence of Ca2+ ions, forms soft,

elastic, less brittle and syneresis-free gels.

11.3.2 Mechanism of gelationBy far the most important gels, particularly in food applications, are the gels

formed with calcium ions. It is considered that calcium alginate gels are formed

by simple ionic bringing of two carboxyl groups on adjacent polymer chains by

calcium ions.

The gel-forming ability is related mainly to the content of guluronic acid: two

contiguous, diaxially linked G (guluronic) residues form a cavity that acts as a

binding site for calcium ions. Long sequences of such sites form cross-links with

similar sequences in other alginate molecules, giving rise to junctions in the gel

network. This is often referred to as the egg-box model of alginate gelation. The

proportion of G blocks is the main structural feature relevant to gel formation.

11.3.3 Preparation of a gelAlginates are capable of producing gels of differing strengths and textures suitable

for a wide range of applications, but correct formulation requires the consider-

ation of the fact that high-G alginates form strong, brittle gels with a tendency

to synerize, whereas high-M alginates form weaker, more elastic gels that are less

prone to syneresis.

The term calcium conversion refers to the ratio of calcium ions to sodium in an

alginate. A molar ratio of 0.5 (where, theoretically, there is sufficient calcium to

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Gelling, emulsifying, stabilizing and foam formation 431

totally replace the sodium) is expressed as a calcium conversion of 100%. For

further details of gelation and syneresis, see Sime (1990, pp. 65–66).

Alginate gels can be prepared by either diffusion or internal setting.

Diffusion setting is the simplest technique and, as the name implies, the gel is set

by allowing calcium ions to diffuse into an alginate solution. Since the diffusion

process is slow, it can only be utilized effectively to produce thin strips or small

spheres or to provide a thin gelled coating on the surface of a food product. The

most common source of calcium ions for diffusion is calcium chloride. Diffusion

setting is ideally suited to the preparation of fruits with an outer skin and a liquid

centre such as blackcurrants and blueberries. An alginate solution and a fruit

purée mix are used, but they are kept separate and fed through nozzles consisting

of two coaxial tubes. This process is sometimes referred to as co-extrusion.

In internal or bulk setting, which is normally carried out at room temperature,

the calcium is released under controlled conditions from within the system. Cal-

cium sulphate, calcium carbonate and calcium hydrogen orthophosphate are the

most common sources of calcium. The rate at which the calcium is made avail-

able to the alginate molecules depends primarily on pH and the amount, particle

size and solubility characteristics of the calcium salt. A small particle size and low

pH favour rapid release of calcium.

Sequestrants which form chelate complexes are used in alginate solutions

either to prevent the alginate from reacting with polyvalent ions (and other con-

taminants) in the solution or to sequester the calcium inherent in the alginate.

The viscosity of an alginate solution is dependent on the molecular weight and

the level of residual calcium. Sequestrants can be used to establish how much of

the viscosity is due to the presence of this residual calcium.

In almost all situations in internal setting, the calcium release during mixing

of the ingredients is so rapid that a calcium sequestrant is required to control

the reaction by competing with the alginate for the calcium ions. Typical food-

approved sequestrants are sodium hexametaphosphate, tetrasodium pyrophos-

phate and sodium citrate. Disodium hydrogen orthophosphate, although it has

little affinity for calcium at pH values below 5, is sometimes used to remove

calcium ions (as insoluble calcium phosphate) from tap water. Removal of the

calcium permits more efficient hydration and solubilization of the alginate.

11.3.4 Fields of applicationAlginate is a powerful thickening, stabilizing and gel-forming agent. At a level of

0.25–0.5%, it improves and stabilizes the consistency of fillings for baked prod-

ucts (e.g. cakes and pies) and of salad dressings and prevents formation of larger

ice crystals in ice creams during storage. Furthermore, alginates are used in a

variety of gel products (e.g. cold instant puddings, fruit gels, dessert gels and

chocolate milks).

Shear-reversible alginate gels are ideal for the production of layered desserts.

The gel can be prepared aseptically in bulk and then pumped into individual

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432 Confectionery and chocolate engineering: principles and applications

containers. As the gel is deposited cold and regains a large proportion of its gel

strength almost immediately after the shearing action is removed, other layers

can be deposited on top without delay.

For further details, see Sime (1990, pp. 53–78).

11.4 Carrageenans

11.4.1 Isolation and structure of carrageenans11.4.1.1 IsolationRed seaweeds (Rhodophyceae) produce two types of galactans: agar and agar-

like polysaccharides, composed of D-galactose and 3.6-anhydro-L-galactose

residues, and carrageenan and related polysaccharides, composed of D-galactose

and 3.6-anhydro-D-galactose, which are partially sulphated in the form of 2-, 4-

and 6-sulphates and 2.6-disulphates. Galactose residues are linked alternately

by 1→3 and 1→4 linkages.

Carrageenans are isolated from Chondrus (Chondrus crispus, Irish moss),

Eucheuma, Gigartina, Gloiopeltis and Iridaea species by hot-water extraction under

mild alkaline conditions, followed by drying or isolated precipitation.

11.4.1.2 StructureCarrageenans are a complex mixture of various polysaccharides. They can

be separated by fractional precipitation with potassium ions. The two major

fractions are 𝜅-carrageenan (the gelling and K+-insoluble fraction) and 𝜆-

carrageenan (non-gelling, K+-soluble), and there also is a smaller fraction

𝜄-carrageenan (iota):

k-Carrageenan is composed of D-galactose, 3.6-anhydro-D-galactose and ester-

bound sulphate in a molar ratio of 6 : 5 : 7. The galactose residues are

essentially fully sulphated in position 4, whereas the anhydrogalactose

residues can be sulphated in position 2 or substituted by α-D-galactose-

6-sulphate or 2.6-disulphate.

𝜆-Carrageenan is characterized by a higher sulphate content, which favours a

zigzag, ribbon-shaped conformation.

The molecular weights of the 𝜅- and 𝜆-carrageenans are 200–800 kDa. The

water solubility becomes higher as the carrageenan sulphate content becomes

higher and as the content of anhydrosugar residue becomes lower.

11.4.2 Solution propertiesCarrageenans typically form highly viscous aqueous solutions. This is due to their

linear macromolecular structure and polyelectrolytic nature. The viscosity of the

solution depends on the type of carrageenan, the molecular weight, the temper-

ature, the ions present and the carrageenan concentration.

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Gelling, emulsifying, stabilizing and foam formation 433

Carrageenan powders tend to pick up water very quickly, and the resul-

tant viscous coating of the particles can lead to clumping, which impedes

dissolution. Therefore, efficient powder dispersal is essential. To achieve this,

one should:

• Always use cold water (or milk) to disperse the carrageenan and then heat to

dissolve

• Use a high-shear mixer, which creates a vortex in the solution (without cavita-

tion, which would entrap air) and add the carrageenan slowly into the vortex

• Add a diluent such as sugar to the carrageenan, at least 3 parts sugar to 1 part

of carrageenan

• Use a solution retardant such as liquid sugar, alcohol or glycerine as an initial

dispersant since carrageenan will not dissolve in them

All carrageenans are soluble in hot water (>75 ∘C). Solutions of up to 10%

of commercial carrageenan can normally be handled by conventional mixing

equipment. The sodium salts of 𝜅 and 𝜄 are soluble in cold water, while salts

of other cations such as Ca2+ and K+ do not dissolve completely but exhibit a

varying degree of swelling. 𝜆 is fully soluble in cold water.

11.4.2.1 Viscosity of carrageenan solutionsCommercial carrageenans are generally available in viscosities ranging from

about 5 to 800 mPa s when measured at 75 ∘C and 1.5% concentration. Car-

rageenans with viscosities less than 100 mPa s have flow properties very close

to Newtonian. The degree of deviation from Newtonian flow increases with

concentration and molecular weight of the carrageenan. The solutions exhibit

pseudoplastic (shear-thinning) flow properties and are sufficiently shear depen-

dent that it is necessary to specify the shear rate used for making a viscosity

measurement.

The pseudoplastic behaviour of carrageenans corresponds to a power-law

(Ostwald–de Waele) equation (Guiseley et al., 1980):

𝜏

D= 𝜂 = kDn−1 (11.9)

where 𝜏 (Pa) is the shear stress, D (s−1) is the shear rate, 𝜂 is the apparent viscosity,

n≤ 1 is the flow behaviour index and k (Pa sn) is a constant. For a wide range of

shear rates (two or more decades), a better fit to the experimental data can be

achieved by adding a quadratic term:

log 𝜂 = log(𝜏

D

)= log a + (n − 1) log D + b(log D)2 (11.10)

where a> 0 and b≤ 0 are constants.

The viscosity increases nearly exponentially with concentration. This behaviour is typ-

ical of linear polymers carrying charged groups and is a consequence of the

increase with concentration of the interaction between polymer chains.

Salts lower the viscosity of carrageenan solutions by reducing electrostatic

repulsion among the sulphate groups. This behaviour, likewise, is normal for

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434 Confectionery and chocolate engineering: principles and applications

ionic macromolecules. At high enough salt concentrations, however, 𝜅- and

𝜄-carrageenan solutions may gel, with an increase in apparent viscosity.

The viscosity decreases with temperature and the change is exponential. The change is

reversible provided that heating is done at or near the stability optimum at ca.

pH 9 and is not prolonged to the point where significant thermal degradation

occurs. On cooling, however, the gelling types of carrageenan show an abrupt

increase in apparent viscosity when the gelling point is reached, provided that

the counter-ions (notably K+ and Ca2+) that promote gelation are present.

The viscosity increases with molecular weight in accordance with the Mark–

Houwink equation:

[𝜂] = KM𝛼 (11.11)

where [𝜂]= lim(c→0) (𝜂sp/c)= lim(c→0) (ln 𝜂r/c) is the intrinsic viscosity, M is

the average molecular weight (since carrageenans are polydisperse) and K and 𝛼

are constants.

11.4.3 Depolymerization of carrageenanLoss of molecular weight may occur through depolymerization of car-

rageenan. Carrageenans are particularly susceptible to depolymerization

through acid-catalysed hydrolysis. This is related to the 3.6-anhydride content.

Cleavage occurs preferentially at the 1.3 glycosidic linkages and is promoted by

the strained ring system of the anhydride. Sulphation of the 1.4-linked units

at C-2 appears to mitigate attack by acid, degradation rates for 𝜄-carrageenan

being roughly one-half those for 𝜅-carrageenan under similar conditions.

Carrageenans in the gel state are more stable to acid than those in the sol state.

The rate of acid-catalysed depolymerization is proportional to the hydrogen

ion activity. Carrageenans are relatively resistant to alkaline degradation, though

this does occur through peeling reactions at high pH. As a consequence, car-

rageenans have maximum stability slightly on the alkaline side, at about pH 9.

11.4.4 Gel formation and hysteresisThe gelling-type (𝜅- and 𝜄-) carrageenans and furcellaran require heat to bring

them into solution. On cooling, the hot solutions set to gels. The anionic car-

rageenans require specific counter-ions, notably potassium and calcium, to be

present for gelation to occur.

According to Rees (1972), the molecular chains of carrageenans in aqueous

jellies associate into double helices. Evidence for double-helix formation has been

found from X-ray diffraction patterns of fibres of 𝜄-carrageenan (Arnott et al.,

1974; Bryce et al., 1974, 1982).

In the case of 𝜄- and 𝜅-carrageenan, only when potassium or other gel-

promoting cations are present can the domains aggregate into a three-

dimensional network. The radius of the hydrated cation appears to be a factor;

bulky cations, such as tetramethylammonium, do not induce gelation.

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Gelling, emulsifying, stabilizing and foam formation 435

The sol–gel transition temperatures of carrageenans typically exhibit hystere-

sis, the melting temperature being higher than the gelling temperature. This

is a function of charge density. Hysteresis is most pronounced for furcellaran

and 𝜅-carrageenan (15–27 ∘C) and least (2–5 ∘C) for 𝜄-carrageenan, which has

the highest half-ester sulphate content of the gelling carrageenans. For further

details, see Rees et al. (1969).

11.4.5 Setting temperature and syneresisThe setting temperatures of carrageenans depend primarily on the concentration

of gelling cations present and are relatively insensitive to the carrageenan con-

centration. Although both K+ and Ca2+ can cause both 𝜅- and 𝜄-carrageenan to

gel, the K+ concentration is the factor controlling the sol–gel transition for 𝜅,

whereas the Ca2+ concentration controls the transition for 𝜄.

The transition temperature data are well fitted by functions of the form

Tg = a + b√

c (11.12)

where a and b are constants, Tg is the gelling temperature and c is the concen-

tration of gelling cation. This linear dependence on the square root of the ion

concentration indicates that Coulombic effects, rather than salting-out effects,

control the sol→ gel transition. The melting temperatures are similarly related to

the cation concentration.

𝜅-Carrageenan and furcellaran gels are relatively rigid and subject to syneresis

in the presence of calcium ions. If potassium is the sole counter-ion, the gels

are compliant, resembling those of 𝜄-carrageenan. 𝜄-Carrageenan by itself yields

compliant gels with very little tendency to undergo syneresis.

11.4.6 Specific interactionsElectrostatic interactions can occur between the negatively charged carrageenans

and positively charged sites on proteins. The commercially important interaction

of carrageenans with milk proteins is an example of this.

It has been established that at least one aspect of the milk reactivity of car-

rageenans is a gelation phenomenon involving a highly specific interaction

between carrageenan and 𝜅-casein. In order for it to manifest itself, two events

must occur:

1 Carrageenan and 𝜅-casein interact to form a complex.

2 The resulting complex aggregates into a three-dimensional gel network.

Gelation is overtly manifested in such applications as blancmange-type pud-

dings, whereas the suspension of cocoa in seemingly fluid chocolate milk occurs

only below a well-defined sol–gel transition temperature (Payens, 1972).

Although carrageenans may interact with other casein fractions (𝛼s1 and 𝛽) in

milk, the binding is much weaker than that with 𝜅-casein and does not result

in gel formation. The presence of the other fractions, such as occurs in whole

casein, in fact decreases the sharpness of the sol→ gel transition.

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436 Confectionery and chocolate engineering: principles and applications

Specific interactions with 𝜅-casein can occur at pH levels above the isoelec-

tric point (IEP) of the protein. (Non-specific interactions can, of course, occur

below this point.) The former type of interaction is a most convenient one from

a commercial standpoint as it permits the carrageenan to be functional with-

out disturbing the integrity of the casein micelles and of the milk as a whole.

This interaction has been ascribed to electrostatic attraction between the nega-

tively charged sulphate groups of the carrageenan and a predominantly positively

charged region in the peptide chain of 𝜅-casein (Snoeren et al., 1975).

Although this association of 𝜅-casein with carrageenan occurs for all car-

rageenan types, it is primarily the gel-forming types (𝜅- and 𝜄-carrageenan) that

exhibit a sol–gel transition with temperature. This is in accord with the practical

observation that 𝜅- and 𝜄-carrageenan are effective for the suspension of cocoa in

chocolate milk, whereas 𝜆-carrageenan is ineffective. This observation confirms

that gelation is required and suggests that the formation of the gel network may

be a function solely of the carrageenan component of the carrageenan–casein

complex. Moreover, suspension of cocoa does not occur if the carrageenan has

a low molecular weight.

For further details, see Stanley (1990, pp. 96–104).

11.4.7 UtilizationThe utilization of carrageenan in food processing, principally in dairy products,

is based on the ability of the polymer to gel, to increase the viscosity of solutions

and to stabilize emulsions and various dispersions.

A level as low as ca. 0.03% in chocolate milk prevents fat droplet separation

and stabilizes the suspension of cocoa particles. Chocolate milk typically contains

1% cocoa, 6% sugar and from 0.025% to 0.035% carrageenan. Vanillin is added

as a flavour modifier. Most commonly, these ingredients are sold to the dairy as a

blended dairy powder to be incorporated into the milk during pasteurization. On

cooling, the interaction between 𝜅-casein and carrageenan produces the delicate

gel structure necessary to keep the cocoa suspended and to give the drink a rich

mouthfeel. 𝜅-Carrageenan is used when the drink is pasteurized; 𝜄 and 𝜆 are

also functional, though less economical. Chocolate syrups are used instead of

powders by some dairies, as well as by consumers. Here the syrup is dispersed

into cold milk at a ratio of about 1 part syrup to 10–12 parts milk. As in other

cold-processed applications, 𝜆-carrageenan is used.

Cooked puddings and pie fillings have traditionally been starch based. How-

ever, 𝜅-carrageenan can be used to provide a more uniform set. For further

details, see Guiseley et al. (1980).

Carrageenans are also used to stabilize ice cream and to clarify beverages. Ice

cream and sherbet have been defined as partly frozen foams, containing a gas

(air) dispersed as small cells in a partially frozen continuous aqueous phase.

Stanley (1990) has given a detailed survey of the applications of carrageenan

in the food industry.

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11.5 Furcellaran

Furcellaran (Danish agar) is produced from red seaweed (algae Furcellaria fasti-

giata). Production began in 1943 when Europe was cut off from its agar suppliers.

After alkali pretreatment of the algae, the polysaccharide is isolated using hot

water. The extract is then concentrated under vacuum and seeded with 1–1.5%

KCl solution. The separated gel threads are concentrated further by freezing, the

excess water is removed by centrifugation or pressing, and, lastly, the polysac-

charide is dried. The product is a potassium salt and contains, in addition, 8–15%

occluded KCl.

Furcellaran is composed of D-galactose (46–53%), 3.6-anhydro-D-galactose

(30–33%) and sulphated portions of both of these sugars (16–20%). The struc-

ture of furcellaran is similar to that of 𝜅-carrageenan. The essential difference is

that 𝜅-carrageenan has one sulphate ester residue per two sugar residues, while

furcellaran has one sulphate ester residue per three to four sugar residues. The

sugar sulphates identified are D-galactose-2-sulphate, D-galactose-4-sulphate

and D-galactose-6-sulphate and 3.6-anhydro-D-galactose-2-sulphate. Branching

of the polysaccharide chain cannot be excluded. Furcellaran forms thermally

reversible aqueous gels by a mechanism involving double-helix formation,

similarly to 𝜅-carrageenan.

The gelling ability is affected by the polysaccharide polymerization degree, the

amount of 3.6-anhydro-D-galactose and the radius of the cations present. K+ and

NH4+ form very stable, strong gels. Ca2+ has a lesser effect, while Na+ prevents

gel setting. Addition of sugar affects the gel texture, which goes from a brittle to

a more elastic texture.

Furcelleran provides good gels with milk and therefore is used as an addi-

tive in puddings. It is also suitable for cake fillings and icings. In the presence of

sucrose, it gels rapidly and retains good stability, even against food-grade acids.

Furcellaran has an advantage over pectin in marmalades since it allows stable

gel setting at sugar concentrations even below 50–60%. The required amount

of polysaccharide is 0.2–0.5%, depending on the marmalade’s sugar content and

the desired gel strength. To keep the extent of hydrolysis low, a cold aqueous

2–3% solution of furcellaran is mixed into a hot cooked slurry of fruit and sugar.

11.6 Gum arabic

Gum arabic is a tree exudate of various Acacia species, primarily Acacia senegal,

and is obtained as a result of tree bark injury. It is collected as air-dried droplets

with diameters from 2 to 7 cm. The annual yield per tree averages 0.9–2.0 kg.

The major producer is Sudan, which produces 50 000–60 000 t/annum, followed

by several other African countries. Gum arabic has been known since the time

of ancient Egypt as kami, an adhesive for pigmented paints.

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438 Confectionery and chocolate engineering: principles and applications

Gum arabic is a mixture of closely related polysaccharides, with an average

molecular weight range of 260–1160 kDa. The main structural units in the exu-

date of A. senegal are L-arabinose, L-rhamnose, D-galactose and D-glucuronic acid.

The proportions vary significantly with Acacia species. Gum arabic has a major

core chain built from β-D-galactopyranosyl residues linked by 1→3 bonds, in

part carrying side chains attached at position 6.

Gum arabic occurs as a neutral or weakly acidic salt. The counter-ions are

Ca2+, Mg2+ and K+. Gum arabic is very soluble in water, and solutions of up

to 50% gum can be prepared. The viscosity of the solution starts to rise steeply

only at high concentrations (above 30 m/m%). This property is unlike that of

many other polysaccharides, which provide highly viscous solutions even at low

concentrations (about 4–5 m/m%).

Gum arabic is used as an emulsifier and stabilizer, for example, in baked prod-

ucts. It retards sugar crystallization and fat separation in confectionery products

and the formation of large ice crystals in ice creams and can be used as a foam

stabilizer in beverages.

Gum arabic is also applied as a flavour fixative in the production of encap-

sulated, powdered aroma concentrates. For example, essential oils may be

emulsified with gum arabic solution and then spray dried. In this process, the

polysaccharide forms a film surrounding the oil droplets, which then protects

the oil against oxidation and other changes.

11.7 Gum tragacanth

Gum tragacanth is a tasteless and odourless plant exudate collected from Astra-

galus species shrubs grown in the Middle East (Iran, Syria and Turkey).

Gum tragacanth consists of a water-soluble fraction, the so-called tragacanthic

acid, and an insoluble swelling component, bassorin. The soluble fraction is

a complex mixture of various acidic polysaccharides. Their basic units are

D-galacturonic acid, D-galactose, L-fucose, D-xylose and L-arabinose. Most of the

carboxyl groups in the insoluble fraction are esterified with methano1; their

hydrolysis yields tragacanthic acid. Its molecular weight is about 840 kDa. The

molecules are highly elongated (450×1.9 nm) in aqueous solution and are

responsible for the high viscosity of the solution. The viscosity decreases strongly

with increasing shear rate.

Gum tragacanth is used as a thickening agent and a stabilizer in salad dressings

(0.4–1.2%) and in fillings and icings in baked goods. As an additive in ice creams

(0.5%), it provides a soft texture.

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11.8 Guaran gum

Guar flour is obtained from the seed endosperm of the leguminous plant Cyamop-

sis tetragonoloba. The seed is decoated and the germ removed. In addition to the

polysaccharide guaran, guar flour contains 10–15% moisture, 5–6% protein,

2.5% crude fibre and 0.5–0.8% ash. The plant is cultivated for forage in India,

Pakistan and the United States (Texas).

Guaran gum consists of a chain of β-D-mannopyranosyl units joined by 1→4

linkages. Every second residue has a side chain, a D-galactopyranosyl residue that

is bound to the main chain by an 𝛼(1→6) linkage. Guaran gum forms highly vis-

cous solutions, the viscosity of which decreases sharply as the shear rate becomes

higher than 8–10 rpm.

Guaran gum is used as a thickening agent and a stabilizer in salad dressings

and ice creams (application level 0.3%). (In addition to the food industry, it is

widely used in the paper, cosmetic and pharmaceutical industries.)

11.9 Locust bean gum

The locust bean (also known as carob bean or St John’s bread) is from an ever-

green cultivated in the Mediterranean area since ancient times. Its long, edible,

fleshy seed pods are also used as fodder. The dried seeds were called carat by

the Arabs and served as a unit of weight (approximately 200 mg). Even today,

the carat is used as a unit of weight for precious stones, diamonds and pearls

and as a measure of the purity of gold (1 carat=1/24 part of pure gold). The

locust bean seeds consist of 30–33% hull material, 23–25% germ and 42–46%

endosperm. The seeds are milled and the endosperm is separated and utilized for

similar purposes like the guar flour. The commercial flour contains 88% galac-

tomannoglucan, 5% other polysaccharides, 6% protein and 1% ash.

The main locust bean polysaccharide is similar to that of guaran gum: a lin-

ear chain of 1→4-linked β-D-mannopyranosyl units, with α-D-galactopyranosyl

residues joined 1→ 6 as side chains. The ratio of mannose to galactose is 3 : 6; this

indicates that, instead of every second mannose residue, as in guaran gum, only

every fourth to fifth is substituted at the C-6 position with a galactose molecule.

The molecular weight of this galactomannan is close to 310 kDa. The physi-

cal properties correspond to those of guar gum, except that the viscosity of the

solution is not as high (it is similar to that of tragacanth).

Locust bean flour is used as a thickener, binder and stabilizer in meat can-

ning, salad dressings, sausages, soft cheeses and ice creams. It also improves the

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440 Confectionery and chocolate engineering: principles and applications

water-binding capacity of dough, especially when flour of low gluten content

is used.

11.10 Pectin

11.10.1 Isolation and composition of pectinPectin is widely distributed in plants. It is produced commercially from the peel of

citrus fruits and from apple pomace (crushed and pressed residue). It is 20–40%

of the dry matter content in citrus fruit peel and 10–20% in apple pomace.

Extraction is achieved at pH 1.5–3 and 60–100 ∘C. The process is carefully con-

trolled to avoid hydrolysis of glycosidic and ester linkages. The extract is con-centrated to a liquid pectin product or is dried by spray or drum drying to a

powdered product. Purified preparations are obtained by precipitation of pectin

with ions that form insoluble pectin salts (e.g. Al3+), followed by washing with

acidified alcohol to remove the added ions, or by alcoholic precipitation using

isopropanol and ethanol.

Pectin is a chain-like polymer consisting of α-D-galacturonic structural units

joined by 1→ 4 linkages. The main chain, however, is one-tenth rhamnose

residues. In segments in which rhamnose is enriched, rhamnose units may

be in adjacent or alternate positions. Pectin also contains small amounts of

D-galactan and arabinan in its extended side chains and, to a lesser extent,

fucose and xylose sugars in its short side chains (1–3 unit chains). These short

side chains are not regarded as typical pectin constituents. The carboxyl groups

of galacturonic acid along the main chain are esterified to a variable extent with

methanol, while the OH groups in the 2- and 3-positions may be acetylated to a

small extent. The stability of pectin is highest at pH 3–4. For further details, see

Rolin and De Vries (1990).

At a pH of about 3, and also at higher pH in the presence of Ca2+ ions, pectin

forms a thermally reversible gel. The gel-forming ability, under comparable con-

ditions, is directly proportional to the molecular weight and inversely propor-

tional to the degree of esterification (DE) (see following text). For gel formation:

• Low-ester pectins require very low pH values and/or calcium ions, but they

set to a gel in the presence of a relatively low sugar content.

• High-ester pectins require an increasing amount of sugar with increasing DE.

• The gel-setting time for high-ester pectins is longer than that for pectin prod-

ucts of low DE.

Commercial pectins are divided into high-ester pectins and low-ester pectins

according to the DE, which is the percentage of galacturonic acid subunits that

are methyl esterified.

11.10.2 High-Methoxyl (HM) pectinsHigh-ester pectins (DE> 50%), also known as high-methoxyl (HM) pectins,intended for gel-making are further subdivided into:

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• Rapid set, DE 70–75%

• Medium-rapid set, DE 65–69%

• Slow set, DE 60–64%

The DE correlates with the setting rate and texture of the gel under other-

wise similar conditions, which means that very HM pectins jellify quicker (e.g.

or at higher temperatures) than less HM pectins. Therefore, slow-set pectin is a

commonly used raw material for confectionery manufacture because flavouring,

colouring and dosing need a certain time before setting.

Citrus pectins with the same DE have a slightly higher setting temperature and

are somewhat more elastic than apple pectins.

11.10.2.1 Gel strength standardizationAlmost all high-ester pectins are standardized to USA-SAG grade 150. This des-

ignation means that 1 part of the pectin is able to turn 150 parts of sucrose into a

jelly prepared under standard conditions and with standard properties as follows:

• Refractometer-soluble solids, 65%

• pH= 2.20–2.40

• Gel strength, 23.5% SAG

This method was implemented by the 1959 IFT Committee for Pectin Stan-

dardization, and a detailed procedure is available (Final Report of the IFT Com-

mittee, 1959).

11.10.3 Low-Methoxyl (LM) pectinsPectins with a proportion of methoxylated polygalacturonic acid units (DE) less

than 50%, known as low-methoxyl (LM) pectins, can jellify with Ca2+ ions. LM

pectins thus form gels not only with sugar and acids but also with less soluble

solids containing calcium ions.

The volume of pectin, type of pectin, content of dry soluble solids, pH range

and concentration of buffer salts and calcium ions contained in the environment

are decisive for the gel strength. A well-matched balance between the pectin

and calcium concentrations leads to an optimal texture. If the calcium optimum

is exceeded, on the other hand, this will produce a brittle gel with a tendency

towards syneresis or, eventually, calcium pectinate formation.

Since gel setting with LM pectins is also possible with a low soluble solids con-

tent and at a high pH value, this opens up numerous possibilities of applications

in dietetic and dairy products.

11.10.4 Low-Methoxyl (LM) amidated pectinsThe degree of amidation (DA) is the percentage of galacturonic acid subunits that

are amidated. Amidated pectins are LM pectins that have been demethoxylated

with ammonia instead of acid. During demethoxylation, some of the ester groups

are replaced by amide groups, which modifies the gelling properties in compari-

son with acid demethoxylated pectins.

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442 Confectionery and chocolate engineering: principles and applications

LM amidated pectins, just like non-amidated pectins, require Ca2+ ions for

gelling; however, they can set sufficiently well with only minor amounts present.

Furthermore, the gel-setting temperature of amidated pectins is much less influ-

enced by the calcium dosage.

11.10.5 Gelling mechanismsA combination of hydrogen bonding and hydrophobic interactions is the mech-

anism accepted to be responsible for gel formation with high-ester pectin. The

ester groups are the hydrophobic parts of the pectin molecules. An energy contri-

bution is associated with the contact between these hydrophobic areas and water;

the hydrophobic areas will tend to aggregate in order to minimize the area of the

contacting surface, in analogy to the coalescence of oil drops in water. Hydrogen

bonds that form between adjacent galacturonan chains contribute even more to

the energy decrease associated with the formation of junction zones (Oakenfull

and Scott, 1984). It has been suggested that the rigidity of the pectin molecule is

positively correlated with the DE and the concentration of sugars in the solution

and that this is also an important factor that plays a role in gel formation with

high-ester pectin (Michel et al., 1984; Plashchina et al., 1985).

The egg-box model has been widely accepted as an explanation of the gelation

of low-ester pectin in the presence of calcium ions. Pectins and pectates are con-

figured in helices with three subunits per turn. However, the junction zones are

organized so that the pectin chains are in the form of helices with only two sub-

units per turn. These twofold helix structures are joined by calcium ions bridging

two opposing carboxyl groups. The model forces us to make the assumption that

the helix structure changes from twofold to threefold when the gel is dried to a

powder.

Since pectin can set into a gel, it is widely used in marmalade and jelly pro-

duction. An example of standard conditions to form a stable gel is pectin content

<1%, sucrose 58–75% and pH 2.8–3.5. In low-sugar products, low-ester pectin

is used in the presence of Ca2+ ions. The use of pectin as a stabilizer for beverages

(to emulsify the essential-oil components) and ice creams is also of importance.

For further details, see Rolin and De Vries (1990).

11.10.6 Technology of manufacturing pectin jellies11.10.6.1 Preparation of high-ester pectin gelsThe conditions necessary for gelation are a fairly low pH and a high soluble solids

concentration. A critical temperature exists above which gelation will not take

place, even though all other conditions for gelation are fulfilled. If the tempera-

ture is reduced below this limit, gelation commences after some time. The gela-

tion temperature depends on the combination of pectin type and the composition

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Gelling, emulsifying, stabilizing and foam formation 443

of the batch; it can, to a great extent, be varied at will by selecting an appropriate

pectin type. It is not usually possible to melt a high-ester pectin gel once it has

solidified.

If a gel batch is stirred or poured while gelation is in progress (it may still

look liquid!), structures that have already formed may be broken. They will not

reform, and the corresponding part of the pectin will not be utilized in the final

gel structure. This phenomenon is known as pre-gelation. Pre-gelation is very sim-

ilar to the situation of poor dissolution or distribution of the pectin. The results

are similar: the gel is weaker than expected, and gelation may, in severe cases,

appear to be absent. The cause of failure is also basically the same in the two

cases: only part of the pectin is utilized.

Two important differences between the gelation of low-ester pectin and of

high-ester pectin must be mentioned. The difference between the setting and

melting temperatures of low-ester pectin gels is modest, and it is possible in

many cases to remelt a low-ester pectin gel. This is in contrast to the situation

for high-ester pectin gels. A low-ester pectin gel solidifies almost immediately

when the gelling conditions are reached; a high-ester pectin gel system shows a

time lag.

The pectin jellies used in confectionery are produced from HM slow-set pectins

with a typical DE of 60–64%. These pectins are produced mostly from apple

or citrus. Since pectin gels are so-called chemo-gels, that is, gelation is induced

by a decrease in pH, an aqueous sugar solution containing pectin is boiled to

about 106 ∘C in a slightly alkaline medium (pH= 7.5–8) containing the seques-

trant (buffer) di/trisodium citrate. After starch syrup has been added, the solution

is coloured and flavoured, and dosing can be started at about 90–95 ∘C: under the

effect of the flavouring acid (in general, a water–citric acid solution in the ratio

1 : 1), gelation starts slowly and must not end until dosing is in progress. The synchro-

nization of dosing and gelation demands the use of slow-set pectin.

The quality of water (i.e. the mineral composition of it) used for solving the

slow-set pectin and the other ingredients plays a key role in producing jellies

of marble broken surface which is a basic quality requirement. The quality and

amount of citrate buffer have to be fitted to the given water quality – this may

be a complicated technological task – or else the jelly consistency becomes such

that of marmalade (entirely amorphous).

Figure 11.2 shows a schematic layout for pectin jelly technology. The technol-

ogy is sensitive to the hardness of the water used; therefore, the amount and

pH of the buffer are fitted to the circumstances of manufacture. The duration of

gelation is relatively short, 2–3 h, which makes the technology very productive.

The water content of the end product is about 21–23%, which, depending on the

conditions of storage, may decrease slowly to about 15% because of the effect of

syneresis in about 6 months.

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444 Confectionery and chocolate engineering: principles and applications

Pectinpowder

Sugarpower

Water Buffer

Mixing Dissolution

Sugar

Evaporation,106 °C Mixing

Coolingto about

90–95 °C

DosingColouring,flavouring

Starchsyrup

Figure 11.2 Schematic layout of pectin jelly technology.

Pectin jellies are favoured because, perhaps, they are mostly similar to the nat-

ural fruits, which also contain pectin; moreover, their texture is such that they are

easily split, and the split jelly layers are translucent and glassy. These properties

of a splitting texture and translucency are the very quality requirements of con-

fectionery jellies.

11.10.6.2 Preparation of low-ester pectin gelsLow-ester pectin gels may be prepared by the same sequence of events as that

described previously for high-ester pectin gels, but it is not necessary to achieve

as high a solids content or as low a pH in order to induce gelling conditions. The

gelation is dependent on calcium, which is in most cases provided by the fruit

material added.

In analogy to high-ester pectin gels, the gel temperature may be varied by

appropriate selection of the combination of pectin type and the properties of

the medium. The same considerations regarding dispersion of the pectin prior

to gelation and the possibility of pre-gelation apply to low-ester pectin gels as to

high-ester pectin gels.

11.11 Starch

11.11.1 Occurrence and composition of starchStarch is widely distributed in various plant organs as a storage carbohydrate.

Starch granules are formed from two glucans, amylose and amylopectin. Most

starches contain 20–39% amylose. New corn cultivars (amylomaize) have

been developed that contain 50–80% amylose. Normal starch granules contain

70–80% amylopectin, while some corn cultivars and millet, referred to as waxy

maize or waxy millet, contain almost 100% amylopectin.

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Amylopectin, when heated in water, forms a transparent, highly viscous solu-

tion, which is ropy, sticky and coherent. Unlike the case with amylose, there is

no tendency to retrogradation. There are no staling or ageing phenomena and

no gelling, except at very high concentrations. However, there is a rapid viscosity

drop in acidic media and when the solution is autoclaved or subjected to a strong

mechanical shear force.

Starch is an important thickening and binding agent and is used extensively in

the production of puddings, soups, sauces, salad dressings, diet food preparations

for infants, pastry fillings, mayonnaise and so on. Amylose films can be used

for food packaging, as edible wrapping or tubing, as exemplified by a variety

of instant coffee and tea products. The uses of amylopectin are also diverse. It is

used to a large extent as a thickener and stabilizer and as an adhesive and binding

agent.

11.11.2 Modified starchesThe properties of starch and of amylose and amylopectin can be improved or

tailored by physical and chemical methods to fit or adjust the properties to a par-

ticular application or food product:

• Pregelatinized starch. Heating of a starch suspension above its gelatinization tem-

perature, followed by suspension drying, provides a starch product that is

soluble in cold water and that gels. These products are used in instant foods

(e.g. puddings) and as baking aids.

• Thin-boiling starch. Partial acidic hydrolysis yields a starch product that is not

very soluble in cold water but is readily soluble in boiling water. The solu-

tion has a lower viscosity than the untreated starch and remains fluid after

cooling. Retrogradation is low. These starches are utilized as thickeners and as

protective films.

• Starch ethers. When a 30–40% starch suspension is reacted with ethylene

oxide or propylene oxide in the presence of hydroxides of alkali and/or

alkaline earth metals (pH 11–13), hydroxyethyl or hydroxypropyl derivatives

are obtained. (These derivatives are also obtained in reactions with the

corresponding epichlorohydrins.) The degree of substitution can be controlled

over a wide range by adjusting the process parameters. These products are

utilized as thickeners for refrigerated foods and heat-sterilized canned foods.

Reaction of starch with monochloroacetic acid in an alkaline solution yields

carboxymethyl starch. This product swells instantly, even in cold water and in

ethanol. Dispersions of 1–3% carboxymethyl starch have an ointment-like

consistency, whereas 3–4% dispersions provide a gel-like consistency. Such

products are of interest as thickeners and gel-forming agents.

• Starch esters. Starch monophosphate esters are produced by dry heating

of starch with alkaline orthophosphate or alkaline tripolyphosphate at

120–175 ∘C. They are used as thickeners and stabilizers, among other things,

in bakery products.

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446 Confectionery and chocolate engineering: principles and applications

On the versatile use of enzyme modified starches in food production, see

Hansen (2008).

11.11.3 Utilization in the confectionery industryModified starches are used in a number of confectionery applications:

• Acid-hydrolysed starches are used in wine gums, jellies, jelly beans and

gelatin replacements. The specific properties used are hot-water solubility,

medium/low viscosity, fast setting and high gel strength.

• Oxidized starches are used in wine gums, jellies and hard gums and for pan coat-

ing and replacement of gum arabic. The specific properties used are hot-water

solubility, medium/low viscosity, slow setting, good clarity and good film for-

mation.

• Dextrinized starches are used in hard gums, pan coating, blazing and replace-

ment of gum arabic. The specific properties used are hot- and cold-water sol-

ubility, low viscosity, slow setting, good clarity and good film formation.

• Enzyme-hydrolysed starches are used in hard gums, pan coating and replace-

ment of gum arabic. The specific properties used are cold-water solubility, low

viscosity, slow set back and good clarity.

• Acetylated starches are used in jellies, hard gums and replacement of gelatin and

gum arabic. The specific properties used are hot-water solubility and stability

against retrogradation.

• Hydroxypropylated starches are used in hard gums, pan coating and replacement

of gum arabic. The specific properties used are hot-water solubility and stability

against retrogradation.

The fields of application of several types of starch, according to function, are:

• Wine gums: gelling

• Jelly pastilles: gelling

• Pan coating: adhesion and film strength

• Hard gums: texturing

• Extruded liquorice: texturing

• Marshmallows: foam strengthening

• Nuts: glazing

• Jelly beans: glazing

• Caramels: stiffness

• Wafers: binding

• Lozenges: binding

• Gums, jellies and centres: moulding

• Chewing gum: dusting

A schematic layout of a starch jelly technology is shown in Figure 11.3. Cook-

ing can be done also by an extruder.

Finally, a typical Rahat Loukoum recipe is as follows: 5 kg thin-boiling starch

is dissolved in 30 kg water, the solution is boiled for 2 min, and then 30 kg sugar,

8 kg starch syrup and 2 kg invert syrup (70%) are added. This solution is boiled

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Gelling, emulsifying, stabilizing and foam formation 447

Instantgelatin +

gum arabic

Water Starchsyrup

Liquoriceextract

Starch Dissolution

Sugar

Pre-cooking Vacuum

cookingCooling

Shaping

Figure 11.3 Schematic layout of a starch jelly technology (liquorice).

to 78–80% dry content and then flavoured with citric acid and rose oil on a

cooling table.

11.12 Xanthan gum

Xanthan gum, an extracellular polysaccharide from Xanthomonas campestris and

some related microorganisms, is produced on a nutritive medium containing glu-

cose, NH4Cl and a mixture of amino acids and minerals. The polysaccharide is

recovered from the medium by isopropanol precipitation in the presence of KCl.

Xanthan gum is a heteroglycan consisting of D-glucose, D-mannose and

D-glucuronic acid in a molar ratio of 2.8 : 2 : 2. Some sugar residues are

acetylated, while some are present as ketals, formed by pyruvate [4.6-O-(1-

carboxyethylidine)-D-glucopyranose]. The molecule consists of a backbone made

of 1.4-linked (β-glucopyranosyl) residues.

The molecular weight of xanthan gum is >106 Da. In spite of this high value,

it is quite soluble in water. The highly viscous solution exhibits a pseudoplas-

tic behaviour. The viscosity is, to a great extent, independent of temperature.

Solutions, emulsions and gels, in the presence of xanthan gums, acquire a high

freeze–thaw stability.

The practical importance of xanthan gum is based on its emulsion-stabilizing

and particle-suspending abilities (it is applied to turbidity problems and

essential-oil emulsions in beverages). Owing to its high thermal stability, it is

useful as a thickening agent in food canning. The addition of xanthan gum to

starch gels substantially improves their freeze–thaw stability.

The properties of xanthan gum can also be utilized in instant puddings: a

mixture of locust bean flour, sodium pyrophosphate and milk powder with

xanthan gum as an additive provides instant jelly after reconstitution in water.

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448 Confectionery and chocolate engineering: principles and applications

The pseudoplastic thixotropic properties, that is, a high viscosity in the absence

of a shear force and a drop in viscosity to a fluid state under a shear force, due

to intermolecular association of single-stranded xanthan gum molecules, are of

interest for the production of salad dressings.

11.13 Gelatin

11.13.1 Occurrence and composition of gelatinCollagen constitutes 20–25% of the total protein in mammals. The high

content of glycine and proline and the occurrence of 4-hydroxyproline and

5-hydroxylysine are characteristic features. Collagen also contains carbohydrates

(glucose and galactose). The collagen chain consists of three polypeptide chains,

and, in the most prevalent species (collagen type I), two chains are the same,

while the third chain differs. The three peptide chains, each of which has a

helical structure, occur together as a triple-stranded helix. Collagen swells but

does not solubilize.

One characteristic of the intact collagen fibre is that it shrinks when heated

(on cooking or roasting). The shrinkage temperature TS is different for different

species of collagen. For fish collagen, the value of TS is 45 ∘C and for mammals,

60–62 ∘C. When native or intact collagen is heated to T> TS, the triple-stranded

helix is destroyed to a great extent, depending on the cross-links. The disrupted

structure now exists as random coils, which are soluble in water and are called

gelatin.

Gelatin, one of the most versatile food substances, is the only natural protein

of commercial importance that is capable of producing clear, thermoreversible

gels in water at near to body temperature.

Composition. The drying loss (water content) is typically not more than

15 m/m% (protein, 84%; ash, 1%). The density is about 1300 kg/m3; the pH

value ranges from 4.0 to 9.0 depending on the type.

The thermoreversibility of gelatin gels, coupled with their typical elastic tex-

ture, melt-in-the-mouth characteristics and excellent flavour release, gives

gelatin-based food products their unique textural and sensory properties.

Gelatin’s unique characteristics give it wide application in the food industry,

where its functional properties are used to gel, thicken, stabilize, emulsify, bind,

form films and allow aeration. Being a protein, it is also a very useful nutritive

component.

Gelatin is extracted from selected beef or pork skin material obtained from

approved abattoirs and meatworks. This collagenous material may be subjected

to an alkaline pretreatment followed by hot-water extraction, yielding type B

gelatin, with an IEP of approximately 5.0. Gelatin obtained from pork skin mate-

rial using an acid pretreatment, yielding type A gelatin, has an IEP between 7.0

and 9.0. These two types of gelatin are entirely interchangeable in most food

product applications.

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Gelling, emulsifying, stabilizing and foam formation 449

11.13.1.1 Structure and amino acid composition of gelatinThe raw materials, type of pretreatment and gelatin extraction conditions dur-

ing manufacture all affect the molecular distribution of the gelatin polypeptides

obtained. Commercial gelatins are a heterogeneous protein mixture of polypep-

tide chains. Gelatin molecules are quite large, with a molecular weight ranging

from a few thousand up to several hundred thousand daltons. The molecular

weight distribution of gelatin has a great bearing on its physical properties and

particularly affects the values of the viscosity and gel strength.

11.13.2 SolubilityGelatin is relatively insoluble in cold water but hydrates readily in warm water.

When added to cold water, gelatin granules swell into discrete swollen parti-

cles, absorbing 5–10 times their weight in water. Raising the temperature above

40 ∘C dissolves the swollen gelatin particles, forming a solution, which gels upon

cooling to the setting point.

The extent to which gelatin granules swell in cold water is dependent on pH,

with the maximum swelling occurring at pH values away from gelatin’s IEP. The

rate of dissolution is affected by factors such as temperature, concentration and

particle size. Gelatin is insoluble in alcohol and most other organic solvents.

11.13.3 Gel formationGelatin forms thermoreversible gels that convert to a solution as the tempera-

ture is increased to 30–35 ∘C. Upon cooling of the gelatin solution to the setting

point, a gel structure is reformed, that is, gelatin gel, similarly to agar gel, is a

typical dissolution gel. This solution-to-gel conversion process is reversible and

can be repeated many times (sol→gel→sol→, etc.). Gelatin gels, therefore, pro-

duce a melt-in-the-mouth characteristic giving excellent flavour release, which is

a desirable property in a number of foods.

Gelatin has the ability, at all pH levels found in food systems, to form gels that

do not undergo syneresis. At the onset of gelation, there is a tremendous increase

in viscosity until a gel has completely formed.

11.13.3.1 Strength of gelatin gelsGelatins are graded and marked according to their Bloom strength, which is a

measurement of the gel strength determined according to international standards

and methodologies (Bloom, 1925; GME, 2004; ISO 9665). For further methods,

see Johnston-Banks (1990).

The strength of gelatin gels depends upon the concentration and the intrinsic

strength of the gelatin used; the intrinsic strength is a function of both the struc-

ture and the molecular weight. This means that for a type of gelatin specified by

its Bloom grade, the gel strength is proportional to the concentration (m/m%)

of gelatin.

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450 Confectionery and chocolate engineering: principles and applications

The gel strength is largely independent of pH over a wide range above a value

of about 5.0 but is sensitive to an acidic medium. This is important in acidic

food systems such as those found in certain confectionery products, water-based

dessert gels and cultured dairy products. Moreover, the gel strength increases

with time as the gel matures, reaching an equilibrium after approximately 18 h

of maturation.

Other factors affecting gel rigidity include temperature, thermal history and

the presence and concentration of electrolytes, non-electrolytes and other ingre-

dients. Unlike most polysaccharide gelling agents, the formation of gelatin gels

does not require the presence of other reagents such as sucrose, salts and divalent

cations and is not dependent on the pH.

11.13.4 ViscosityThe viscosity characteristics displayed by a gelatin of given Bloom grade are pri-

marily related to the molecular weight distribution of the gelatin molecules. The

viscosity of gelatin solutions increases strongly with increasing concentration and

with decreasing temperature.

In salt-free solutions, the minimum viscosity occurs at the pH of the iso-ionic

point of the gelatin. Changes in the molecular shape and charge distribution

result in changes in viscosity at different pH values.

The viscosity of gelatin plays a significant role in certain food systems.

Examples of this include applications in starch-moulded confectionery, where

the high working speeds demanded by modern processing equipment require

a gelatin with a low viscosity to prevent the formation of tails, together with

a rapid distribution in the moulds. The viscosity also affects the gel properties,

including the setting and melting points. High-viscosity gelatin gives gels with

higher melting and setting temperatures and produces a quicker setting rate

than gelatins of lower viscosity. Gelatins of higher viscosity are preferred for

stabilizing certain emulsions.

11.13.5 Amphoteric propertiesGelatin, like other proteins, displays amphoteric characteristics, having both

acidic (carboxyl) and basic (amino and guanidine) amino acid groups.

At a unique pH, gelatin has an equal number of negative and positive charges

on the molecule. In the case of salt-free solutions, the pH at which there is no

net charge on the molecule is referred to as the iso-ionic point (pI). In the case of

gelatin solutions that contain salts or other electrolytes, the pH where the net

charge on the molecule is zero and no movement occurs in an electric field is

called the IEP. For deionized solutions, the pI and the IEP are virtually identical.

Type A gelatin has a pI of pH 7.0–9.0, whereas type B gelatin has a pI of 4.8–5.2

(see Section 11.13.1).

The ionic character of gelatin as a function of pH is illustrated in Figure 11.4.

Irrespective of the pH, type A gelatin is positively charged in all food

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Gelling, emulsifying, stabilizing and foam formation 451

Figure 11.4 Electric charge of a type A and type

B gelatin molecule as a function of pH of

solution. pI= iso-ionic point.

3 5 7 9 11

pHPlAPlB

Type A

Type B

Ele

ctr

ic c

ha

rge

Po

sitiv

eN

eg

ative

systems, whereas type B gelatin can be either positively charged or negatively

charged.

The pI controls the charge density and net charge on the gelatin molecule as

a function of the pH of the food system in which the gelatin is employed. The

charge upon the gelatin and its intensity determine whether the gelatin remains

compatible with the other substances present as ingredients. Negatively charged

polysaccharides such as xanthan gum, carrageenan and alginates will coacervate

with gelatins that are positively charged if the conditions are favourable, result-

ing in removal of some of the gelatin from the system and a consequent loss

in functionality. When negatively charged polysaccharides are combined with

gelatin, as is done in certain applications, type B gelatin should be used to ensure

compatibility and to avoid a loss in functionality.

11.13.6 Surface-active/protective-colloid propertiesand utilization

Gelatin, like virtually all proteins, possesses surface-active properties and will adsorb

at air–water and oil–water interfaces, making it capable of assisting in the forma-

tion and stability of foams and emulsions such those found in marshmallow,

toffee and mousse (and also mayonnaise and certain meat products).

The emulsifying and emulsion-stabilizing ability of gelatin is linked to its abil-

ity to generate a film around the dispersed phase. A gelatin content increases

the viscosity of the aqueous phase in oil-in-water (O/W) emulsions, assisting in

emulsion stability. The surface-active properties of gelatins are influenced by the

pH of the food system in which they are employed because of the influence of

the pH on the charge balance.

Gelatin acts as a protective colloid in supersaturated solutions such as that found

in ice cream, icings and marshmallow, where it is able to restrict the growth of

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452 Confectionery and chocolate engineering: principles and applications

ice and sugar crystals and therefore gives the desired mouthfeel and shelf-life

stability to the product.

Consequently, gelatin is used as a functional ingredient in many food product

applications. Use is made of its multifunctional properties, together with its ease of

dissolution and neutral flavour, to achieve food products of desirable texture and

mouthfeel and to provide shelf-life stability. Gelatin is used in food systems as a

gelling agent, thickener, film former, protective colloid, adhesive agent, stabilizer,

emulsifier, foaming/whipping agent and beverage fining agent. It is important

to recognize that in many commercial food product applications, more than one

functional property of gelatin is utilized at any one time.

11.13.7 Methods of dissolutionThe following methods are those most often used for hydrating gelatin in solu-

tion.

11.13.7.1 Cold-water swelling methodsAlthough they take longer to carry out, cold-water swelling methods are advan-

tageous as the solutions are produced free from entrained air, which is an essential

requirement:

1 Gelatin may be swollen in cold water for a specific time depending on the

particle size. The swollen particles are then hydrated by heating in a jacketed

vessel under gentle agitation to 60 ∘C.

2 Gelatin may be swollen in cold water and then directly added to warm liquids

such as sugar syrups, in which it fully hydrates.

11.13.7.2 Hot-water dissolution methodsHot-water dissolution provides a rapid way to obtain gelatin solutions of high

concentration and is extensively used, particularly in the confectionery industry,

where concentrations of up to 40% w/w are often prepared.

Gelatin is added to hot water at 90 ∘C in a vortex created by mechanical agita-

tion. Once dispersion has taken place, the agitation speed should be reduced to

avoid air entrainment. Dual-speed agitators are recommended for this purpose.

If air entrainment occurs, standing the solution at 60 ∘C will allow air bubbles to

escape and the solution will clear.

For preparing concentrated solutions, coarse-mesh gelatins should be used as these

disperse easily without lumping problems. Johnston-Banks (1990, p. 253) rec-

ommends 16–28 mesh BSI (18 mesh BSI= 0.85 mm; 30 mesh BSI= 0.5 mm). To

obtain rapid hydration in the preparation of concentrated gelatin solutions, the

water temperature used should be from 75 to 90 ∘C. Lower temperatures, that is,

60–75 ∘C, may be used, but this significantly increases the time needed to hydrate

the gelatin particles.

The method used to prepare gelatin solutions depends on a number of fac-

tors, which include the end product to be manufactured, the particle size of

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Gelling, emulsifying, stabilizing and foam formation 453

the gelatin, the concentration of gelatin required, the time available, equipment

available (degree of agitation, type of stirrer, etc.) and the viscosity of the gelatin.

At a given concentration, high-viscosity gelatins are more difficult to hydrate

than gelatins of lower viscosity.

11.13.7.3 General precautions

1 To prevent extensive thermal hydrolysis, never boil gelatin solutions.

2 To avoid clumping problems, always add gelatin to water and not water to

gelatin.

3 To prevent unnecessary hydrolysis, never dissolve gelatin in the presence of

acids or fruit juices.

4 Care should be taken to ensure that complete dissolution of the gelatin has

occurred. In many instances, failure of gelatin to perform properly results from

incomplete hydration of the gelatin, with a consequential deficient concentra-

tion in the final product.

5 If the water/gelatin mixture is agitated, no air must be introduced into the mixture,

which easily forms unwanted foam.

For further details, see Johnston-Banks (1990).

11.13.8 Stability of gelatin solutionsOnce in solution, gelatin can suffer a loss in gel strength and viscosity when

exposed to elevated temperatures for any prolonged period of time. This loss can

be magnified under acidic conditions arising from the presence of fruit juices and

organic acids. As with other proteins, the presence of proteolytic enzymes can also

degrade gelatin solutions.

The loss of gel strength and viscosity is a result of hydrolysis of the gelatin

molecules. The rate of hydrolysis is a function of temperature, time and the pH

of the solution. To avoid unnecessary hydrolysis, the addition of acid to a product

formulation should be delayed until the latest possible time in the process.

11.13.9 Confectionery applicationsThe main areas of application of gelatin in confectionery are summarized in

Table 11.2. A schematic layout of the technology for gelatin jellies is shown in

Figure 11.5.

11.14 Egg proteins

11.14.1 Fields of applicationEggs are capable of performing various useful functions in foods, including foam-

ing, coagulating or gelling and emulsifying. All liquid components of eggs have

the capacity to form gels upon heating. This important property is a major factor

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454 Confectionery and chocolate engineering: principles and applications

Table 11.2 Main areas of application of gelatin

in confectionery.

Bloom grade

Recommended: type A

Marshmallow (extruded) 200–280

Marshmallow (deposited) 120–240

Angel kiss 100–200

Recommended: type A or B

Soft-boiled sweets 100–200

Jellies 180–260

Dragées 100–180

Tablets 100–180

Water

Water

Starchsyrup Cooling

(100 °C)

MixingSoaking Cooling

Dissolution

Sugar

Cooking(113–121 °C)

Colouring,flavouring

Shaping

Gelatin

Figure 11.5 Schematic layout of technology for gelatin jellies.

in the daily consumption of eggs, in which they are scrambled, fried, poached,

hard-boiled and used in the preparation of omelettes, quiches, soufflés, custards

and cakes.

Egg white is used in candy to incorporate air, control the growth of sugar crys-

tals, provide structural support through thermal coagulation and prevent synere-

sis (Cotterill et al., 1963; Baldwin, 1986). The main fields of application are in

roasted gingerbreads (geröstete Nusslebkuchen in German), macaroons (Makronen

in German) and meringues.

Although egg-yolk gels or sets in any food in which it is cooked, it has little

application outside traditional egg cookery, such as in custards, cakes and related

foods in which the flavour, texture and colour depend on the yolk.

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Gelling, emulsifying, stabilizing and foam formation 455

11.14.2 StructureThe liquid portion of shell eggs consists of about 67–70% albumen and 30–33%

yolk. For detailed information on the chemistry and composition of eggs and egg

proteins, the reader is referred to reviews of these topics: Cook (1968), Shenstone

(1968), Baker (1968), Cotterill and Geiger (1977), Osuga and Feeney (1977),

Powrie and Nakai (1986) and Cook and Briggs (1986).

Egg albumen is made up of thick and thin white, with the thick white compris-

ing about 60% of the albumen in a fresh egg (Shenstone, 1968). The thin white

has no apparent structural organization. The thick white has been described as a

weak gel, with its rigidity attributed to ovomucin, a high-molecular-weight gly-

coprotein that is organized into fibres. The thick-white gel is broken down to thin

white during the normal ageing of eggs. This is termed egg-white thinning, and in

this process the pH of the albumen rises from about 7.6 to 9.3 owing to a loss of

CO2 through the pores of the shell. Thick white is also easily broken down by

mechanical means, such as blending and homogenization. Egg albumen can be

regarded as a solution of globular proteins containing ovomucin fibres (Powrie

and Nakai, 1986).

Egg yolk, on the other hand, is a complex structural system in which sev-

eral types of particles are suspended in a protein solution or plasma (Robinson,

1979; Powrie and Nakai, 1986). These particles include spheres (4–150 μm diam-

eter), granules (0.3–2 μm), profiles or low-density lipoproteins (LDL) (25 nm)

and myelin figures (56–130 nm in length). Further references are Grodzinski

(1951), Romanoff and Romanoff (1961), Bellairs (1961) and Bellairs et al. (1972).

11.14.3 Egg-white gelsEgg white has been preferred over egg yolk and whole egg for its gelling abilities

in food systems for several reasons. The foaming ability of egg white broadens its

range of gelling applications.

The preparation of egg gels or of food gels containing eggs consists of three

steps:

1 The egg product is brought into a liquid state by rehydrating a powder or thaw-

ing a frozen product as necessary.

2 Next, any desired ingredients are incorporated, such as starches, salts, sugars,

buffers or acids.

3 Finally, the liquid is poured into the desired type of container, heated to the

desired temperature and cooled.

Common methods of heating include immersion in a water bath, steam injec-

tion, baking and frying. Most research on egg gels has been conducted on gels

heated by immersion in a water bath. This is the usual method also in the con-

fectionery industry.

It is important to understand the factors controlling the gelation of albumen

in order to maximize its function in any given food product.

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456 Confectionery and chocolate engineering: principles and applications

The quality of egg-white gels is greatly affected by pH and ionic conditions, sim-

ilarly to the gels of most globular proteins. The gel strength and cohesiveness

are at their minimum at the pH value where the net charge of the protein is

minimum, in the range of pH 6–7 for egg white. The behaviour of albumen gels

with respect to pH is of critical importance in food gels. When egg white is gelled

alone, the normal pH is 9, and gels of excellent quality are obtained. However,

when egg white is added to other food systems, the pH is lowered and egg white

functions much less effectively in gelling. This fact must not be overlooked if egg

white is to be used successfully in combination with other foods. Further refer-

ences are Meyer and Hood (1973), Nakamura et al. (1978), Hegg et al. (1979),

Beveridge et al. (1980), Egelandsdal (1980), Hickson et al. (1980, 1982), Holt et al.

(1984), Diehl and Gardner (1984), Gossett et al. (1984), Woodward and Cotterill

(1986a) and Powrie and Nakai (1986).

Since heat is the driving force behind protein denaturation and gelation, the

temperature of heating is of major importance in forming gels. Egg albumen

begins to lose fluidity at about 60 ∘C with the denaturation of conalbumin (Hick-

son et al., 1982; Montejano et al., 1984; Baldwin, 1986).

The hardness of the gel increases logarithmically with protein concentration

(Beveridge et al., 1980; Woodward and Cotterill, 1986a). As the protein concen-

tration is increased, egg white has an enhanced tendency towards aggregation,

resulting in increased fracturability of the gel (Woodward and Cotterill, 1986a,b).

One inherent property of protein gels is an ability to bind or trap water. In albu-

men gels, water-binding ability is influenced by the same factors that control

gel hardness. Water-binding ability is enhanced by increasing the pH, heating

temperature and protein concentration (Woodward and Cotterill, 1986a,b).

11.14.4 Egg-white foamsEgg white (egg albumen) is an excellent foaming material because of the spe-

cial functional properties of its constituent proteins (Dickinson, 1992). The main

constituent proteins are (in m/m%) ovalbumin (53–55), conalbumin (12–14)

and ovomucoid (10–12). The effectiveness of egg white as a foaming agent in

meringues and cake batter arises from successful teamwork between the various

constituent proteins and glycoproteins in chicken egg albumen. Not only is egg

white effective in stabilizing the liquid polyhedral foam, but it is involved also in

converting the liquid foam into a solid polyhedral foam during baking.

A reasonably acceptable meringue can be made with just the major com-

ponent, ovalbumin, although the resulting texture is coarser than that of

whole-egg-white meringue, and it takes much longer to do the beating. Oval-

bumin is easily denatured by heat, and its foaming properties are enhanced by

prior heat treatment. Egg albumen with the ovalbumin completely removed

gives satisfactory foamability and short-term stability, but the foam collapses

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Gelling, emulsifying, stabilizing and foam formation 457

after baking. In whole egg white, it appears that the main functional role of

the ovalbumin (and conalbumin) is to convert the liquid foam into a more

permanent solid foam as the protein becomes thermally denatured during

baking. The presence of highly surface-active globulins is essential for forming

a meringue (or a cake batter) with small bubbles and a smooth texture. The

glycoprotein ovomucoid is largely responsible for the high viscosity of egg

albumen, which assists foam stability by retarding foam drainage. In contrast

to ovalbumin, ovomucoid is extremely stable to heat. The complexing of

lysozyme (ca. 3.5 m/m%) with other egg-white proteins, especially ovomucin (ca.

1.5 m/m%), leads to a reduction in foaming capacity, but once formed, the

complex increases the film strength and hence enhances foam stabilization.

Lysozyme alone is a rather poor foaming agent.

Apart from egg white, two other ingredients are usually included in recipes

for meringue dishes and cakes: sugar and lemon juice. Sugar is added slowly with

continued beating, but only after the egg white has first been beaten into a stable

foam. Caster sugar should be used in preference to ordinary granulated sugar,

since the crystals of the latter are too large to dissolve properly in the aqueous

phase of the walls surrounding the air bubbles.

The purpose of the lemon juice is to reduce the pH towards the IEPs of the

acidic egg-white proteins. This leads to enhanced surface rheological proper-

ties and hence better foam stability. All the surface rheological parameters reach

maximum values at the IEP.

11.14.5 Egg-yolk gelsEgg yolk contains about 16% protein, including livetins, phosvitin and various

lipoproteins. In native egg yolk, the proteins are arranged structurally in yolk

spheres (up to 150 μm in diameter) and granules (0.3–1.7 μm in diameter). When

yolk is heated in a shell egg, the spherical structures are heat set independently

of one another, producing the familiar coarse, mealy texture of a hard-cooked

egg yolk (Woodward and Cotterill, 1987a).

However, stirring of raw yolk easily disrupts the spheres, resulting in a pro-

tein solution that is capable of forming firm gels with a texture similar to that of

albumen (Hawley, 1970; Woodward and Cotterill, 1987a). Egg-yolk gels have

minimum hardness at pH 6 and increase in hardness as the pH is increased

(Woodward and Cotterill, 1987b). The effects of pH are not as pronounced in yolk

as in albumen gels, however. Yolk gelation appears to be initiated at about 70 ∘C,

and the gel strength increases with increasing temperature. Egg-yolk gels have a

much greater capacity for binding water than egg-white gels do. Water-binding

capacity is increased with increasing pH, protein concentration and heating tem-

perature (Woodward and Cotterill, 1987b). For the role of LDL in the gelation of

egg yolk, see Nakamura et al. (1982), Meyer and Hood (1973) and Kojima and

Nakamura (1985).

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458 Confectionery and chocolate engineering: principles and applications

11.14.6 Whole-egg gelsWhole egg has many properties in common with egg white, since it is composed

of approximately 67% albumen and 33% yolk. Beveridge and Ko (1984) found

that whole-egg gels were very similar to egg-white gels. The hardness increased

linearly from a minimum at pH 5 to a maximum at pH 9. The hardness also

increased as the temperature was increased from 77 to 90 ∘C and as the time of

heating was increased from 5 to 25 min. Dilution of whole egg caused a logarith-

mic decrease in hardness.

Whole egg has a greater gelling capacity than either albumen or yolk, based on

the interaction of the yolk and albumen components (Woodward, 1984; Wood-

ward and Cotterill, 1986b). Perhaps the most important interaction is the binding

of iron from the yolk by conalbumin, which results in an increase of its denatu-

ration temperature from 61 ∘C in egg white to 78 ∘C in whole egg. The stability of

proteins in heated whole egg is enhanced with increasing pH and the addition of

sucrose. The optimum heating temperature for maximum water binding is about

80 ∘C; excessively high temperatures or long heating times result in overcoagu-

lation and syneresis (Baldwin, 1986, p. 345).

Non-fat milk solids, starches and food gums have been used to improve water

binding in whole-egg gels (Bengsston, 1967; Ziegler et al., 1971; O’Brien et al.,

1982).

11.15 Foam formation

11.15.1 Fields of applicationSome typical confectionery foams are listed in Table 11.3.

11.15.1.1 Ice creamIce cream is a partly frozen foam containing emulsified fat (ca. 10 m/m%) and an

air content of about 50% by volume. The role of the air cells is to give ice cream

its soft, light texture. Without air, the frozen emulsion would be too cold for the

mouth and too rich for the stomach.

Table 11.3 Foamed confectionery products.

Product Density (kg/l)

Angel kiss 0.2

Foamed wafer filling 0.2

Marshmallow 0.25–0.4

Montelimar >0.65

Fondant/foamed caramel 0.85–1.2

Frappé 0.4–0.55

Meringue 0.6–0.8

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Gelling, emulsifying, stabilizing and foam formation 459

The main ingredients of an ice cream mix are (milk) fat, sugar (ca. 15 m/m%),

non-fat milk solids (including lactose) (ca. 10 m/m%) and water. In addition,

commercial products contain emulsifiers, stabilizers, colours and flavours. The

ingredients are mixed, pasteurized, homogenized and rapidly cooled. After the

O/W emulsion has been aged, it is passed into a chamber whose temperature

is low enough to partly freeze the mixture, and at the same time air is beaten

in. The technological objective of the freezing/aeration stage is the formation of

a stable foam through partial destabilization of the emulsion. Beating without

freezing does not give a stable foam. The temperature of the ice cream mix falls

by about 10 ∘C during its short residence time (ca. 20 s) in a scraped-surface

heat exchanger. Air is incorporated intensively as the mix is frozen against

the cylinder wall. The ice crystals that begin to form at the wall are vigorously

scraped off by the blades of the rotor, and the solid foam leaves the freezer at a

temperature of ca. −5 ∘C. An acceptable texture is achieved with an overrun (see

Section 11.15.2) of 100%. Too little foam makes the product appear wet, hard

and excessively cold. Too much foam gives a texture that is dry and crumbly.

The air cells should be of the order of 100 μm in size. If the air cells are too

large, the ice cream melts too quickly. On the other hand, if the air cells are

too small, the foam becomes too stable, and an undesirable head is left on

melting.

Ice cream has a complex colloidal structure, being both a foam and an emul-

sion. The solid foam is held together partially by emulsified fat and partially by a

network of small ice crystals dispersed in a sweetened aqueous macromolecular

solution. The role of the emulsifier (e.g. glycerol monostearate) is to assist in the

controlled destabilization of the emulsion in the freezer.

Polymorphic changes in the solidified fat during ageing of the ice cream mix

cause distortion of the initial spherical shape of the globules, which, in combi-

nation with the partially loosened protein film, cause shear-induced clumping in

the freezer.

In whipped cream, the fat content is ca. 35–40 m/m%, which is enough to

stabilize the foam with a fat globule network alone. The additional stabilization

of the air bubbles of ice cream is due to the ice crystals (size 𝜈 ∼ 50 μm) and the

highly viscous aqueous phase, the viscosity of which is often increased by addi-

tion of polysaccharide stabilizers (e.g. carrageenan or locust bean gum).

Ice cream is one of the most complex food colloids – not only a foam but also an

emulsion, a dispersion and a gel. However, the majority of confectionery colloids

are similarly complex systems.

11.15.2 Velocity of bubble riseAt the onset of formation by injection methods, a foam represents a gas emulsion.

The rate of its transformation into a polyhedral foam depends on the velocity of

bubble rise, and the consequent drainage of the excess liquid from the foam thus

formed. The size of the bubbles, the gas volume fraction (gas concentration in

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460 Confectionery and chocolate engineering: principles and applications

the liquid) and the surfactant concentration determine the velocity of bubble

rise. Bubble rise has a destructive effect on foam stability.

In the absence of a surfactant, the velocity at which individual gas bubbles rise

is expressed by an equation due to Hadamard and Rybczynski (Dukhin et al.,

1986):

u =(2

3

)(𝜌2 − 𝜌1)g

(R2

𝜂2

)𝜂2 + 𝜂1

2𝜂2 + 3𝜂1

≈𝜌2gR2

3𝜂2

(11.13)

where 1 refers to the gas phase, 2 refers to the liquid phase, 𝜌 is the density, 𝜂 is

the dynamic viscosity and R is the radius of the spherical bubbles. As is known,

the velocity of ascent (or descent) of solid particles is expressed by Stokes’ law:

uS =(2

9

) 𝜌2gR2

𝜂2

. (11.14)

From Eqns (11.13) and (11.14),

uuS

= 32

, (11.15)

that is, the rise of bubbles is 1.5 times faster than that of solid particles.

The regime of gas bubble rise depends significantly on the hydrodynamic con-

ditions, that is, on the Reynolds number Re, where

Re =2𝜌2uR

𝜂2

. (11.16)

From Eqns (11.13) and (11.16),

u2 =RgRe

6(11.17)

Bubbles with a diameter smaller than 0.01 cm= 100 μm (Re≤ 0.5) rise as solid

particles and obey Stokes’ law.

When Re> 0.5, a deviation from Stokes’ law is observed, but the spher-

ical shape of the bubbles is retained up to Re values close to 1500. When

Re>200–300, the velocity of bubble rise in the absence of a surfactant satisfies

the following equation (Levich, 1962):

u =𝜌2gR2

9𝜂2

. (11.18)

The following relation was derived from the results on the velocity of rise of

large (R= 2–10 mm) bubbles (Harrison and Leung, 1962):

u = 0.792g1∕2(VB)1∕6 (11.19)

where VB is the bubble volume.

For further details, see Exerowa and Kruglyakov (1998, Chapter 1).

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Gelling, emulsifying, stabilizing and foam formation 461

Example 11.1Let us calculate the velocity of bubble rise according to Eqn (11.17) if Re=0.5

and R= 10−4 m:

u2 =RgRe

6≈ 10−4 m × 10 (m∕s2) × 0.5

6≈ 0.8 × 10−4 (m∕s)2 → u ≈ 0.9 cm∕s.

Let us calculate the dynamic viscosity 𝜂2 of the liquid phase if 𝜌2 = 1.02×103 kg/

m3:

Re = 0.5 =2𝜌2uR

𝜂2

= 2 × 1.02 × 103 × 0.9 × 10−2 × 10−4

𝜂2

→ 𝜂2 =(

2 × 1.02 × 103 × 0.9 × 10−2 × 10−4

0.5

)Pa s ≈ 3.6 × 10−3 Pa s.

Comment: This is a rather low value of dynamic viscosity. From Eqn (11.13),

it is evident that the dynamic viscosity and the bubble rise are in an inverse

relationship. For example, if 𝜂2 = 3.6×10−1 Pa s (which is a common value in

practice), then u≈ 0.9×10−2 cm/s, that is, the bubble rise will be 10 times slower.

Example 11.2Let us calculate the velocity of rise of a bubble of radius R= 5 mm according to

Eqn (11.19):

u = 0.792 ×√

10 m (s−1)(√

m)[4 × (5 × 10−3)3 × 3.14

3

]1∕6

≈ 22.3 cm∕s.

A rather high velocity!

When an ensemble of bubbles rises, the collective velocity U depends also on

the volume fraction 𝜑 of the dispersed gas. In the absence of a surfactant, the

collective velocity of bubble rise in the Stokes hydrodynamic regime of bubble

movement (Re≤ 0.5), as given by Gal-Or and Walso (1968) and Rulev (1970), is

U =(𝜌2gR2

3𝜂2

)(1 − 𝜑1∕3). (11.20)

In the regime 100≤Re≤ 1500, the corresponding equation is

U =𝜌2gR2(1 − 𝜑)2

9(1 − 𝜑1∕2). (11.21)

For the regime 0.5≤Re≤100, no analytical expression for the collective velocity

U has been obtained.

Surfactants exert a significant influence on the collective velocity of rise. The

ratio between the collective velocity of rise and the velocity of a single bub-

ble (U/u) is given in Figure 11.6 (Rulev, 1970). In the presence of a surfactant

(curve 1), the dependence of U and 𝜑 is more pronounced.

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462 Confectionery and chocolate engineering: principles and applications

–1 –2

1: Stokes regime (with surfactant)

2. Stokes regime (no surfactant)

3. High Reynolds number (no surfactant)

–3

1.00.500

0.5

1.0

U/u

φ

Figure 11.6 Bubble rise ratio U/u as a function of volume fraction 𝜑 in various regions of

Reynolds number. Source: Exerowa and Kruglyakov (1998). Reproduced with permission

from Elsevier.

In relation to foam formation, the amount of air incorporated is described by

the overrun or expansion ratio. This is the gas-to-liquid ratio in an aerated product

expressed as a percentage on a volume basis. So, a 200% overrun means that 1 l

of liquid has taken up 2 l of gas to form 3 l of foam, that is,

𝜑 = 21 + 2

= 23

.

11.15.3 WhippingThere are three main ways of making food foams:

• Whipping (beating)

• Bubble formation at an orifice

• Bubble generation in situ

Whipping (or beating) is the traditional way of making a foam from egg white or

cream. Air is entrapped in the viscous liquid in the form of large bubbles, which

are then broken down into smaller bubbles by mechanical action. In principle,

there is an unlimited amount of air available for incorporation; but, in practice,

the overrun is limited by the fact that no new air can be introduced once the

whipping rod is covered by foam.

The initial bubble formation takes place in the region immediately behind the

moving rod where the local hydrostatic pressure is low. The newly formed bub-

bles become elongated by the stress in the liquid and break into a number of

smaller bubbles. For inducing this kind of bubble deformation and rupture, elon-

gational motion of the liquid is more effective than shear flow. Agitation during

whipping causes local pressure fluctuations, which in turn induce surface tension

fluctuations due to rapid changes in bubble volume and surface area. Beyond

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Gelling, emulsifying, stabilizing and foam formation 463

Figure 11.7 Density of foam as a function

of time of whipping (values for

information only).

0

1.0

0.5

5 10

Time of whipping (min)

Slow whippingRapidwhippingD

ensity o

f fo

am

(kg/l)

0.4

0.3

0.2

0.1

40 50 60

Sugar dry content (m/m%)

De

nsity o

f fo

am

(kg

/l)

70

Starc

h syr

up

Sucrose

Inve

rt su

gar

Figure 11.8 Density of foam as a function of sugar dry content (values for information only).

a certain whipping speed, the surface tension fluctuations become so intense

that the liquid films between the pulsating bubbles rupture, and hence the foam

collapses. This is the explanation for the sharp maximum in the plot of foam

volume against whipping speed observed experimentally with kitchen mixers.

Figures 11.7–11.9 show the dependence of the foam density on various tech-

nological parameters.

11.15.4 Continuous industrial aerationThis method is often applied by introducing the required gas volume into the

liquid by generating bubbles at an orifice and then reducing them in size later on

in the process with a mixer or whipping rod.

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464 Confectionery and chocolate engineering: principles and applications

Time of whipping (min)

De

nsity o

f fo

am

(kg

/l)

0 2

4.0%

0.5%

1.0%

2.0%

4 6 8 10

1.4

1.2

1.0

0.8

0.6

0.4

0.2

Figure 11.9 Density of foam as a function of time of whipping with various concentrations of

whipping agent (values for information only).

For a bubble emerging from a single orifice, there are two forces acting: the

buoyancy (or Archimedes) force,

FA =(

4𝜋r3

3

)𝜌g, (11.22)

and the surface tension force at the orifice,

FS = 2𝜋R𝛾 (11.23)

where r is the radius of the bubble, 𝜌 is the density of the liquid, g is the gravita-

tional acceleration, R is the radius of the orifice and 𝛾 is the surface tension of the

liquid. (The density 𝜌g of the gas can be neglected. For example, the density of

air at 20 ∘C is ca. 29 g/24 l=1.208 kg/m3; however, the liquids used in food pro-

duction have densities in the region of 103 kg/m3, and, consequently, 𝜌≈ 𝜌− 𝜌g.)

From Eqns (11.22) and (11.23),

r =(

3𝛾R

2𝜌g

)1∕3

. (11.24)

In the presence of a surface-active material, the surface tension 𝛾 of the

growing bubble is higher than the equilibrium tension owing to the finite

dilatational viscosity. This results in the development of larger bubbles; see Eqn

(11.24).

Example 11.3The parameters in an industrial aeration process are R= 5×10−3 m, 𝛾 =2×10−2 N/m and 𝜌= 1.01×103 kg/m3. Let us calculate the radius r of the bubbles

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Gelling, emulsifying, stabilizing and foam formation 465

WaterIngredients

Filtered air

Whipping Colouring,flavouring

ShapingDissolutionWhipping

agent

Water

Filtered air

Whipping Mixing

Otheringredients

Colouring,flavouring

Shaping

Dissolution

Whippingagent

Sugar

(a)

(b)

Figure 11.10 Foaming by (a) one-step method and (b) two-step method.

according to Eqn (11.23):

r3 =3 × 5 × 10−3 m × 2 × 10−2 (N∕m)

2 × 1.01 × 103 kg∕m3 × 8.91 (m∕s2)= 15.1 × 10−9 m3

and r= 2.47 mm.

11.15.5 Industrial foaming methodsFigure 11.10 shows schematic layouts for foaming by one- and two-step

methods.

11.15.6 In Situ generation of foamAn important example of this is the in situ generation of carbon dioxide bubbles

by yeast cells or by baking powder during the baking of cakes (and bread). When

baking powder is used, vapour (and ammonia) is also generated.

The baking powders usually used are represented by the following chemical

reactions:

2NaHCO3 → Na2HCO3 + H2O + CO2 (11.25)

(NH4)2CO3 → 2NH3 + H2O + CO2 (11.26)

NaHCO3 + KHC4H4O6 → KNaC4H4O6 + H2O + CO2 (11.27)

2NaHCO3 + Na2H2P2O7 → Na2P2O7 + 2H2O + 2CO2 (11.28)

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466 Confectionery and chocolate engineering: principles and applications

8NaHCO3 + 3CaH4(PO4)2 → Ca3(PO4)2 + 4Na2HPO4 + 8H2O + 8CO2 (11.29)

NaHCO3 + NH4Cl → NaCl + NH3 + H2O + CO2 (11.30)

The list of permitted components in baking powder is legally regulated.

For further details of foams and foam films, see Exerowa and Kruglyakov

(1998).

Although the generation of foams by yeast cells is a general method of prepar-

ing several types of dough, this type of biochemical operation is beyond the scope

of this book.

Further reading

Anon (1985) The Dairy Handbook, Alfa-Laval AB, Lund.

AVEBE. Technical brochures/specifications.

Brenner, T., Tuvikene, R., Parker, A. et al. (2014) Rheology and structure of mixed

kappa-carrageenan/iota-carrageenan gels. Food Hydrocolloids, 39, 272–279.

Boomgaard, T.V.D., van Vliet, T. and van Hooydonk, A.M.C. (1987) Physical stability of chocolate

milk. International Journal of Food Science & Technology, 22, 279–291.

CABATEC (1991) Dairy Ingredients in the Baking and Confectionery Industries. An audio-visual open

learning module, Ref. C6, The Biscuit, Cake, Chocolate and Confectionery Alliance, London.

Copenhagen Pectin A/S. Technical brochures/specifications.

Carrillo-Navas, H., Hernández-Jaimes, C., Utrilla-Coello, R.G. et al. (2014) Viscoelastic relaxation

spectra of some native starch gels. Food Hydrocolloids, 37, 25–33.

DGF Stoess. Technical brochures/specifications.

Dickinson, E. (2006) Structure formation in casein-based gels, foams, and emulsions. Colloids

and Surfaces A: Physicochemical and Engineering Aspects, 288, 3–11.

Friberg, S.E., Larsson, K. and Sjöblom, J. (2003) Food Emulsions, Marcel Dekker, New York.

Germain, J.C. and Aguilera, J.M. (2014) A close look at protein-stabilized foams: review. Food

Structure. doi: 10.1016/j.foostr.2014.01.001

Goldsmith, S.M. and Toledo, R.T. (1985) Studies on egg albumin using nuclear magnetic reso-

nance. Journal of Food Science, 50, 59.

Gossett, P.W. and Baker, R.C. (1983) Effect of pH and succinylation on the water retention

properties of coagulated, frozen, and thawed egg albumen. Journal of Food Science, 48, 1391.

Harris, P. (ed.) (1990) Food Gels, Elsevier Applied Science, London.

Heyman, B., De Vis, W.H., Van der Meeren, P. and Dewettinck, K. (2014) Gums tuning the

rheological properties of modified maize starch pastes: differences between guar and xanthan.

Food Hydrocolloids, 39, 85–94.

Ingleton, J.F. (1971) Agar agar in confectionery jellies. Confectionery Production, 37 (9), 544.

IPPA (International Pectin Producers Association). Technical brochures/specifications.

Karimi, N. and Mohammadifar, M.A. (2014) Role of water soluble and water swellable frac-

tions of gum tragacanth on stability and characteristic of model oil in water emulsion. Food

Hydrocolloids, 37, 124–133.

Kirsty, E.A., Dickinson, E. and Murray, B. (2006) Acidified sodium caseinate emulsion foams

containing liquid fat: a comparison with whipped cream. LWT - Food Science and Technology,

39 (3), 225–234.

Lees, R. (1972) Use of alginates for the manufacture of confectionery. Confectionery Production,

38 (8), 416–418.

Lucas Meyer. Technical brochures/specifications.

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Gelling, emulsifying, stabilizing and foam formation 467

Ma, J., Lin, Y., Chen, X. et al. (2014) Flow behavior, thixotropy and dynamical viscoelasticity of

sodium alginate aqueous solutions. Food Hydrocolloids, 38, 119–128.

Mellema, M., van Opheusden, J.H.J. and van Vliet, T. (1999) in Food Emulsions and Foams. Inter-

faces, Interactions and Stability Special Publication, No. 227 (eds J.M. Dickinson and R. Patino),

Royal Society of Chemistry, Cambridge, p. 176.

Mullin, J.W. (2001) Crystallization, 4th edn, Butterworth-Heinemann, Oxford.

Murray, B.S., Dickinson, E. and Wang, Y. (2009) Bubble stability in the presence of oil-in-water

emulsion droplets: Influence of surface shear versus dilatational rheology. Food Hydrocolloids,

23, 1198–1208.

Nakauma, M., Ishihara, S., Funami, T. and Yamamoto, T. (2014) Deformation behavior of agar

gel on a soft substrate during instrumental compression and its computer simulation. Food

Hydrocolloids, 36, 301–307.

National Starch. Technical brochures/specifications.

Ottone, M.L., Peirotte, M.B. and Deiber, J.A. (2009) Rheokinetic model to characterize the mat-

uration process of gelatin solutions under shear flow. Food Hydrocolloids, 23, 1342–1350.

Perry, R.H. (1972) Turkish delight: Halwa, Chalwa, Rahat, Lokhum, Baslogke. Confectionery Pro-

duction, 38 (6), 317–318, 326.

Sajedi, M., Nasirpour, A., Keramat, J. and Desobry, S. (2014) Effect of modified whey protein

concentrate on physical properties and stability of whipped cream. Food Hydrocolloids, 36,

93–101.

Scholey, J. et al. (1975) Physical Properties of Bakery Jams. BFMIRA Report 217.

Scholey, J. and Vane-Wright, R. (1973) Physical Properties of Bakery Jams – An Investigation

into Methods of Measurement. BFMIRA Technical Circular 540.

Snoeren, T.H.M. (1976) Kappa-carrageenan, a study on its physico-chemical properties, sol–gel

transition and interaction with milk protein. PhD thesis. Wageningen, The Netherlands.

Snoeren, T.H.M., Both, P. and Schmidt, D.G. (1976) An electron-microscopic study of car-

rageenan and its interaction with kappa-casein. Netherlands Milk and Dairy Journal, 30,

132–141.

Verkroost, J.A. (1979) Some Effects on Recipe Variations on Physical Properties of Baker Jams.

BFMIRA Report 297.

Wang, Z., Yang, K., Brenner, T. et al. (2014) The influence of agar gel texture on sucrose release.

Food Hydrocolloids, 36, 196–203.

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CHAPTER 12

Transport

12.1 Types of transport

Two types of transport are studied here:

1 Flow of non-Newtonian fluids in a tube of circular cross section, with remarks

on cases where the cross section is different. The fluids are chocolate mass,

fondant mass and praline mass.

2 Transport of flour with air; although this operation is common in the milling

industry, it is of great importance in the confectionery industry as well.

12.2 Calculation of flow rate of non-newtonian fluids

Taking into account the fact that the flow curve of a non-Newtonian fluid is of

the form

𝜏 = 𝜏0 + 𝜂P1D (12.1)

the flow rate Q=Q(Δp) can be calculated using the following integral (the

Rabinowitsch–Mooney equation):

Q = 𝜋R3

𝜋3R∫

𝜏R

𝜏0

D𝜏2 d𝜏 (12.2)

where

𝜏 =rΔp

2L(12.3)

and R is the radius of the tube (r is used as a variant), L is the length of the tube,

𝜏0 = r0Δp/2L is the yield stress, r0 is defined by Eqn (12.3), Δp is the pressure

difference between the two ends of the tube and 𝜂Pl is the plastic (dynamic) vis-

cosity of the fluid. Sections A3.1 and A3.2 show the flow rate for the most com-

monly used fluid models, calculated on the basis of the Rabinowitsch–Mooney

equation.

Mohos developed a method that decomposes the flow rate Q for the most

frequently used models of non-Newtonian fluids into a product. This product

consists of a factor K, which is proportional to the pressure difference Δp, and a

factor M(Bu) containing Δp but not proportional to it. Values of M as a function

Confectionery and Chocolate Engineering: Principles and Applications, Second Edition. Ferenc Á. Mohos.© 2017 John Wiley & Sons Ltd. Published 2017 by John Wiley & Sons Ltd.

468

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Transport 469

of Bu (the Buckingham number) can be tabulated according to this method. For

further details, see Appendix 3.

The physical basis of the decomposition is that, on the one hand, the volumet-

ric rate

Q =R4𝜋Δp

8L𝜂

has a dimension m3/s. On the other hand, since the plastic viscosity or Casson

viscosity 𝜂Pl and the other types of viscosity (except the surface viscosity) have the

same dimension as that of the dynamic viscosity (kg/m s), the following dimen-

sionally correct equation can be written:

[Q] =R4𝜋Δp

8L𝜂= NP1 ×

R4𝜋Δp

8L𝜂Pl

= NCA ×R4𝜋Δp

8L𝜂CA

= NX ×R4𝜋Δp

8L𝜂X

where the symbol [ ] means the dimension and the N values are pure numbers.

The N values are as follows:

NPl = 1 − (4∕3)Bu + (1∕3)Bu4, a number depending on the Buckingham

number Bu,where Bu = 𝜏0∕𝜏; 𝜏 = RΔp∕2L, 𝜏0 is the yield stress, and

R and L are the radius and length of the tube, respectively.

NCAis a number referring to a Casson fluid (and the Casson viscosity).

NX is a number referring to an arbitrary fluid, etc.; see Sections 3.1 and 3.2.

Because the Casson equation in both the original (n= 1/2) and the general-

ized form is mostly used for linearization of the flow curves of molten chocolate

masses, this is dealt with in detail in Sections 3.3–3.7. Examples of calculations

are given in Appendix 3.

The following examples present the evaluation of flow curves according to the

Bingham, Casson and Ostwald–de Waele models. These flow models are the ones

most frequently used in the confectionery industry.

Example 12.1Table 12.1 shows a flow curve evaluated according to the Bingham (n= 1) and

Casson (n= 0.5) models. The results are:

According to the Bingham model, 𝜏 =8.47 (Pa)+ 28.3 (Pa s) D.

Correlation coefficient: 0.988481.

According to the Casson model, 𝜏1/2 = 2.14 (Pa)1/2 + 3.94 (Pa s) 1/2 D1/2.

Correlation coefficient: 0.998945.

It can be seen that the evaluation according to the Casson model provides

a slightly better correlation than that according to the Bingham model. This

example shows that there is no exclusively acceptable method of flow curve

evaluation.

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470 Confectionery and chocolate engineering: principles and applications

Table 12.1 Evaluation of the flow curve of a milk chocolate according

to the Bingham (𝜏; D) and Casson (𝜏0.5; D0.5) models.

t (Pa) D(s−1) 𝝉0.5 D0.5

23 0.16 4.795832 0.4

26.1 0.36 5.108816 0.6

53.2 2.42 7.293833 1.555635

75 4.4 8.660254 2.097618

91 7 9.539392 2.645751

139 13.7 11.78983 3.701351

Slope Constant Slope Constant

8.469394 28.30303 2.141655 3.938165

Table 12.2 Evaluation of the flow curve of a truffle mass according to the Ostwald–de Waele

model.

𝝉 (Pa) D (s−1) ln 𝝉 ln D Exponent ln(intercept)

73 0.5 4.290459 −0.69315 0.378806 4.546189

169 5 4.290459 1.609438 Intercept

435 50 6.075346 3.912023 94.27241

606 150 6.40688 5.01063 r=0.9994

708 200 6.562444 5.298317

Example 12.2Table 12.2 shows the flow curve of a truffle mass and its evaluation (Machikhin

et al., 1976). The resulting flow curve is described by

𝜏 = 94.27(Pas0.379

)D0.379

12.3 Transporting dessert masses in long pipes

Lapitov and Filatov (1963) developed a calculation method for viscoelastic

masses, in fact for dessert masses, which starts from the Buckingham equation

written in the following form by Mohos:

Q =[

R4𝜋Δp

8L𝜂Pl

]{1 −

(43

)Bu +

(13

)Bu4

}(12.4)

where Bu= 𝜏0/𝜏. Lapitov and Filatov (1963) worked with the ratio d0/d

(=Bu) of the diameters of the undeformed material and of the tube.

However, they calculated with Bu2 instead of Bu4 and also assumed that

Bu> 0.75. After these simplifications, the following linear function was applied:

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1− (4/3)Bu+ (1/3)Bu4 ≈ 0.32(1−Bu). The Buckingham equation (Eqn 12.4)

was written

𝜆 = 200Re′

(12.5)

𝜆 =2Δp

L𝜌V 2(12.6)

where 𝜆 is the generalized friction coefficient; Re′ =Vd𝜌/𝜂 is the generalized

Reynolds number; 𝜂 = 𝜂Pl + d𝜏0/25V; V=4Q/𝜋d2 (d=diameter of pipe), that is,

the average linear velocity of the mass; L is the length of the pipe; and Δp is the

pressure difference.

According to experimental results, instead of Eqns (12.5) and (12.6), the follow-

ing can be used:

𝜆′ = 200(Re′)0.92

(12.7)

Δp

L= 91.6 × 𝜂0.92 × V 1.08 × D0.08

d1.92(12.8)

The interval of validity of these equations is given by V=0.01–0.2 m/s,

𝜏0 = 100–1000 Pa, 𝜂Pl = 10–200 Pa s and d= 0.03–0.08 m. For these experiments,

the calculated values varied from 𝜆′ =2590 and Re′ = 0.082 to 𝜆′ = 164 200 and

Re′ =0.000734 as the diameter of the tube was varied from 42 to 69 mm.

12.4 Changes in pipe direction

If the direction of the pipe changes, the length of its track has to be taken into

account when L is calculated. Machikhin and Birfeld (1969) gave a method of

calculation that takes into account sudden changes in the pipe diameter, which fol-

lows the method of Bagley (1957): it calculates with a fictive length of pipe

L′ =N×L, where the value of N is about 6–8 and needs to be experimentally

determined.

If the pipe has a perpendicular part, then two additional pressure differences

need to be calculated to obtain Δp in Eqn (12.8): a hydrostatic pressure difference

Δph,

Δph = 𝜌gH (12.9)

and a pressure difference ΔpV depending on the average linear velocity V of the

mass,

ΔpV = KV𝜌H (12.10)

KV = 1.08 + 0.563 × V 0.5 (12.11)

where 𝜌 is the density of the mass, g is the gravitational acceleration and H is the

length of the perpendicular part of the pipe.

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472 Confectionery and chocolate engineering: principles and applications

12.5 Laminar unsteady flow

A detailed discussion of laminar unsteady flow in long pipes was presented by

Letelier and Céspedes (1986). These authors published a mathematical tool called

one-dimensional analysis, by means of which the equations of motion can be easily

dealt with; it was used for discussion of viscoelastic flow (Coleman–Noll and

Maxwell fluids) and power-law flow (Ostwald–de Waele fluids). A description of

this method is beyond the scope of this book.

12.6 Transport of flour and sugar by airflow

12.6.1 Physical parameters of airThe density of air as a function of temperature and pressure is given by the

equation

d = dN

(p

pN

)273∘

237∘ + t(12.12)

where dN = 1.295 kg/m3 is the density of air in the normal state, pN =101337 N/m2

is the normal atmospheric pressure, p is the pressure of the air and t (∘C) is the

temperature of the air. Some physical parameters of air are given in Table 12.3.

12.6.2 Airflow in a tubeThe pressure drop in a straight tube with a rough inner surface can be

expressed as

Δp(Pa) = f( L

D

) dv2G

2(12.13)

where f is the air friction coefficient, L is the length of the tube (m), D is the

diameter of the tube (m), d is the density of the air (kg/m3) and vG is the velocity

of the air (m/s). The friction coefficient f is a function of the Reynolds number of

the air (see Fig. 12.1):

Re =DvG

vG

(12.14)

where 𝜈G is the kinematic viscosity of air (m2/s). Figure 12.1 shows the air friction

coefficient as a function of the Reynolds number for smooth and rough tube

surfaces (see Egry, 1973a,b).

The values of f for a smooth surface should be used because, during transport,

the surface will become smooth within a short time.

Table 12.3 Physical parameters of air at normal atmospheric pressure.

Temperature (∘C) 0 20 40 60 80

Density (kg/m3) 1.295 1.207 1.13 1.06 1

Viscosity [kg/(m s)]×106 17.17 18.15 19.1 20 20.9

Kinematic viscosity (m2/s)× 106 13.3 15.1 16.9 18.9 20.9

Source: Egry (1973a,b). Reproduced with permission from Egry.

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Transport 473

0.03

f

0.02

0.01

0

0

Re × 10–3

100 200 300

Smooth

Rough

400 500

Figure 12.1 Air friction coefficient as a function of Reynolds number for smooth and rough

tube surfaces. Source: Egry (1973a,b). Reproduced with permission from Egry.

Example 12.3For a tube with L= 30 m and D=0.12 m and t=25 ∘C, vG = 22 m/s and

p= 0.95×105 Pa, let us calculate the pressure drop at the end of the tube.

The density of the air is

d = dN

(p

pN

)273∘

273∘ + t= 1.295 × 0.95

1.01337× 273

298= 1.112kg∕m3

From Table 12.3, a good approximation for the kinematic viscosity 𝜈G (at 25∘C) is

15.5×10−6 m2/s. Thus Re= 0.12×22/(15.5× 10−6)= 170 323. From Figure 12.1,

f≈0.017, and therefore

Δp(Pa) = f( L

D

) dv2G

2= 0.017 × 30

0.12× 1.112 × 222

2= 1143.7Pa

The absolute pressure at the end of the tube is (95 000− 1143.7) Pa=93856.3 Pa.

12.6.3 Flow properties of transported powdersMaterials transported in a powder state cannot be characterized by a single par-

ticle size value but must be characterized by a particle size distribution; however,

for the purpose of calculation, a so-called reduced particle size x is used:

x(m) =(

6M𝜋dM

)1∕3

(12.15)

where M is the mass of one particle (or grain) (kg) and dM is the density of the

material transported in the powder state (kg/m3). This calculation of the reduced

particle size assumes a globular shape of the particles, which is a good approxi-

mation if x< 0.1 mm.

The reduced cross section of a particle is defined as

A(m2) =

[𝜋

(3M4dM

)2]1∕3

(12.16)

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474 Confectionery and chocolate engineering: principles and applications

From Eqns (12.15) and (12.16), a practical relation can be obtained:

A = x2𝜋

82∕3≈ 0.78x2 (12.17)

The airflow acts on a particle with a force F (N), equal to

F =CEAdw2

2(12.18)

where CE is the hydrodynamic friction coefficient of the particles, which depends

on the Reynolds number ReM referred to the material transported in the powder

state; vM is the velocity of the transported material (m/s); and w= vG − vM is the

difference between the velocities of the air and the particles (m/s). The usual

definition of the slip s is

s = wvG

= 1 −vM

vG

(12.19)

The definition of ReM is

ReM = xwvG

(12.20)

Values of CE are shown in Figure 12.2, which presents the hydrodynamic fric-

tion coefficient of globular particles as a function of the Reynolds number (Egry,

1973a,b).

For the limiting velocity c of a floating particle,

hydrodynamic friction force = weight of particle,

that is,CEAdc2

2=(4

3

)( x2

)πdMg (12.21)

and

c =

√(4

3

)(dM

d

)(xg

CE

)(12.22)

where g is the gravitational acceleration (=9.81 m/s2).

103

CE

ReM

102

101

100

10–1

10–2

10–2 10–1 100 101 102 103 104 105 106 107

Figure 12.2 Hydrodynamic friction coefficient CE of globular particles as a function of Reynolds

number. Source: Egry (1973a,b). Reproduced with permission from Egry.

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Example 12.4The size of a particle is x=0.05 mm= 5×10−5 m, dM =400 kg/m3, w= 25 m/s,

t=25 ∘C, 𝜈G (at 25 ∘C)=15.5×10−6 m2/s and d= 1.112 kg/m3. Let us calculate

ReM and the limiting velocity c of a floating particle:

ReM = xwvG

= 5 × 10−5 × 25

15.5 × 10−6= 80.65

From Figure 12.2, CE ≈2:

c =

√(4

3

)(dM

d

)(xg

CE

)=

√(4

3

)( 4001.112

)(5 × 10−5 × 9.81

2

)≈ 0.343m∕s

12.6.4 Power requirement of airflowIf ΔpΣ < 105 Pa, air can be regarded as incompressible, and then

P =VΔp∑

𝜂(12.23)

where P is the power requirement of the air flow (in W=N m/s), ΔpΣ is the total

pressure drop of the transporting air flow (N/m2), V is the volume velocity of the

air (m3/s) and 𝜂 is the efficiency of the pneumatic machinery. At higher values

of ΔpΣ, the power requirement is calculated by taking isothermal compression

into account:

P =p1V1 ln(p1∕p2)

𝜂(12.24)

where p1 and p2 are the initial and final pressure, respectively (p1 < p2), and V1

is the volume velocity of the air (m3/s) at p1.

12.6.5 Measurement of a pneumatic systemAccording to Pápai (1965), the principle of measurement is the summation of

the partial pressure drops along the pneumatic pipe.

First, the air volume velocity V is determined from the following equation if

the material flow QM (kg/s) and the mixing ratio r are given (r=QM/QAIR):

VG =QM

rd(12.25)

The recommended mixing ratio r for flour is in the range 1–4. From this equation,

the calculated cross section A of the pipe can be determined:

A =VG

vG

(12.26)

In the general case a pneumatic pipe consists of a vertical section of length L

and diameter D, a curved section, a cyclone, a pipe section behind the cyclone,

a ventilator and a powder filter.

The following equation for the total pressure drop Δp3 is valid:

Δp3(N∕m2) = Δp1 + Δp2 (12.27)

where Δp1 is the pressure drop of the pipe and Δp2 is the pressure drop arising

from the effect of the cyclone up to the end of the powder filter.

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476 Confectionery and chocolate engineering: principles and applications

The partial pressure drops are

Δp1 = Δp10 + Δp11 (12.28)

where Δp10 is the pressure drop of the pipe containing only air (vacant run) and

Δp11 is the pressure drop of the pipe containing air+material. Here,

Δp10 =[𝜁IN +

f (L + LE)D

]dv2

G

2(12.29)

where 𝜁 IN =1.2− 2 is the input air friction coefficient, LE =1.5LC is the equivalent

length of the curved section if the ratio of the radius R to the diameter D is high

(≥10) and LC is the length of the curved section, and

Δp11 = Δp111 + Δp112 + Δp113 + Δp114 + Δp115 (12.30)

In detail,

Δp111 = 𝜁ACQMvM∕A is the pressure drop derived from acceleration of material

(where 𝜁AC = 1.2–1.4, depending on the method of input; when a

sucking head is used, 𝜁AC = 1.7–1.9)

Δp112 = kHLHQMvG∕A is the pressure drop in the horizontal section of the pipe.

Δp113 = HgQM∕vMA is the pressure drop derived from lifting through a height H.

Δp114 = kFLFQMvM∕A is the pressure drop derived from collisions of particles

in the vertical straight section of the pipe (for collisions in the vertical

section, kF = 0.05–0.12 m−1; for collisions in the horizontal section,

kF = 0.04–0.1 m−1).

Δp115 = kCYLCYQMvM∕A is the pressure drop in the curved section.

Also,

Δp2 = Δp21 + Δp22 + Δp23 (12.31)

where

Δp21 = 𝜁CYdv2G∕2 is the pressure drop in the cyclone; 𝜁CY = 2–8 is the friction

coefficient of the cyclone

Δp22 = Δp10 is the pressure drop in the pipe section between the cyclone

(+ventilator) and the filter; this is practically equal to the pressure drop

for a vacant run

Δp23 is the pressure drop in the filter, which depends on its type

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Transport 477

Vg min Vg

To

tal p

ressu

re d

rop Characteristic

of ventilator

2

1

Figure 12.3 Choice of ventilator. Source: Egry (1973a,b). Reproduced with permission from

Egry.

Figure 12.3 shows how to choose a suitable ventilator, taking into account the

minimum volume velocity of the air (Vg min) on the basis of the characteristics of

the ventilator. The formulae for the various partial pressure drops show that the

total pressure drop is a quadratic function of the velocity (and volume velocity)

of the air. The continuous line in Figure 12.3 represents the values of the volume

velocity of air in the run. A ventilator of type 1 is not suitable, because it cannot

produce a sufficient pressure difference to provide Vg min.

For further details, see Leschonski (1975), Bohnet (1983), Schmidt et al.

(1992), Tomas (1992), Wilms (1993) and Schulze (1993).

Further reading

BEPEX/HUTT. Technical brochures.

Boger, D.V., Crochet, M.J. and Keiller, R.A. (1992) On viscoelastic flows through abrupt con-

tractions. J Non-Newtonian Fluid Mechanics, 44, 267–279.

Carle & Montanari. Technical brochures.

NETZSCH-Mohnopumpen. Technical brochures.

Rohsenow, W.M., Hartnett, J.P. and Cho, Y.I. (eds) (1998) Handbook of Heat Transfer, 3rd edn,

McGraw-Hill Handbooks. McGraw-Hill, New York.

Sollich. Technical brochures.

Tomay, T. (ed.) (1973) Gabonaipari kézikönyv, Technológiai gépek és berendezések (Manual of Grain

Processors, Technological Machines and Equipments of the Grain Silos, in Hungarian),

Mezogazdasági Kiadó, Budapest, pp. 942–954.

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CHAPTER 13

Pressing

13.1 Applications of pressing in the confectioneryindustry

Pressing of cocoa mass (cocoa liquor) is used for producing cocoa butter and

cocoa powder, which are essential in chocolate manufacture. (The machinery for

pressing cocoa mass can also be used for decreasing the fat content of hazelnut

paste, which is made from roasted, unshelled, comminuted hazelnuts.)

13.2 Theory of pressing

Pressing can be regarded as filtration under the effect of excess pressure – in

filtration, the driving force for separation originates from the hydraulic pressure

of the slurry.

The Ruth equation can be used to describe the evolution of the pressing process

over time:

w = dV∕dt =Δp∕𝜂

𝛼(1 − 𝜀)hC + 𝛽(13.1)

where V (m) is the volume of filtrate VB (m3) per unit area A (m2) of filter, t (s) is

the time, w (m/s) is the rate of pressing, Δp (Pa) is the pressure applied, 𝜂 (Pa s) is

the dynamic viscosity of the filtrate, 𝜀 (dimensionless) is the porosity of the cake,

hC (m) is the height of the cake, 𝛼 (m/m3 =m−2) is the average flow resistance

of the cake per unit volume and 𝛽 (m−1) is the average flow resistance of the

filter used.

The total volume VSL of slurry can be imagined as consisting of two parts:

VSL = VC + VB (13.2)

where VC is the volume of cake and VB is the volume of filtrate. The correspond-

ing heights are as follows:

hSL: height of slurry at the beginning of pressing

hC: height of cake as a function of t

hB: height of filtrate as a function of t.

Confectionery and Chocolate Engineering: Principles and Applications, Second Edition. Ferenc Á. Mohos.© 2017 John Wiley & Sons Ltd. Published 2017 by John Wiley & Sons Ltd.

478

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Pressing 479

If s is the volume concentration of the suspension, that is,

s =VC

VSL

then

VB =(1 − s)VC

s(13.3)

and

V =VB

A= (1 − s)(1 − 𝜀)hc

s(13.4)

Differentiating both sides,

w = dVdt

= [(1 − s)(1 − 𝜀)]s

(dhC

dt

)(13.5)

If we consider the case of a non-compressible cake, that is, 𝜀= 0, the Ruth

equation (Eqn 13.1) can be written in a simpler form:

w = dVdt

=Δp∕𝜂

[𝛼yV + 𝛽](13.6)

where y=VC/VB and yV=VC/A.

There are two usual methods for integration of the differential equation (13.6).

Case 1Suppose that w= dV/dt= constant and Δp increases up to its maximum value

(Δp)max. If Δp= (Δp)max, then V=VB/A=Vmax and, from Eqn (13.6),

Vmax =(

1𝛼y

)[ (Δp)max

w𝜂− 𝛽

](13.7)

The duration of pressing 𝜏, during which Δp increases to (Δp)max, is, from

Eqn (13.7),

𝜏 =Vmax

w=(

1𝛼yw

)[ (Δp)max

w𝜂− 𝛽

](13.8)

Case 2Suppose that Δp is constant. From Eqn (13.6), we obtain V= 0 at the beginning

of pressing, that is,

w(t = 0) =(

dVdt

)

0

=Δp

𝜂𝛽(13.9)

Furthermore, Eqn (13.6) can be written in the form(

dVdt

)[𝛼yV + 𝛽] =

Δp

𝜂

or (dVdt

)(𝛼yV ) +

(dVdt

)𝛽 =

Δp

𝜂

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480 Confectionery and chocolate engineering: principles and applications

After separating the variables, we obtain

dV𝛼yV + dV𝛽 =(Δp

𝜂

)dt

After integration (V= 0→V=V when t=0→ t= 𝜏),

V 2 +(

2𝛽

𝛼y

)V = 𝜏

2Δp

𝜂𝛼y(13.10)

or

V 2 + 2CV = K𝜏 (13.11)

where C (m)= 𝛽/𝛼y and K (m2/s)= 2Δp/𝜂𝛼y.

From the quadratic equation (13.11), the value of V=V(𝜏) can easily be cal-

culated:

V =−2C =

√4C + 4K𝜏

2(13.12)

The empirical constants of pressing can also be determined from Eqn (13.11):

𝜏∕V = V( 1

K

)+ 2C

K(13.13)

In a plot of 𝜏/V versus V, the intercept is 2C/K and the slope is 1/K. Therefore

intercept ×(

1slope

)=(2C

K

)K = 2C (13.14)

where 1/slope=K.

13.3 Cocoa liquor pressing

Cocoa powder is manufactured by hydraulic pressing of finely ground cocoa

liquor, which must have been made from well-winnowed, high-grade cocoa

beans.

Hydraulic presses can automatically and accurately obtain the required fat con-

tent in the cocoa cake. In modern horizontal presses, 12–14 pots are mounted in

a horizontal frame and each pot is provided with a metal filter screen supported

on plates in the pot. The press, when closed, is filled automatically with hot cocoa

mass under pressure, and a proportion of the free cocoa butter is removed during

the filling operation. A higher pressure (up to 400–450 bar with older machines

and 800–850 bar with modern machines) is then applied. The ultimate fat con-

tent of the cocoa cake is controlled by the time cycle, the weight of cocoa butter

and the distance of travel of the ram.

The pressing resistance of the cake is strongly dependent on the size distribu-

tion and moisture content of the cocoa liquor that is being pressed. The moisture

content is critical; the optimum interval is 0.8–1.5 m/m% but the recommenda-

tions of the manufacturer of the press are always decisive. For efficient pressing,

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Pressing 481

cocoa liquor has to be coarser than for chocolate: 98–99% through a 200-mesh

(74 μm) sieve.

In modern practice, the best results are obtained from pressing at 95–105 ∘C,

since – as the Ruth equation (Eqn 13.1) shows – if the dynamic viscos-

ity decreases, the pressure difference needed for pressing also decreases:

dV/dt∼Δp/𝜂. However, temperatures that are higher than this range result in

inferior, strongly flavoured cocoa butter without any improvement in yield.

The output is strongly dependent on the fat content of the cocoa cake: ca. 3 t/h

for 24% and 0.5–0.7 t/h for 10–12%.

Example 13.1A horizontal cocoa-pressing machine has 12 pots of 15 kg cocoa mass capacity;

the total capacity is 12× 15 kg= 180 kg. The cocoa mass, which has a cocoa butter

content of 54 m/m%, is pressed to a cocoa butter content of 16 m/m%. The tem-

perature of pressing is 80 ∘C. The pressing resistance can be calculated assuming

that the resistance of the filter (𝛽) can be neglected. The time required to press

a charge is 𝜏 =600 s (=10 min). Let us calculate the amount of cocoa press cake

and cocoa butter.

The mass balance of cocoa butter is

0.54 = 0.16x + 1 − x → x = 1 − 0.541 − 0.16

≈ 0.55

That is, the proportion of press cake is x≈0.55 and the proportion of cocoa butter

pressed is

1 − x ≈ 0.45.

For 180 kg of cocoa mass, the amount of press cake is 180 kg×0.55= 99 kg

and that of cocoa butter pressed is 81 kg. Consequently, the output is

6×99 kg= 594 kg of cocoa cake/h.

The diameter d of a pot is 0.45 m; therefore, the distance of the ram from

the filter screen at the start of pressing is (assuming a density of cocoa liquor of

984 kg/m3 at 80 ∘C)

H = 15 kg × 4

0.452 × 3.14 m2 × 984 kg∕m3≈ 0.096m

According to Rapoport and Sosnovsky (1951, pp. 171–179), the density of cocoa

mass is 1075 kg/m3, the density of cocoa butter is 872 kg/m3 (both at 80 ∘C) and

the dynamic viscosity (centipoise) as a function of temperature T= 35–80 ∘C can

be described by

log 𝜂 = 2.2 − 0.0145T

that is at 80 ∘C, 𝜂 (cocoa butter)≈ 10.96 cP≈ 0.011 Pa s.

At the end of pressing, the height of the cocoa cake is

hC = 15 kg × 0.55 × 4

0.452 × 3.14m2 × 1075kg∕m3≈ 0.048m

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482 Confectionery and chocolate engineering: principles and applications

At the end of pressing, the distance moved by the ram is

hB = 15kg × 0.45 × 4

0.452 × 3.14m2 × 872kg∕m3≈ 0.049

(It can be seen that H≈0.096 m≈ hC + hB = 0.097 m.) Since hB =Vmax = 0.097 m,

w =hB

600s= 0.097m

600s

Since 𝛽 ≈0 and the pressure increases continuously up to (Δp)max = 400× 105 Pa,

Case 1 is applicable here. Applying Eqn (13.8),

𝜏 =Vmax

w=(

1𝛼yw

)[ (Δp)max

w𝜂− 𝛽

](13.8)

Since y=VC/VB =hC/hB = 0.048/0.049≈ 1, 𝜂 =0.011 Pa s and 𝛽 =2× 107 m−1 (an

assumed value), Eqn (13.8) can be written as

600s =( 600s𝛼0.097m

)×[

400 × 105 Pa600 s∕(0.097m × 0.011Pa s)

− 2 × 107 m−1

]

and 𝛼 = (1/0.097)(2.474×1011 − 2×107)≈ 2.55×1012 m−2.

The usual ranges of values are 𝛼 =1012–1014 m−2 and 𝛽 = (1.6–6.5)×107 m−1.

See Fábry (1995, p. 146).

Further reading

Bauermeister (Probat Group). Technical brochures.

Beckett, S.T. (ed.) (1988) Industrial Chocolate Manufacture and Use, Van Nostrand Reinhold, New

York.

Beckett, S.T. (2000) The Science of Chocolate, Royal Society of Chemistry, Cambridge.

Cakebread, S.H. (1975) Sugar and Chocolate Confectionery, Oxford University Press, Oxford.

Carle & Montanari. Technical brochures.

Meursing, E.H. (1983) Cocoa Powders for Industrial Processing, 3rd edn, Cacaofabriek de Zaan, Koog

aan de Zaan, The Netherlands.

Minifie, B.W. (1999) Chocolate, Cocoa and Confectionery, Science and Technology, 3rd edn, Aspen Pub-

lications, Gaithersburg, MD.

Nemeth, J. and Horanyi, R. (1970) Untersuchungen uber die Teilchengrosse als Kennwert der

Leistung schneller Klarzentrifugen. Periodica Polytechnica Ch XIV , 2, 183–193.

Pratt, C.D. (ed.) (1970) Twenty Years of Confectionery and Chocolate Progress, AVI Publishing, West-

port, CT.

Wieland, H. (1972) Cocoa and Chocolate Processing, Noyes Data Corp., Park Ridge, NJ.

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CHAPTER 14

Extrusion

14.1 Flow through a converging die

14.1.1 Theoretical principles of the dimensioning of extrudersFirst, it should be emphasized that both shear and extensional viscosity play an

important role in flow through a converging die.

The extensional viscosity 𝜂E must not be confused with the volumetric viscosity

𝜂V, which latter appears in the constitutive (Navier–Stokes) equation of isotropic

compressible Newtonian fluids:

t = 2𝜂(Gradv)s + (𝜂v div v − p)𝛅 (14.1)

where t is the deformation tensor, v is the velocity vector, 𝛅 is the unit tensor,

p is the pressure (scalar), 𝜂 is the shear (or dynamic) viscosity and the index ‘s’

refers to the symmetric part of the tensor Grad v.

If the fluid is incompressible,

divv = 0 (14.2)

The term containing the volumetric viscosity becomes zero, and Eqn (14.1) can

be simplified:

t = 2𝜂(Gradv)s − p𝛅 (14.3)

Now, the volumetric viscosity is not taken into account.

In the extensional deformation of incompressible bodies, the shape of the body

is deformed, but its volume is unchanged. However, flow through a converging

die may occur with both incompressible and compressible fluids (div v≠ 0). In

Chapter 15, the case of incompressible fluids will be discussed exclusively. How-

ever, it should be mentioned that among the fluids used in the confectionery

industry (chocolate, fat masses, cremes based on fondant, etc.), there are some

types that are compressible (see Section 15.4.3).

The literature on construction of extruders for shaping various fondant masses,

fat compounds and so on. The reason for this deficiency is likely to be the fact

that, on the one hand, an exact mathematical discussion of the questions that

arise is possible only in some simple cases and, on the other hand, the solutions

obtained in those cases are not sufficiently accurate. As a consequence, methods

based on empirical values have been in widespread use.

Confectionery and Chocolate Engineering: Principles and Applications, Second Edition. Ferenc Á. Mohos.© 2017 John Wiley & Sons Ltd. Published 2017 by John Wiley & Sons Ltd.

483

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484 Confectionery and chocolate engineering: principles and applications

In the following, an attempt is made to summarize certain parts of this branch

of science in a substantially simplified form and to make it applicable in practice.

Steffe (1996, Chapter 4) discussed in detail the extensional type of flow, which

is of great importance in food process engineering. He described many rheolog-

ical methods for determination of the extensional viscosity of several foods and

also the appropriate rheological calculations for obtaining relationships between

the extensional flow rate and the extensional viscosity. Discussions concerning

rheometry are beyond the scope of this book.

Steffe (1996, Section 4.4) discussed calculation methods related to flow

through a converging die. The following description briefly presents these

methods.

14.1.1.1 Cogswell–Gibson methodBoth Cogswell (1972, 1978, 1981) and Gibson (1988) assumed that the entry

pressure drop 𝛿Pen across an area of converging flow, from a circular barrel of

radius Rb into a capillary die of radius R, was made up of two components, one

related to shear flow (𝛿Pen.S) and one related to extensional flow (𝛿Pen.E):

δPen = δPen.E + δPen.S (14.4)

Cogswell (1981) experimentally determined the total entry pressure loss 𝛿Pen by

the procedure of Bagley (1957). In a Bagley plot, the pressure drop 𝛿P is plotted

versus L/d at a constant value of the volume flow rate Q (m3/s), that is,

δP vs(L

d

)where Q = constant (14.5)

or at a constant value of the shear rate D (s−1)=4Q/𝜋R3, where L is the length,

d= 2R is the diameter and R is the radius of the tube, that is,

(δP) vs(L

d

)where D = constant (14.6)

In these plots, the intercept (L/d=0) gives the entry pressure drop 𝛿Pen at a given

value of Q (or D). Visibly, the Bagley plot provides data on the effect of the geom-

etry of the device; therefore, this effect cannot be ignored when the total entry

pressure drop is calculated.

The pressure drop due to shear flow associated with convergence is calculated

from

δPen.S = Qn[3n + 1

4n

]n [ 2K3n tan 𝛼

][1 −

(RRb

)3n]

(14.7)

where 𝛼 is the acute angle between the wall of the barrel and the axis of the tube.

The shear viscosity parameters K and n are calculated for Ostwald–de Waele fluids

from

𝜏 = KDn. (14.8)

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Extrusion 485

The pressure drop due to extensional flow associated with convergence is calcu-

lated from

δPen.E = Qm

(2KE

3m

)( tan 𝛼2

)m[

1 −(

RRb

)3m]

(14.9)

The extensional viscosity parameters KE and m are calculated for Ostwald–de

Waele fluids from

𝜏E = KEDm (14.10)

(The Cogswell equations and the Gibson equations relate to Ostwald–de Waele

fluids.)

The steps of the calculation are as follows:

1 From the Bagley plot, 𝛿Pen is determined.

2 Then 𝛿Pen.S is calculated with the help of K and n, which are determined from

shear rheological data.

3 From Eqn (14.4), 𝛿Pen − 𝛿Pen.S = 𝛿Pen.E is calculated.

4 Finally, from Eqn (14.9), the parameters KE and m are calculated by regression

analysis of ln(𝛿Pen.E) versus ln Q:

ln (δPen.E) = m ln Q + ln

{(2KE

3m

)( tan 𝛼2

)m[

1 −(

RRb

)3m]}

(14.11)

From the slope, m can be calculated (Q is known), and from the intercept,

ln{ }; KE is the only unknown, and thus it also can be calculated. (Step 4 can be

regarded a special method of rheometry for determination of the extensional

viscosity parameters.)

This method can be successfully applied up to die angles 𝛼 ≈ 45∘. In the region

10∘ <𝛼 < 45∘, both shear and extensional flows are present in some proportions.

If 𝛼 <10∘, shear flow is dominant. However, if 𝛼 > 45∘, materials form their own

convergence pattern (Cogswell, 1981); this is a characteristic feature for food

fluids, which have a relatively high yield stress. A special case is 𝛼 = 90∘, for which

Cogswell (1972) provided simple relations.

14.1.1.2 Gibson methodThe Gibson method uses another approach. The pressure drop due to shear flow

associated with convergence is calculated from

δPen.S = Qn[3n + 1

4n

]n[

2Ksin3n𝛼

3n𝛼3n+1

][1 −

(RRb

)3n]

(14.12)

where 𝛼 is in radians.

The pressure drop due to extensional flow associated with convergence is calcu-

lated from

δPen.E = QmKE

{( 23m

)[(sin 𝛼)(1 + cos 𝛼)

4

]m[

1 −(

RRb

)3m

+ Φ4m

]}(14.13)

where Φ= f(m, 𝛼) is a tabulated integral.

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486 Confectionery and chocolate engineering: principles and applications

Using these expressions, the calculation steps of the Gibson method are as

follows:

1 The shear viscosity parameters K and n are obtained from Equation (14.10)

and used for calculating 𝛿Pen,S from Equation (14.12).

2 From Equation (14.1): 𝛿Pen,E = 𝛿Pen − 𝛿Pen,S; 𝛿Pen is obtained from the Bagley

plot (14.5)

3 Calculating ln 𝛿Pen,E, the slope is m

4 Since m and 𝛼 [radian] are known, the value of Φ can be obtained from appro-

priate table, finally KE is obtained from the intercept.

The Gibson method is suitable for determining the extensional viscosity for the

full range of die angles up to 90∘ (= 𝜋/2 radian).

14.1.1.3 Empirical methodSteffe (1996) presented also an empirical method, according to which the exten-

sional viscosity may be estimated using a standard material. Assuming that the

shear contribution to the pressure loss is small, an average extensional viscosity

can be calculated. From Eqn (14.10),

𝜂E = KEDm−1 (14.14)

Assuming that m= 1, then

𝜂E = KE (14.15)

From Eqns (14.13) and (14.15), a simpler form for 𝛿Pen is obtained:

𝛿Pen.S =(

D𝜋R3

4

)𝜂EC1 (14.16)

That is, the average extensional viscosity is given by

𝜂E =CδPen

D(14.17)

where D= 4Q/𝜋R3 is the apparent wall shear rate and C is a constant.

It is assumed that the dimensionless constant C is a function of the system

geometry but independent of the strain rate and the rheological properties of the

sample. The numerical value of C could be estimated using a standard Newtonian

material with a known value of 𝜂E.

14.1.2 Pressure loss in the shaping of pastesMachikhin and Machikhin (1987, Chapter 6) discussed the case of flow in short

tubes for which the ratio of the length L to the diameter D is less than 10. This

is exactly the case in which a mass is shaped by extrusion. The total decrease in

pressure Δpt can be expressed as

Δpt = −Δph +∑

Δpvis +∑

Δpg + ΔpE + Δpkin + Δpin + Δprel (14.18)

Let us consider the various terms in this sum:

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Extrusion 487

Δph: This is the hydrostatic pressure, which helps the flow in machines with a

horizontal structure (the minus sign shows this fact).

ΣΔpvis: This term takes into account the viscous losses involved in front of the

matrices and in the matrix channels.

ΣΔpg: This term originates from the sudden geometrical change of the surface

and tubes of the extruder.

ΔpE: This term takes into account the pressure loss originating from extensional

deformation during the shaping process:

ΔPE = 𝜂E𝜀′E (14.19)

where 𝜂E is the extensional viscosity (Pa s) and 𝜀′VE is the extensional deforma-

tion rate (s−1).

Δpkin: This term takes into account the pressure loss associated with increasing

the kinetic energy of the mass that is being shaped.

Δpin: This term takes into account the pressure loss associated with accelerating

the mass in a non-steady state, that is, the pressure loss related to the inertia

of the mass.

Δprel: This term takes into account the pressure loss originating from pressure

relaxation in the mass:

Δprel = p0 − f (p0, t) (14.20)

where p0 is the initial pressure (at t= 0). The determination of Δprel is difficult,

and therefore the approximation p0 =Δpt/2 is generally used, which assumes

that p0 =Δpt/2 decreases to Δprel when the relaxation is stopped.

As a result, the following equation is obtained from Eqn (14.20):

Δpt

2=∑∑

Δp − f

(Δpt

2, t

)(14.21)

where Σ ΣΔp denotes the known terms on the right-hand side of Eqn (14.18).

Equation (14.21) can be solved for Δpt/2 if the function f is known.

For viscoplastic Bingham fluids, the pressure loss associated with shaping (Δp)

can be calculated for tubes of circular cross section:

Δp =(

2L𝜂Pl

R+ C1

)( 4Q

R3𝜋

)+

8L𝜏0

3R+ C2 (14.22)

where L is the length of the tube (m), 𝜂Pl is the plastic viscosity of the fluid that

is being shaped (Pa s), R is the radius of the tube (m), C1 is a material constant

(Pa s), Q is the flow rate (m3/s), 𝜏0 is the yield stress of the fluid (Pa) and C2

is a material constant (Pa). Machikhin and Machikhin (1987, Chapter 6) cited

some products for which the values of the constants are in the region 77≤ C1

(Pa s)≤ 2570 and 7850≤C2 (Pa)≤ 63 700.

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488 Confectionery and chocolate engineering: principles and applications

Example 14.1L= 0.4 m, R= 0.03 m, 𝜂Pl = 15 Pa s, 𝜏0 = 5 Pa, Q= 10−3 m3/s, C1 = 2000 Pa s and

C2 =50 000 Pa. From Eqn (14.22),

Δp =(

2 × 0.4 × 1.50.03

+ 2000)[

4 × 10−3

33 × 10−6 × 3.14

]+ 8 × 0.4 × 5

3 × 0.3+ 50000

≈ 1.46 × 105 Pa = 1.46bar

To determine the material constants, the following relationship is taken into

consideration:𝜕(Δp)𝜕Q

=(

2L𝜂Pl

R+ C1

)4

R3𝜋

Consequently, from a Bagley plot of Δp versus Q,

Slope =(

2L𝜂Pl

R+ C1

)4

R3𝜋(14.23)

and

Intercept =8L𝜏0

3R+ C2 (14.24)

The unknown material constants C1 and C2 can be calculated from the slope and

intercept, respectively.

14.1.3 Design of converging dieThe rheological properties of plastics used for moulding are similar to those of the

fluids used in the confectionery industry (e.g. Bingham or Ostwald–de Waele

fluids); consequently, knowledge from this field can be applied in the area of

confectionery.

Sors et al. (1981) analysed three cases; for simplicity, circular sections were

considered:

1 A section with a uniformly converging diameter (convex velocity diagram)

2 A section where the velocity increases in proportion to the distance travelled

(linear velocity diagram)

3 A section where there is a uniformly accelerating flow (concave velocity dia-

gram)

Any other profile can be referred back to a circular section by introducing the

hydraulic radius

rh = 2TK

(14.25)

where rh is the hydraulic radius, T is the area of the cross section and K is the

circumference of the cross section.

However, the following considerations need to be taken into account:

1 If identical inlet and outlet cross sections are assumed in all three cases, then,

naturally, the inlet and outlet velocities will be identical too.

2 In the case of a profile with a uniformly converging diameter, the flow veloc-

ity, starting from the inlet cross section, will first increase at a lower rate, and

then, on approaching the outlet, this rate will rapidly increase.

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Extrusion 489

3 If the flow velocity increases in proportion to the distance travelled, the diam-

eter of the profile will decrease at a fast rate in the vicinity of the inlet cross

section but will hardly decrease at all in the vicinity of the outlet cross section.

Thus, the profile is trumpet shaped.

4 In the case of a uniformly accelerating flow, the flow velocity will increase

rapidly at the inlet cross section, but the rate of increase will be less in the

vicinity of the outlet cross section. The section will converge steeply at the

inlet, while its convergence will be flat in the vicinity of the outlet section.

The longitudinal section is trumpet shaped in this case too.

Since the friction that arises in a flowing melt increases in proportion to the

velocity squared, it can be stated that a profile with a uniformly decreasing

diameter is very unfavourable, whereas the two trumpet shapes are much more

favourable.

Taking these aspects into account, the case of a uniformly accelerating flow

will be considered here.

Trumpet-shaped longitudinal sections can be plotted very simply (Fig. 14.1).

Length of extruder

4

3

2

P

60°

D/2 = 4.5d

d

1

10

0.1

0.2

0.3

0.4

0.5 Flowvelocity(n = 9)

1/y2

0.6

0.7

0.8

0.9

1.00 0.5 1.0Z

2 3 4 5 6 7

Figure 14.1 Plot of adaptor zone profile and flow velocity. Source: Sors et al. (1981).

Reproduced with permission from John Wiley & Sons.

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490 Confectionery and chocolate engineering: principles and applications

If the inlet diameter is D, the outlet diameter is d (n=D/d) and the diameter at

a distance z from the diameter D is denoted by y, then

y = D − (D − d)zL

(14.26)

where z=ZL. It is known that the velocity of a uniformly accelerating motion at

a cross section at a distance of z= ZL from the inlet cross section is

vz = v0 +√

2az (14.27)

where a (a constant) is the acceleration. Without giving further details, we state

that a function f= f(n; z; d) can be obtained, so that

y = nd√1 + (n2 − 1)

√Z

= Kd (14.28)

and K = n/√

(1 + (n2 − 1)√

Z) is constant if n and Z are fixed.

First the value of n=D/d is determined (in the example illustrated in Fig. 14.1,

n= 9) and measured at a certain point on the y-axis of a coordinate system (see

Fig. 14.1). From this point, taking the viscosity of the melt into consideration,

a straight line is drawn at an angle of 120–150∘ to the positive direction of the

x-axis (i.e. 60–30∘ to the positive direction of the y-axis). (An angle of 150∘ is

used with higher viscosities and 120∘ at lower viscosities, according to Sors et al.

(1981).) Starting from the intersection point of this straight line and the straight

line y= 1 (=d), both straight sections are divided into an equal number of parts

(up to seven parts in the direction of the +x-axis), and the points with opposite

numbers are connected:

x-axis y-axis

6 1

5 2

4 3

These connecting lines cover a curve of second order.

The lower diagram in Figure 14.1 shows the value of 1/y2 as a function of Z if

n is fixed (in the present example, n= 9).

For more details, see Sors et al. (1981, Section 2.2) and Sors and Balázs (1989).

The latter gives a collection of examples and designs.

Machikhin and Machikhin (1987, pp. 219–221) dealt with dimensioning in

the case of a fluid of Ostwald–de Waele type as well and with cases where the

extrusion die was of quadrangular section and the shape of the extruder was

conical. This discussion started from the fact that, according to Prager and Hodge

(1956), the pressure acting in the direction of the z-axis can be calculated from

Δp =(

1 + 𝜋

2

)𝜏0 (14.29)

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Extrusion 491

The surface of the velocity distribution is a rotational paraboloid in a cylinder of

radius R− 𝛿, where the width of the laminar boundary layer is

𝛿 =𝜂Plu

𝜏0

(14.30)

and u is the linear velocity of the mass at the surface of the boundary layer.

This method assumes rotation-free flow and is intended to calculate conditions

such that the linear velocities of the mass at the surface of the boundary layer

and inside the die are the same. The cross section of the die proposed is a rota-

tional parabola of third degree. However, while the trumpet profile proposed by

Sors et al. (1981) is biconcave, Machikhin and Machikhin (1972, pp. 219–221)

proposed a biconvex profile.

14.2 Feeders used for shaping confectionery pastes

14.2.1 Screw feedersSeveral types of feeders are frequently used in the confectionery operations of

shaping by extrusion, transportation and dosage of masses.

Machikhin and Machikhin (1972, pp. 221–229) discussed these questions in

detail. Neglecting the complicated hydrodynamic calculations, the results can be

summarized as follows. The flow rate of a spiral feeder can be calculated from

Q =[𝜋2D2nH sin𝜑 cos𝜑

2

]Fd𝜓 −

[𝜋DH3sin2𝜑

12𝜂

] [p2 − p1

L

]Fa (14.31)

where Q is the flow rate or transport output (m3/s), n is the rate of revolution

(s−1), D is the outside diameter of the screw (m), H is the depth of the thread

(m), 𝜑 is the ascent angle of the thread (radians), Fd is a correction coefficient

depending on the shape of the thread, 𝜓 is a correction coefficient taking into

account the non-Newtonian behaviour of the fluid, 𝜂 = 𝜂Pl + 𝜏0/𝛾 ′ is the dynamic

viscosity of the fluid (Pa s) (where 𝛾 ′ is the shear rate), p2 is the pressure in the

screw (Pa), p1 is the pressure outside (Pa), L is the length of the screw and Fa is

a correction coefficient related to the shape of the flow.

The corresponding values of H/W, Fd, Fa and 𝜓 have been tabulated (see

Machikhin and Machikhin, 1972, p. 219, Table 93). The ratio H/W relates to

tubes of square cross section (where H=height and W=width).

Example 14.2Let us calculate the flow rate if the parameters of the screw are D= 0.1 m,

H=0.05 m, 𝜑= 20∘, 𝜂 =10 Pa s, p2 − p1 =3× 103 Pa, L= 0.4 m, n=3 s−1, Fa =0.74,

Fd =0.78 and 𝜓 =0.697:

Q =[𝜋2D2nH sin𝜑 cos𝜑

2

]Fd𝜓 −

[𝜋DH3sin2𝜑

12𝜂

] [p2 − p1

L

]Fa

= 3.142 × 10−2 × 3 × 5 × 10−2 × 0.342 × 0.9397 × 0.6972∕2

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492 Confectionery and chocolate engineering: principles and applications

− (3.14 × 10−2 × 125) × 10−6 × 0.3422 × 3 × 103 × 0.74∕(12 × 10 × 0.4)

= (16.564 − 2.123) × 10−4 m3∕s = 1.4441 × 10−3 m3∕s

For a twin screw, the flow output can be calculated from the formula

Q = n(2𝜋 − 𝛼)(𝜋D tan𝜑 − b)(D − H)H −(2𝜋 − 𝛼)D𝛿3 tan𝜑(p2 − p1)

12𝜂b(14.32)

where b is the width of the screw in the axial direction (m), 𝛿 is the size of the

gap (m) and 𝛼 is the central angle, for which

cos 𝛼 = 1 − 2HD − H

+ H2

2(D − H)2. (14.33)

Example 14.3Let us calculate the output of a twin screw which, in addition to those given

in Example 14.2, has the parameters b=5× 10−3 m, 𝛿 =10−3 m (tan 20∘ = 0.364)

and cos 𝛼 =1− 2×0.05/0.05+0.052/(2× 0.052)=−0.5→ 𝛼 = 120∘ = 2𝜋/3:

Q = 3 × (2𝜋 − 2𝜋∕3)(𝜋 × 0.1 × 0.364 − 5 × 10−3) × 0.05 × 0.05 − (2𝜋 − 2𝜋∕3)

× 0.1 × 10−9 × 0.364 × 10−3∕(12 × 10 × 5 × 10−3) = 3.42 × 10−3 m3∕s

14.2.2 Cogwheel feedersThe benefits of a cogwheel feeder are uniform feeding, a high pressure and simple

construction. For the materials used in the food industry, the vacuum created by

the feeder is insufficient to supply the material into the space between the cogs,

and therefore a constrained additional supply is applied (Machikhin and Birfeld,

1969). The usual revolution rate is 5–20 min−1.

The efficiency coefficient is defined by the formula

𝜑 = 1 −Qg + Qf

Qt

(14.34)

where Qg is the loss associated with the gap (kg/min), Qf is the loss associated

with the feeder (kg/min) and Qt is the theoretical output of the feeder (kg/min).

For dessert masses, the dependence of the efficiency on the revolution rate n

(min−1) is given by the equation

𝜑 = 0.8 + 0.017(min)2n − 0.0009(min)n2 (14.35)

The theoretical output can be calculated from a formula given by Yudyin

(1964):

Qt = 2𝜋𝜌bnm2(z + sin2𝛼) × 10−6 (14.36)

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where 𝜌 is the density of the mass (kg/m3), b is the width of the cogs (mm), n is

the revolution rate (min−1), m is the modulus (mm), z is the number of cogs and

𝛼 is the coupling angle of the cogs.

Example 14.4The parameters of a cogwheel feeder are 𝜌= 1200 kg/m3 (the density of the

mass), b= 30 mm, n=8 min−1, m=3 mm, z= 15 and 𝛼 = 20∘ (sin 20∘ = 0.3420).

The output (see Eqn 14.36) is

Qt(kg∕min) = 2 × 3.14 × 1200 × 30 × 8 × 32 × (15 + 0.34202) × 10−6

= 738.21kg∕min

The optimal region of the feeding efficiency 𝜑 is n= 8–15 min−1; the maximum

of 𝜑 can be obtained when n= 9.5 min−1.

For more details, see Machikhin and Machikhin (1987, Chapter 6).

14.2.3 Screw mixers and extrudersScrew-type mixers, or extruders, of which there are numerous design config-

urations, are widely employed for extrusion of various confectionery products

consisting of fondant mass, fats, milk powder, soy meal, etc. These products con-

tain some proportion of molten phase, and from this point of view, both fats

and fondant mass behave similarly: they tend to melt under the effect of heat or

pressure, and the resulting molten phase forms the liquid phase of the products

in question. (The word fondant means melting, although the phenomenon that

takes place in fondant mass as a result of the effect of heat is actually solution.)

The main application area of extruders in the confectionery industry is shaping

of rope in order to produce centres for coated products.

Mixing and material extrusion can be accomplished in single or double rotating

screw machines.

In single-screw mixers, the mixing quality is determined by the total shear

deformation for a given material volume. The total shear deformation may be

increased by decreasing the height of the screw channel, by varying the angle

of pitch of the helix and/or by increasing the countercurrent or sinking through

an increase in the head resistance.

There are two types of flow in the channel of a single-screw mixer: longitudinal

(along the helical axis of the channel) and transverse (circulatory). Bernhard

(1962) and Lukach et al. (1967) recommended Moore’s equation, among others,

for determining the shear strains. The shear strain parallel to the screw axis (in

the z direction) is

Dz =(L

h

){A − B

1 − a

}(14.37)

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494 Confectionery and chocolate engineering: principles and applications

where L is the length of the screw, h is the height of the screw channel, 𝜓 is the

helix angle, a is the ratio of the countercurrent rate to the rate of forced flow and

A and B are dimensionless functions of the ratio y/h of the base and height of the

thread channel. The shear strain perpendicular to the screw axis is

Dx =(L

h

){A

tan𝜓− B tan𝜓

1 − a

}(14.38)

By integrating these equations over the cross-sectional area of the flow, an aver-

age value of the shear strain is obtained.

Twin-screw mixers are more effective because they process material by the action

of intermeshing screws. The material streamlines are interrupted when they pass

through a zone of low velocity gradient with low mixing effects. However, over-

all, the bulk of the material volume enclosed between the wall of the casing and

the screw surfaces undergoes a highly efficient form of mixing. A successful mod-

ification of the screw mixer has working members comprising one screw and an

interrupted helix (teeth and gaps are located on the helix). The material between

the meshing teeth is thus subjected to longitudinal, axial and radial shear.

Another variation is the KO kneader, which can handle light- and medium-stiff

pastes. In this design, a worm runs along a horizontal casing fitted with teeth.

The worm is interrupted at regular intervals by gaps. The shaft not only turns

but also reciprocates in the axial direction, so that the teeth periodically clean

the gaps on the casing. This periodic reciprocation minimizes the material flow

in one direction only. However, the intensive shearing strain in this machine

is periodic, and the gaps tend to reduce the effective shear stress. Large surface

areas of material are exposed as a result of the shear stresses generated by large

torques. This limits the viscosity or rigidity of material to be mixed.

For the theoretical principles of design, the work of Cheremisinoff (1988,

pp. 828–857) can be recommended, from which the calculation of dosing-zone

capacity and head resistance presented here has been taken.

The volumetric flow capacity through the head is directly proportional to the

pressure drop and inversely proportional to the material’s dynamic viscosity:

Q =KΔp

𝜂(14.39)

where K (with dimensions of volume) is a coefficient depending on the head

geometry. On the other hand, the effective material flow is the difference

between the flow injection and the countercurrent flow+ leakage:

Q = 𝛼n −(Δp

𝜂

)(𝛽 + 𝛾) (14.40)

where n is the rotation rate (rot/s), 𝛼 is the coefficient of the injection flow, 𝛽

is the coefficient of the countercurrent flow and 𝛾 is the coefficient of leakage.

These coefficients (with dimensions of volume) can be determined for screws of

both variable pitch and variable depth.

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Combining Eqn (14.29) with Eqn (14.30), we obtain

Q = 𝛼KnK + 𝛽 + 𝛾

(14.41)

The capacity of a screw mixer can be readily determined from information

about K for various screw-mixer heads. For each head, there is an optimum

screw-channel geometry that provides the maximum capacity. For details of the

design of heads and the optimization of the working conditions of an extruder,

see Cheremisinoff (1988, pp. 840–843).

Example 14.5Let us calculate the values of K, 𝛼, 𝛽 and 𝛾 if Δp= 5×105 Pa, 𝜂 = 50 Pa s,

Q=10× 10−6 m3/s, n= 4 s−1, 𝛽 =0.1K and 𝛾 = 0.02K.

According to Eqn (14.40),

Q = 10 × 10−6 m3∕s = K × 5 × 105 Pa∕50Pas

that is, K= 10−9 m3 → 𝛽 = 0.1×10−9 m3 and 𝛾 =0.02×10−9 m3.

According to Eqn (14.41),

Q = 10 × 10−6m3∕s = 𝛼nKK(1 + 0.1 + 0.02)

or

𝛼n = 1.12 × 10−5 m3∕s → 𝛼 = 0.28 × 10−5 m3

14.2.3.1 Modelling of single- and twin-screw mixersSilin (1964) applied a similar theory to develop design correlations for screw

mixers. The study of the flow was based on the following dimensionless relation:

Eu = CRen(l∕d)m (14.42)

where Eu=Δp/𝜌v2 (the Euler number); Re= dv𝜌/𝜂 (the Reynolds number); Δp is

the pressure drop in the channel; 𝜌 is the density of the material melt; v is the

average velocity of the material; 𝜂 is the dynamic viscosity of the material; l and d

are the length and inner diameter, respectively, of the screw; and C is a constant.

Further references are Janssen and Smith (1975), Spreckley (1987), Treiber

(1988) and Klasen and Mewes (1991).

14.3 Extrusion cooking

Extrusion cooking is a process of forcing a material to flow under a variety of

conditions through a shaped hole (die) at a predetermined rate to achieve various

products (Dziezak, 1989).

Extrusion cooking of foods has been practised for over 50 years. Initially, the

role of an extruder was limited to mixing and forming macaroni and ready-to-eat

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496 Confectionery and chocolate engineering: principles and applications

(RTE) cereal pellets. Today, the food extruder is considered as a high-temperature

short-time bioreactor that transforms raw ingredients into modified intermedi-

ate and finished products (Harper, 1989). Extrusion cooking technology is used

today for the production of pasta, breakfast cereals, breadcrumbs, biscuits, crack-

ers, croutons, baby foods, snack foods, confectionery items, chewing gum, tex-

turized vegetable protein (TVP), modified starch, pet foods, dried soups and dry

beverage mixes (Linko et al., 1983). For the benefits of extrusion cooking, see

Wiedmann and Strobel (1987).

Three major types of extruders are used in the food industry: piston extruders,

roller-type extruders and screw extruders (Thorz, 1986).

A piston extruder can consist of a single piston or a set of pistons that deposit

a precise amount of product onto conveyors or trays. Piston extruders are pri-

marily used for forming product shapes and are used in both confectionery and

bakery production facilities. One example of the function of a piston extruder

is where cake, cookie or muffin dough is deposited onto a sheet with the use

of a wire cutter, or into individual cups in an already shaped pan, and is then

conveyed to an oven for baking. Another example is in the depositing of fillings

into doughnuts, cupcakes and chocolate-type products.

Roller extruders are used to form the shape of a product. A roller extruder con-

sists of two counterrotating rollers that turn at similar or differential speeds. This

process is also referred to as calendering in the dough industry. The roller surfaces

can be smooth to create a long thin strip or can be perforated to form the dough

into shaped products. The roller extruder can be altered to control the width of

the layer of product moving between the rollers. Products such as crackers and

hard cookies can be formed by creating the desired shape within the rollers and

conveying the dough between the rollers. The dough is forced into the pattern

on the roller and is then conveyed to an oven for baking. Excess dough can be

collected and reused. Products such as graham crackers and saltines are created

using smooth roller systems to form thin layers.

Screw extruders utilize single, twin or multiple screws rotating within a metal

cabinet called the barrel. The screws convey the material forward and through a

small orifice called a die, which can take many shapes and sizes. Several external

parameters such as screw speed and configuration, the temperature of the barrel,

the size and shape of the die and the length of the barrel affect the properties of

the final product. The first food application of extrusion occurred in the 1800s

in the production of ground sausage and meats, stuffed into natural casings. The

pasta press was introduced in 1935 for forming and shaping pasta dough.

Screw extruders providing both cooking and forming capabilities came in

around 1950 for the production of animal feeds. Because of the demand for

pre-cooked cereals and starches in the 1960s, large machines were required.

These larger cooker extruders led to new applications in RTE cereals and snack

products, as well as expanding the dry-pet-food market. Pre-cooked infant

foods were also developed. Improvements to the cooker extruder in the 1970s

led to the development of soft, moist pet foods and co-extrusion; the use of

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two extruders, one for cooking and another for forming, was developed. The

1980s saw expanded use of the twin-screw extruder owing to its versatility and

productivity (Harper, 1989). For further details, see Dziezak (1989) and Gray

and Chinnaswamy (1995).

14.4 Roller extrusion

14.4.1 Roller extrusion of biscuit doughsBiscuit doughs are dense solid–liquid pastes that exhibit complex rheological

behaviour. The sheeting of doughs using roll mills is a prominent operation in the

production of biscuits. Rolling is well understood in the context of many opera-

tions: the body of literature describing the production of metal sheets is consid-

erable (e.g. Orowan, 1943), and the rolling of polymer melts, called calendering,

has also been studied extensively. The roller extrusion of food materials such as

doughs, however, is a broad area in which current practice still frequently relies

on approximations and pilot plant testing. Castell-Perez (1992) and Rao (1992)

described the sizeable gap that exists between the material models of practical

use in the analysis of forming processes and the observations of the complex

history-dependent response of the materials themselves.

First, Levine et al. (2002) developed a model describing the two-dimensional

calendering of finite-width sheets. The main objective of this work was to take

into account both the lengthwise and the widthwise flow occurring during the

processing of viscous polymeric materials, the rheology of which can be char-

acterized by flow curves with a power law. The model appropriately describes

two-dimensional calendering and predicts reasonably well the sideways defor-

mation of the calendered material. Results show that as narrower and thicker

sheets are fed to the rollers, the sideways spread of the sheet increases. The

same effect is observed with larger-diameter rollers. Furthermore, as the feed

becomes narrower, the maximum pressure exerted on the material, as well as the

forces developed and the power consumed per unit width, decreases. Although

the model does not describe the real flaking process, which is characterized by

unsteady-state conditions, it could be used as a first approximation to solve this

problem. For the mathematical details, see Levine et al. (2002).

Peck et al. (2006) studied the roller extrusion of short and hard biscuit doughs.

Short doughs are relatively crumbly materials because of their high percentage

of fat (25–30 wt% of the flour or more) and are poorly cohesive and fairly inelas-

tic. Hard doughs are more elastic and glutinous because they contain less fat and

are mixed more aggressively to develop the three-dimensional network of the

dough. In this work, Peck et al. (2006) studied the analysis of hot rolling of met-

als given by Orowan (1943), which was used to describe the rolling behaviour

of stiff ceramic pastes with moderate success. Peck et al. determined that this

analysis could not be used for calendering, because as the rolled sheet exits the

nip (the narrowest point between the rollers), the thickness of a hot metal sheet

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498 Confectionery and chocolate engineering: principles and applications

does not change, unlike that of a biscuit sheet, which increases. In their experi-

ments, the measured exit sheet thickness was slightly larger than the estimated

nip separation (e.g. by up to 6%), which could be the result of elastic effects.

Although the standard plasticity model for sheet metal was modified to include

strain rate dependence, the behaviour of neither of the doughs could be ade-

quately described by this model.

In response to the problems encountered in characterizing these materials,

Benbow and Bridgwater (1993) developed an approximate method of material

characterization via capillary extrusion. In this approach, the total pressure drop

required to extrude a soft solid is composed of two terms. The first term repre-

sents the work due to the paste undergoing quasi-plastic deformation associated

with the contraction. The second term represents the work due to the effects

of stresses in the region of the die surface. The Benbow–Bridgwater approach

therefore describes the deformation behaviour of a soft solid in terms of two

distinct properties of the material, namely, the bulk deformational response and

the wall slip response.

The Benbow–Bridgwater analysis assumes that shearing of the dough occurs

only at the die wall. However, internal shearing may be expected as the wall yield

stress approaches the shear yield stress of the dough. Horrobin (1999) provided

a relation for the uniaxial yield stress for the system, 𝜎y ≈0.82𝜎0 (assuming that

the extrusion pressure does not depend on the extrudate velocity), where y is

perpendicular to the direction x of the sheet velocity. Applying a von Mises yield

criterion, the plug flow assumption would be therefore be valid if(

0.82√3

)𝜎0 > 𝜏0 + 𝛽V n (14.43)

(the die wall shear stress term), where 𝛽 is a parameter in the second term of

the Benbow–Bridgwater equation, V is the mean velocity of the material and n

is the index in the second term of the Benbow–Bridgwater equation, used with

V to introduce a strain rate dependence of the yield and shear stresses.

If a value of 𝜎0 = 0.1 MPa is employed, then internal shearing is unlikely, even

at the highest extrudate velocity. However, the wall yield stress term rises to

about 80% of the bulk shear yield stress; therefore, it may be concluded that

internal shearing could be having an influence, and so an alternative character-

ization approach, such as that of capillary analysis, must be considered.

A power-law-fluid fit makes a corresponding calculation for the die entry

region during extrusion possible. The key principle behind this analysis is the

separation of the die entry pressure drop into two components, the first due to

the simple shear viscosity and the second to the extensional viscosity (Steffe,

1996), by using the Gibson equations (see Eqns 14.13 and 14.14).

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Extrusion 499

The rheological characteristics of the two doughs were quantified by a

power-law model. The results indicated that the doughs were not ideally suited

to a quasi-plastic analysis. The power-law parameters varied noticeably between

the doughs, but both were strongly shear thinning (power-law shear indices of

0.25 and 0.5) with large extensional viscosities, as the relatively high Trouton

numbers (45–141) also show. It was ascertained that the underpredictions of the

power-law model were in contrast to those provided by the modified plasticity

approach. In the die entry region of the ram extrusion tests, the material

undergoes a large reduction in cross-sectional area (by over 98%), and so its

extensional response governs the extrusion behaviour. Therefore, the plasticity

model predicts larger values than those predicted by the power-law-based fluid

mechanics model.

The rolling of the two doughs was modelled by Peck et al. (2006) using the

analysis of Levine (1996) incorporating a power-law rheology. The model predic-

tions were too low. The reasons can be summed up: thus as the high extensional

viscosities of the doughs acted to increase the measured roller torque and sep-

arating force, in line with observations, the deviation of the materials from a

power-law-based description became evident from the impossibility of generat-

ing power-law parameters to satisfy both the torque and the force comparisons

simultaneously.

The characterization of doughs requires further work for full use to be made

of a more complete model of the operation. In addition, a finite element solu-

tion such as that developed by Levine et al. (2002), which includes shear and

extensional deformation terms, seems to be an area that would benefit from

further work.

14.4.2 Feeding by roller extrusionFeeding by roller extrusion was discussed by Machikhin and Machikhin (1987,

Chapter 6). For calendering, Ardichvili gave the following relation for the mass

flow Q considered as the velocity of a plane (cited by Machikhin and Machikhin,

1987, Section 6.4):

Q(m2∕s) = vh −(

dp

dx

)h3

12𝜂(14.44)

where v (m/s) is the circumferential velocity of the cylinders, h (m) is the gap

between the cylinders, dp/dx (Pa/m) is the pressure gradient created by the cylin-

ders at right angles to the direction of movement of the plane and 𝜂 (Pa s) is the

dynamic viscosity of the material rolled.

The feeding capacity is given by

Q(m2∕s) = vhminK =vhminQact

Qther

(14.45)

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500 Confectionery and chocolate engineering: principles and applications

where hmin (m) is the minimum gap, Qact (m2/s) is the actual capacity and Qther

(m2/s) is the theoretical capacity.

When the machine is fed with bread dough, the following relations between

the driving moment M (N m/s) and the other parameters can be used:

M vs hmin∶ M = a1hmin exp(−a2hmin) (14.46)

M vs n∶ M = b1 + b2n (14.47)

M vs L∶ M = c1 + c2L (14.48)

where a1, a2, b1, b2, c1 and c2 are coefficients of appropriate dimension, which are

experimentally determined; n (s−1) is the rotation rate; and L (m) is the width of

the matrix.

Further reading

Almond, N. et al. (1991) Biscuit, Cookies and Crackers, Elsevier Applied Science, London.

BEPEX/HUTT. Technical brochures.

Berman, G.K., Machikhin, Y.A. and Lunyin, L.N. (1972) Flow of visco-plastic food mass in

extruder (in Russian). Khlebopekarnaya i Konditerskaya Promyshlennost, 3, 18–20.

Bloksma, A.H. (1990) Dough structure, dough rheology and baking quality. Cereal Foods World,

35 (2), 237.

Biscuit and Cracker Manufacturers Association (1970) The Biscuit and Cracker Handbook, Biscuit

and Cracker Manufacturers Association, Chicago, IL.

Ellis, P.E. (ed.) (1990) Cookie and Cracker Manufacturing, Biscuit and Cracker Manufacturers Asso-

ciation, Washington, DC.

Faridi, F. (ed.) (1994) The Science of Cookie and Cracker Production, Chapman and Hall, New York.

Georgopoulos, T., Larsson, H. and Eliasson, A.-C. (2004) A comparison of the rheological prop-

erties of wheat flour dough and its gluten prepared by ultracentrifugation. Food Hydrocolloids,

18 (1), 143.

Hasegawa, T. and Nakamura, H. (1991) Experimental study of the elongational stress of dilute

polymer solutions in orifice flows. Journal of Non-Newtonian Fluid Mechan, 38, 159–181.

Keleb, E.I. (2004): Continuous agglomeration processes using a twin screw extruder, PhD theses,

Al-Fateh University, Libya, Laboratory of Pharmaceutical Technology, Gent.

Kulp, K. (ed.) (1994) Cookie Chemistry and Technology, American Institute of Baking, Kansas.

Letang, C., Piau, M. and Verdier, C. (1999) Characterization off wheat flour-water doughs. Part

I: Rheometry and microstructure. Journal of Food Eng, 41 (2), 121.

Manley, D. (1998) Biscuit, Cookie and Cracker Manufacturing Manuals (Vol. 1: Ingredients; Vol.

2: Biscuit Doughs; Vol. 3: Biscuit Dough Piece Forming; Vol. 4: Baking and Cooling of Biscuits;

Vol. 5: Secondary Processing in Biscuit Manufacturing; Vol. 6: Biscuit Packaging and Storage),

Woodhead, Cambridge.

Smith, W.H. (1972) Biscuit, Crackers and Cookies, Applied Science Publishers, London.

Sollich. Technical brochures.

Wade, P. (1988) Biscuit, Cookies and Crackers, Elsevier Applied Science, London.

Whiteley, P.R. (1971) Biscuit Manufacture, Applied Science Publishers, London.

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CHAPTER 15

Particle agglomeration:instantization and tabletting

15.1 Theoretical background

15.1.1 Processes resulting from particle agglomerationIn studying particle agglomeration, Rumpf (1974) performed fundamental inves-

tigations. The present discussion of the theoretical background is to a great extent

based on his results.

Particle agglomeration (or aggregation) is the direct mutual attraction between

particles (e.g. atoms or molecules) via van der Waals forces or chemical bonding.

When particles in fluid collide, there is a chance that they will attach to each

other and become a larger particle. There are three major physical mechanisms

of formation of aggregates: Brownian motion, fluid motion forced by shear and

differential settling forced by gravitation. Table 15.1 summarizes the binding

mechanisms and technical operations for dry and wet agglomeration.

The practical ways of forming agglomerates are the result of formation of solid

bridges:

1 By sintering: molecular diffusion caused by thermal effects

2 By chemical reactions

3 By melting in the case of thermoplastic materials

4 By additives (e.g. limestone in ore briquettes)

5 By crystallization of soluble materials

If an elastic material of unit cross-sectional area (1 m2) is subjected to a tensile

force and as a result it breaks, two new surfaces will be created. If both sides

of the broken material are of the same composition, then the work of cohesion is

defined as

Wcoh(N m∕m2) = 2𝛾 (15.1)

where 𝛾 (N/m) is the surface tension of the material.

In the situation in which two dissimilar materials of unit cross-sectional area

are in intimate contact, there are intermolecular forces present that are lost when

the materials are separated, that is, an interfacial energy may have been present

before the materials were split apart. As this energy is lost after the two surfaces

are separated, we must subtract it from the energy used to create the two new

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Table 15.1 Binding mechanisms and technical operations of dry and wet agglomeration.

Binding mechanism Operation Dry Wet

van der Waals forces Agglomeration in dispersion or in bulk × ×Electrostatic forces Building up agglomerate in dispersion or

in bulk

× ×

Fluid bridges, capillary forces,

binders

Shaping by extrusion ×Shaping rope by extrusion × ×Compression by cylinders ×Tabletting ×

Bridges of solid particles Drying × ×Mechanical interlocking Heating (plastifying, sintering, etc.) × ×

Source: Rumpf (1974). Reproduced with permission from John Wiley & Sons.

surfaces according to the Dupré equation:

Wadh(N m∕m2) = 𝛾1 + 𝛾2 − 𝛾12 (15.2)

where Wadh (N m/m2) is the work of adhesion, 𝛾1 and 𝛾2 are the surface tensions

of the two materials created by splitting and 𝛾12 is the interfacial tension (surface

energy) of the material before splitting.

15.1.1.1 Capillary forces in freely moving fluid surfacesFirst, wet and dry aggregation must be distinguished.

Three cases of wet aggregation were discussed separately by Rumpf (1958a,b):

1 Fluid bridges exist between the solid particles.

2 Capillary forces due to fluid surfaces in the holes between the particles cause

aggregation.

3 Fluid droplets saturated with solids attempt to unite in order to provide stabi-

lization.

Let P be a point on a curved surface of a freely moving fluid, the surface tension

of which is 𝛾, and let the surface at this point be characterized by two circles of

radii R1 and R2 which are in planes perpendicular to each other. The pressure

difference at point P is defined by the Laplace equation:

Δp = 𝛾

(1R1

+ 1R2

)(15.3)

If both radii are oriented towards the inside of the curved (concave) surface, their

signs are positive, and the force generated is oriented towards the inside of the

surface. If the signs are different because the orientations of the radii are opposite

(i.e. we have a saddle surface), then Δp is decreased.

In Case 1, the capillary forces are oriented towards the fluid surface at the

solid–fluid–gas interface, and this additionally involves a decreased pressure in

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Particle agglomeration: instantization and tabletting 503

the network of fluid bridges. Both of these effects cause an attraction between

the solid particles.

In Case 2, the holes between the solid particles are saturated with fluid, and

the capillary forces of the fluid affect the surface of the granulate (the entire

assembly of particles) only. However, since the fluid surface is concave (viewed

from the gas side) around the particles, attractive forces of a certain strength bond

the particles together.

In Case 3, the fluid surface is convex. Consequently, and in contrast to Case

2, the binding forces are lost, and the surface tension is the only force holding

the droplets together. As a result of the effect of this surface tension, two fluid

droplets are inclined to unite.

15.1.1.2 Cohesion and adhesion without freely moving fluid surfaces

1 Bonds by viscous binder. Since no equilibrium of the forces defined by the Laplace

equation can be involved in the case of viscous fluids, their effect is not impor-

tant. However, the binding forces of binders exceed that defined by the Laplace

equation; additionally, some binders harden later.

2 Bonds by adsorption layers. An adsorption layer of water can be established

by a high pressure (e.g. during briquetting), which is not thicker than 30 Å

(30× 10−10 m). The attraction between such layers is rather strong.

15.1.1.3 No material bridges between solid particles

1 Molecular forces. The effective distance of covalent forces is very short; therefore,

they play practically no role in aggregation. However, van der Waals forces,

with a range of ca. 100 Å (=10−8 m), have some effect.

2 The effect of electrostatic forces must not be entirely neglected in studying aggre-

gation.

15.1.1.4 Mechanical interlockingThe surfaces of solid particles are not smooth and are full of lock and key sites at

which they can be linked together. Adhesion stimulates such couplings.

15.1.2 Solidity of a granuleThe solidity of a granule is characterized by a tensile strength 𝜎t related to the

mean cross-sectional area of a granulate consisting of particles. It is supposed

that:

• The number of particles in the cross section is high.

• The particle size distribution in both the cross-sectional area and the entire

granulate is the same.

• A representative mean binding force of effective size H may characterize the

solidity of the granule.

The following calculations relate to globular particles of various sizes, which

the granule is assumed to be composed of.

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504 Confectionery and chocolate engineering: principles and applications

According to Rumpf (1974),

σt =(1 − 𝜀)kH

𝜋d2≈ 2H

d2(15.4)

where 𝜎t is the tensile strength; 𝜀 is the fraction of hole volume in a granule

(0<𝜀< 1); k is the coordination number, indicating how many neighbouring

particles are in contact with the particle studied; H is a representative binding

force; and d is the diameter of a globular particle.

Equation (15.4) can be applied to the most frequently encountered values of

these parameters.

15.1.3 Capillary attractive forces in the case of liquid bridgesAccording to Batel (1956), a good approximation can be obtained from

the formula

H ≈ (2.2 − 2.7)𝛾d (15.5)

and

𝜎t =2.2(1 − 𝜀)k𝛾

𝜋d(15.6)

On the basis of this, Rumpf (1974) recommended

𝜎t ≈4.4𝛾

d(15.7)

Example 15.1In the case of water, 𝛾 = 72 dyn/cm=72×10−5 N/(10−2 m)= 72×10−3 N/m.

If d= 1 μm= 10−6 m, then 𝜎t ≈ 4.4×72×103 N/m= 3.168×105 N/m – this is a

considerable value.

Figure 15.1 demonstrates the effect of the distance between the particles. In

a model with two spherical particles of diameter d separated by a distance a,

the central angle of the bridge is 2𝛽, and the contact angle is 𝛿 if the surface

tension of the fluid is 𝛾. The surfaces of the particles are assumed to be entirely

smooth.

The variables in the plot are two dimensionless numbers, H/d𝛾 plotted versus

a/d. Along each of the curves, Vliq/Vsol is constant (where Vliq is the volume of

the liquid bridge and Vsol is the volume of the solid particles). The intercept on

the H/d𝛾 axis relates to the values when a/d→0; this gives the maximum value

of H. In the case of contact between the particles, a= a0 ≈ 4 Å and H=Hmax (for

particles with a smooth surface).

15.1.4 Capillary attractive forces in the case of no liquidbridges

The surface of the solid particles is saturated with fluid, but it retains its concave

form. The decreased pressure binding the particles together is determined by

pt =𝛾

m(15.8)

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Particle agglomeration: instantization and tabletting 505

3.0

2.5

2.0

1.5

1.0

0.5

0

0 0.05

5 × 10–5

10–4

0.00050.001

0.005

0.05

0.01

0.1

H Hd

0.10

a/d

H/dγ

0.15 0.30

a

δ

βd

Figure 15.1 Effect of distance between particles. The curves are labelled with values of

Vliq/Vsol; see text for details. Source: Rumpf (1974). Reproduced with permission from John

Wiley & Sons.

where m= 𝜀/[S(1− 𝜀)] is the mean hydraulic radius. Here, S is the specific surface

area of the particles per unit volume. For spheres of radius r,

S = 4𝜋r2

4𝜋r3∕3= 3

r= 6

d(15.9)

As a result,

pt =6𝛾(1 − 𝜀)

𝜀d(15.10)

However, the tensile strength is dependent on the proportion of solid matter:

𝜎t = 𝜀pt = 𝛾(1 − 𝜀)S (15.11)

For globular particles,

𝜎t =6𝛾(1 − 𝜀)

d(15.12)

A comparison of the two effects represented by Eqns (15.6) and (15.11) can

be made as follows:

𝜌 = 𝜎t

(fluid bridges)σt(saturation)

= Sd𝜋2.2k

(15.13)

Since in general k𝜀≈3.1 (constant),

𝜌6𝜋𝜀

3.1 × 2.2≈ 2.75𝜀 (15.14)

Consequently, this ratio is proportional to the volume of holes relative to the

particles.

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506 Confectionery and chocolate engineering: principles and applications

15.1.5 Solidity of a granule in the case of dry granulationWhereas in wet granulation the range of the particle size distribution is about

1–100 μm and the characteristic size (60–80%) is about 60 μm, in dry granulation

this range is that of very fine powders (particle sizes<1 μm), and the applied

pressure may be rather high. For such small particles, van der Waals forces have

to be taken into account.

Hamaker (1937) determined a formula for the van der Waals forces on the

basis of the London–Heitler theory:

H = Ad24a2

(15.15)

where A (J) is a constant, d is the diameter of the particles (spheres) and a is the

distance between the two spheres. Equation (15.15) has been proved valid for

the range a< 1000 Å.

For the range a>2000 Å, the theory of Casimir and Polder (1948) and Lifschitz

(1955) gave the equation

H = Bd36a3

(15.16)

where B (J m) is a constant.

Krupp (1967) gave a formula for the van der Waals forces:

HvdWLd

8𝜋a2(15.17)

where L denotes the Lifschitz–van der Waals constants.

Figure 15.2 presents the theoretical tensile solidity of granules as a function of

the distance between two spheres a and the diameter of the spheres d (Rumpf,

1958a). From Figure 15.2, it is evident that in dry granulation, high solidity can

be achieved only by the use of high pressure.

15.1.6 Water sorption properties of particlesIt is observed that dry granulation can be performed more easily in a wet than in

a dry environment, that is, if the water content w of the bulk material consisting

of particles is below a typical value wlow, dry granulation is hard to perform, if

it can be performed at all. However, if wlow <w<wup, where wup is an upper

limit, dry granulation can easily be performed. The explanation is evident: the

adsorbed water is located in the cavities of the rough surfaces of the particles, and

as a result the shape of the particles becomes more or less spherical. The effect is

double: the van der Waals forces produce an additional attraction between the

spheres, and the distance a between two spheres is reduced, which increases the

attraction (see Eqn 15.15).

The thickness of a monomolecular water layer (slow) is about 3 Å (3× 10−10 m),

and the upper limit of the layer thickness (sup) is about 30 Å; namely, if the

water layer is thicker, the case of a freely moving fluid has to be considered (i.e.

slow →wlow and sup →wup).

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Particle agglomeration: instantization and tabletting 507

10

5

1

0.5

0.1

0.05

0.01

0.1 2

d = 1 µm

a (distance between particles) (10–9 m)

Te

nsile

so

lidity σ

1 (

10

5 P

a)

3 4 5 6 7 8 9 10

d = 0.1 µm

d = 0.01 µm

Figure 15.2 van der Waals forces. d=particle diameter. Source: Rumpf (1974). Reproduced

with permission from John Wiley & Sons.

Rumpf (1974) gave an equation for the water content w of a particle with a

rough surface:

w =(6

d

)sq (15.18)

where w is the water content per unit volume of solid, s is the thickness of the

water layer (m), q is the roughness factor and d is the particle diameter (m). For

a better understanding, we note that 6/d= S/V, that is, the specific surface area

of a particle of volume V; the product (6/d)s gives the volume of the water layer

on a particle, which is then corrected by factor q for roughness.

Example 15.2Let us calculate the thickness of a water layer if the characteristic particle

size is d= 5×10−6 m, the water content of a sucrose powder is 0.02 m/m%

(ca. 40% relative humidity), the density of sucrose is about 1600 kg/m3 and

q= 1.2.

w=0.02 kg water/kg sucrose= 0.02×1.6 m3 water/m3 sucrose= 0.02×1.6

From Eqn (15.18),

0.02 × 1.6 =(6

d

)sq =

(65× 10−6

)s × 1.2 → s ≈ 2.22 × 10−8 m = 222 Å

[A relative humidity curve for sucrose was published by Junk and Pancoast

(1973, p. 14).]

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508 Confectionery and chocolate engineering: principles and applications

If d=1× 10−6 m, then

w = 0.02 × 1.6 = 6 × 106 × 1.2 × s → s ≈ 44.4Å

This value is close to the limit of total coverage by a water layer.

It should be noted that finely powered sucrose can be relatively easily dry

compressed.

The tensile solidity of a granule can be calculated (Rumpf, 1974) as follows.

The area A on which the cohesive tension acts is approximately

A = 𝜋

(Smax

2d

)(15.19)

where Smax is the maximum value of the distance between two spherical parti-

cles. Then the cohesive force is

H = 𝜎cohA = 𝜋

(Smax

2d

)𝜎coh (15.20)

and the theoretical tensile solidity is

𝜎theo,t =2Hd

= 𝜎coh𝜋

(Smax

d

)(15.21)

where 𝜎coh is the cohesive tension.

The concept of a theoretical tensile solidity supposes that there is no distance

between the particles, that is, a=0, which makes Eqns (15.15)–(15.17) diver-

gent. The size of the theoretical tensile solidity is probably rather high (>108 Pa),

but because of defective sites it is actually much lower. The size of smax is about

30 Å.

15.1.7 Effect of electrostatic forces on the solidity of a granuleA regular arrangement of positive and negative charges may not be assumed in

granulation; consequently, the following calculations concern a maximum value

of the electrostatic forces. However, these effects cannot be entirely neglected;

this means that the charges of different signs that are certainly formed during

granulation will not neutralize each other entirely. This is taken into account

by a factor of 0.2905 and also by assuming that neighbouring particles have a

repulsion that decreases the attraction between the two particles studied.

According to Coulomb’s law,

H = −(

Q1Q2

L2

)(1 − 2a

d

)(15.22)

where L is the distance between the centres of the charges Q1 and Q2, of spherical

shape. If a≪ d, then L≈ d, and

H ≈ −Q1Q2

d2(15.23)

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Particle agglomeration: instantization and tabletting 509

If

− Q1 = Q2 = 𝜑𝜋d2 (15.24)

where 𝜑 is the surface density of charge, then

H ≈ (𝜑𝜋d)2 (15.25)

In a network of particles,

Heff = 0.2905H (15.26)

As a result,

𝜎t =2Heff

d2≈ 5.7𝜑2 (15.27)

Rumpf (1974) proposed, for the maximum surface density of charge, that

𝜑max ≈ 1.6(√

dyn)∕cm ≈ 0.506(√

N∕m) (15.28)

By using Eqn (15.27),

𝜎t.max ≈ 1.459 N∕m2

which is a very low value.

Bodenstedt (1952) measured the highest electric charging in powders of cere-

als (explosion danger!), although he estimated the value of 𝜑max to be about five

times lower than the value estimated by Rumpf (1974).

Rumpf (1974) calculated the maximum distance between two particles (dmax)

within which the weight of a particle is compensated (or exceeded) by electro-

static attraction:Q1Q2

(a + d)2= (𝜑𝜋2d)2

(a + d)2= π

(d3

6

)𝜌g (15.29)

where 𝜌= 1000 kg/m3 for the sake of simplicity. From Eqn (15.29),

√K√

d − d = a (15.30)

where K= 6𝜋𝜑2/1000 g. From Eqn (15.30),

𝜕a𝜕d

=(1

2

)√Kd− 1 = 0

(The second derivative shows that this is a maximum.)

It can be stated that the electrostatic force exceeds the weight of a particle

within approximately 123 μm under the conditions assumed. Since the electro-

static attractive forces are not sensitive to the surface roughness of particles (see

later text), their additional effect in accelerating the agglomeration process is

important in dry systems.

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510 Confectionery and chocolate engineering: principles and applications

15.1.8 Effect of crystal bridges on the solidity of a granuleRumpf (1974) calculated this effect using the equation

𝜎t ≈ xf

(𝜌

𝜌X

)(1 − 𝜀)𝜎X (15.31)

where x is the concentration of the dissolved substance X from which the gran-

ulate is built up (m/m), f is the water content of the crystallized substance X

before drying (m/m), 𝜌 is the density of substance X, 𝜌X is the density of sub-

stance X inside at crystal bridge, 𝜀 is the hole volume ratio in the granulate and

𝜎X is the tensile solidity of substance X inside the crystal bridge. An approximate

calculation shows that 𝜎t ≪𝜎X. If 𝜌/𝜌X ≈ 1, x= 0.3, f= 0.02 and (1− 𝜀)=0.65, then

𝜎t ≈ 0.3 × 0.02 × 0.65𝜎X ≈ 0.0039𝜎X (15.32)

If the order of 𝜎X is 105 Pa (=1 bar), then 𝜎t ≈390 Pa.

In agglomeration, the strongest attractive binding effect is exerted by fluid

bridges.

15.1.9 Comparison of the various attractive forces affectinggranulation

On the basis of the theoretical considerations previously discussed, Rumpf

(1958a) summarized the values of the theoretical solidity of granules (Fig. 15.3).

0.010.01

0.1

1

3

A: van der W

aalsB: van der W

aals

C: C

apillary forces

II: Crystallized salts

D: S

intering

Tensile

solid

ity σ

1 (

10

5P

a)

10

100

1000

0.1 1 10

d (size of particle) (10–6 m)

100 1000

σthe 0,t

I: Briquetting,material

interlocking

Figure 15.3 Theoretical solidity of a granule. Source: Rumpf (1958a). Reproduced with

permission from John Wiley & Sons.

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Particle agglomeration: instantization and tabletting 511

The upper part of this figure (I. Briquetting, material interlocking) (𝜎t ≥ 3×105 Pa)

shows the range of forces that operate in briquetting and sintering. In this range,

the particle size plays a relatively small role.

The ranges shown by oblique lines concern the various types of forces between

the particles:

A. Range of very weak van der Waals forces, for which w<wlow, where w is the

water content (see Section 15.1.6)

B. Range of van der Waals forces, for which wlow <w<wup

C. Range of capillary forces (𝛿 = 0; see Fig. 15.1)

D. Range of sintering, briquetting and material interlocking

These values, although they are based on theoretical considerations, have

proved basically correct.

15.1.10 Effect of surface roughness on the attractive forcesLet us consider a particle of diameter d, on the surface of which there are hemi-

spheres of radius r to represent surface roughness. The distance between two

particles is a, and the minimum distance is a0 = 4 Å.

Figure 15.4 presents the maximum values of the forces acting between

smooth-surfaced spherical particles of diameter d. Hmax is calculated assuming

a0 = 4 Å. The parameters relating to Figure 15.4 are:

Liquid bridges: 𝛽 = 20∘, 𝛾water = 0.072 N/m, 𝛿 =0 (see Fig. 15.1).

Van der Waals forces: L= 5 eV (see Eqn 15.17).

1

0.1

0.01

Hm

ax (

10

–5 N

)

0.001

0.0001

0.1 1 10

d (diameter) (10–6 m)

100

Liquid brid

ges

Van der W

aals fo

rces

Electrica

l conducto

rs

Ele

ctric

al n

on-c

ondu

ctor

s

Figure 15.4 Comparison of forces acting between particles. Source: Rumpf (1974).

Reproduced with permission from John Wiley & Sons.

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512 Confectionery and chocolate engineering: principles and applications

Electrical conductors: surface potential U= 0.5 V.

Electrical non-conductors: density of elementary charge 𝜓 = 102 e/μm2 =1014 e/m2,

which corresponds to an electric field of about 20 000 V/cm (close to the dielec-

tric breakdown field of air).

Evidently, in the range below 100 μm, the effect of the electrostatic attractive

forces can be neglected compared with the van der Waals forces and the effect

of liquid bridges if the particle surfaces are smooth. The roughness of the parti-

cle surface changes this situation: because the effective distance of the van der

Waals forces is short, they are much more sensitive to surface roughness (r). If

we study the change of H as a function of r, a minimum can be observed in the

interval 0.01–0.1 μm. This fact may be exploited in practice: agglomeration may

be hindered by addition of a powder of high particle fineness.

Liquid bridges are much less sensitive to surface roughness. If 𝛽 (see Fig. 15.1)

is not too small, for example, 𝛽 ≈20∘, the small protrusions contribute to the

distance between the particles. The smaller the angle 𝛽, the larger the distance.

If 𝛽 ≈2.5∘, which a value of r≈0.1 μm corresponds to, the liquid bridges will be

torn apart, and they will remain between particles less than 0.1 μm in size only.

If 𝛽 < 2.5∘, capillary condensation becomes increasingly important. If 𝛽 ≈ 1∘ (the

corresponding value of r≈ 0.05 μm), the capillary condensation on the peaks of

the protrusions is pronounced, and the forces of the liquid bridges exceed the

van der Waals forces.

The electrostatic forces, in the case of both conductors and non-conductors,

are hardly influenced by surface protrusions. Assuming a density of elemen-

tary charge 𝜓 = 102 e/μm2 = 1014 e/m2, the electrostatic attractive forces between

spherical particles of diameter 50 μm are stronger than the van der Waals forces

over the entire interval of r.

For further references, see Schubert (1973, 1979), Zorli (1988) and Borho et al.

(1991).

15.2 Processes of agglomeration

15.2.1 Agglomeration in the confectionery industryIt is reasonable to study the various types of agglomeration (frequently called

aggregation) taking the continuous phase into consideration.

In the following discussions, the term agglomeration is used when the product is

not powder-like, that is, its size is of the order of centimetres. The term granulation

is used when the product consists of small granules, that is, powder-like products

with pieces having a size of the order of millimetres or smaller.

In this understanding, the initial operations of both agglomeration and

granulation are mostly comminution and mixing (blending); the actual oper-

ation in which agglomeration or granulation is performed is shaping and is

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Particle agglomeration: instantization and tabletting 513

characteristic of each particular type of product. Chapters 6 and 7 deal in detail

with comminution and mixing, respectively; the majority of sweets are a blend

of comminuted components.

15.2.2 Agglomeration from liquid phase• Fat crystallization. The continuous phase of the dispersion, also containing

another ingredient (sucrose, cocoa, etc.), is molten fat; agglomeration is a

result of crystallization of the fat in moulds. It is similar to sintering, but it

takes place as a result of cooling. Various chocolate and compound products

are manufactured in this way. This topic is discussed in Chapter 10.

• Sucrose crystallization. Sucrose is crystallized from aqueous solution, and other

soluble components, mainly glucose and/or invert syrup, control the crystal-

lization. All fondant products are produced by this method. The sintering effect

is induced by cooling, similarly to the previous case. This topic is discussed in

Chapter 10.

• Agglomeration under the effect of gelling/foaming agents. An aqueous solution of

sucrose, glucose syrup and gelling or foaming agents (plus other ingredients)

solidifies under the effect of attractive forces between the molecules of the

gelling/foaming agent and dissolved carbohydrates. Confectionery jellies and

foams are manufactured in this way. Since solutions of carbohydrates are pro-

duced in these operations, comminution means dissolving these carbohydrates

in water. This topic is discussed in Chapter 11.

• Agglomeration by baking. All confectionery biscuits, wafers, cakes, etc. are pro-

duced in this way. The attractive forces in this type of agglomeration are essen-

tially of chemical nature. (Some similarity between baking and sintering may

perhaps be mentioned in this context.).

• Granulation from liquid phase (wet granulation). This is the typical method of man-

ufacturing various instant products, for example, cocoa drink powders. The

fluidized-bed method is typically used for this purpose. In addition, wet gran-

ulation frequently provides semi-products for tabletting as well. During wet

granulation, particle development can occur in two ways:

– Crystallization of sugars on solid seeds, which may be soluble or insoluble

in water.

– Solidification of material without any preliminary seeding; this process gen-

erally takes place in other steps, during which crystals are formed as seeding

kernels (e.g. crystallization of lactose during the powdering of milk).

15.2.3 Agglomeration of powders: tabletting or drygranulation

In tabletting, a bulk powder is compressed without any wetting process;

therefore, this operation is called dry granulation. In order to make a powder

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514 Confectionery and chocolate engineering: principles and applications

suitable for tabletting, previous handling may be necessary, during which the

powder is wetted by an aqueous solution of binding agents (carbohydrates

and/or gelling agents). The bulk material produced by wet granulation is then

compressed. Because of its simplicity and high efficiency, dry granulation is a

preferred method.

Wet and dry granulation will be discussed further later, Section 15.4.2, focus-

ing on their use in confectionery practice. Further references are Schilp (1975),

Hermann (1979), Leuenberger et al. (1980, 1981), Stahl (1983), Pahl (1985),

Dötsch and Sommer (1985), Schmidt (1989), Heinz et al. (1989), Koch (1991)

and Bakele (1992).

15.3 Granulation by fluidization

15.3.1 Instantization by granulation: wetting of particlesInstant cocoa and fruit powders are popular confectionery products that are man-

ufactured by granulation. The essence of instantization is that capillary forces

help in the wetting and disintegration of particles in contact with the aqueous

medium (milk, water, etc.). Under the usual conditions, non-instant particles float

on the surface of a drink because the surface tension of the liquid compensates for

gravitation, and although the soluble ingredients (sugars, emulgator, flavouring

ingredients etc.) slowly start to dissolve, this effect is not sufficient for penetra-

tion of the particles into the liquid. However, in the case of instant powders, the

liquid phase penetrates into the capillaries of the particles, and this induces the

immersion and disintegration of the particles.

For the theoretical basis, see Section 5.3.3.2 (Eqns 5.19–5.23). Example 5.2 is

related to instantization.

Using a Schmidt–Enslin instrument (Pfalzer et al., 1973), the process of liquid

penetration can be investigated, as a result of which plots of h2 versus t (lines)

are obtained:h2 =

tr𝛾LV cos 𝜃

2𝜂(5.21)

The steeper the line, the quicker the penetration is. A commonly used quality

parameter for wettability is the ratio h2/t (mm2/s) at given values of t (e.g. 10 s)

and of 𝜃 (the apparent contact angle).

If the line of a plot is broken, this indicates that the particles have two systems

of cavities, which have different hydraulic radii: the external value rEx and the

internal value rIn. The air penetration method (Carman, 1956) is suitable for

determination of the external hydraulic radius.

According to Pfalzer et al. (1974), the wettability of porous solids is primar-

ily determined by the external system of cavities: the larger the radius of this

system, the quicker the penetration, that is, the wettability of fine particles is

poor, and, consequently, the fine portion of the bulk powder becomes separated

and re-agglomerated. The larger particles, about 2–3 mm in size, have excellent

wettability because they contain large cavities.

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Particle agglomeration: instantization and tabletting 515

For details of the process of wetting and dissolution in instant foods, see

Dörnyei (1981), and for the determination of the wettability of instant cocoa

powder in water, see IOCCC Analytical Method 27 (1988b).

15.3.2 Processes of fluidizationA discussion of the theoretical background of fluidization is beyond the scope of

this book, and the following references are recommended: Leva (1959), Davidson

and Harrison (1971), Kunii and Levenspiel (1991) and Steinmetz (2001).

Ormós (1975) summarized the various methods of granulation in a fluidized

bed:

• Partial melting of the particle surfaces and then agglomeration and cooling (US

Patent 3 514 510)

• Preliminary wetting of particles and then drying, with no addition of solids

(Henszelman and Blickle, 1959)

• Wetting of particles by vapour plus addition of a binding agent and then

agglomeration and drying (Hungarian Patent 152 386)

• Increase in the size of the particle crust by addition of a solution or suspen-

sion of another ingredient and solidification of particles by drying or cooling

(Wurster, 1960)

• Wetting the particle surfaces with a solution of a binding agent and then solid-

ification by drying, cooling or chemical reaction (Contini and Atasoy, 1966)

For further details, see Pintauro (1972), especially for chocolate drink powders

(pp. 46–78), for natural sugars (e.g. brown sugars and fondant mixtures) and syn-

thetic sweeteners (pp. 102–139), for soluble coffee and soluble tea (pp. 141–172)

and for flour and cake mixes (pp. 175–219).

Granulation takes place in the space around a grid. Fluidization is carried out

by filtered, heated air coming from under the grid and by vibration. Dosing of

the powder provides the kernels of the granules, which are wetted by a solution

of binder sprayed from the top of a tower. The end product is transported out

by airflow. Running is possible both in a charged and in a stationary state. (In

view of the many kinds of machines, the details of the technological calculations

are beyond the scope of this book.) The usual arrangement of a fluidized bed is

shown in Figure 15.5.

For cocoa drink powders, Dörnyei (1981) proposed a ratio 2 : 1 of sucrose to

cocoa powder; some deviations from this value are possible, but this value can

be taken as a good guide. For further recipes and details of the technology and

machinery, see Pintauro (1972). For further details on cocoa powder agglomer-

ation, see Omobuwajo et al. (2000), Vu et al. (2003) and Mércia de Freitas and

Caetano da Silva Lannes (2007). Further references include Schügerl (1974),

Hein et al. (1982), Furchner et al. (1990), Schubert (1990), Uhlemann (1990),

Bauckhage (1990), Troetsch (1991), Weber (1993), Ratti and Mujumdar (1995)

and Ruiz-López et al. (2008).

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516 Confectionery and chocolate engineering: principles and applications

Air

SolutionAir

(filtered, heated)

Air

(filtered, heated)

Vibration

Spraying

Granulation Product

Outlet

Air for outlet

of product

Grid

Dosing

of powder

Figure 15.5 Aggregation in a fluidized bed.

15.4 Tabletting

15.4.1 Tablets as sweetsTablets can be regarded as hard sugar confectionery. The fact that boiling

is not used in their manufacture makes tablet manufacture attractive and

relatively cheap. An additional advantage is the high efficiency of tabletting

machines.

The surface of a tablet may be either coated, that is, the tablet serves as a centre

(corpus) for a coated product, or uncoated.

The most commonly used raw materials for tabletting are (flavoured) sucrose,

dextrose, sorbitol and a mixture of various vitamins for use with these carbohy-

drates (e.g. enrichment with ascorbic acid, citric acid, etc.).

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Particle agglomeration: instantization and tabletting 517

15.4.2 Types of tablettingDuring tabletting, granular substances are compressed. Two types of tabletting

can be distinguished:

• In direct tabletting/compression, all the raw materials are blended and directly

compressed after having been loaded into the tabletting machine.

• In indirect tabletting, the raw materials are blended and mixed with surfactant

agents, which wet the surface of the components and increase the interfacial

forces, that is, adhesive forces. This wetting process, which results in a granu-

late, is usually followed by a drying period and finally the compression of the

mixture. This is called wet granulation. Another method of indirect tabletting is

dry granulation.

15.4.2.1 Manufacture of tablets by wet granulationGranulation is still the most frequently used method of preparing a tablet-

ting mixture. There are at least four different variations of the pro-

cedure:

1 Granulation of the active substance (+ filler) with a binder solution

2 Granulation of a mixture of the active substance (+ filler) and a binder with

the pure solvent

3 Granulation of a mixture of the active substance (+ filler) and a portion of the

binder with a solution of the remaining binder

4 Granulation of the active substance (+ filler) with a solution of a portion of

the binder followed by dry addition of the remaining binder to the finished

granulate

A number of factors dictate which of the aforementioned four kinds of method

is used. With many formulations, method 1 gives tablets with a shorter disinte-

gration time and quicker release of the active substance than method 2 (Wan

and Lim, 1990). Also, in many cases, method 1 gives somewhat harder tablets

than method 2. Method 3 is useful if method 1 cannot be used, as when the

tabletting mixture lacks the capacity for the quantity of liquid required for the

total amount of binder. If the disintegration time of a tablet presents a problem,

it is worth trying method 4, mixing in about a third of the binder together with a

lubricant and, last of all, the disintegrant. Methods 2 and 3 have proved best for

active substances of high solubility, as the quantity of liquid can be kept small to

avoid clogging the granulating screens.

The capacity of the powder mixture to bind liquid is one of the parameters

determined in wet granulation. Every powder mixture to be granulated has a

different binding capacity. Water is nowadays the most commonly used solvent.

Sometimes, if water cannot be used, as with effervescent tablets, active ingredi-

ents that are prone to hydrolysis, ethanol or isopropanol are used as the solvent,

although fluidized-bed granulation is preferred. However, this field is beyond the

scope of this text.

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518 Confectionery and chocolate engineering: principles and applications

15.4.2.2 Manufacture of tablets by dry granulationDry granulation is less widely used than wet granulation as a method for

preparing tabletting mixtures. The best-known dry granulation technique is

compaction. It is the method of choice whenever wet granulation cannot be

used for reasons of stability and when the physical properties of any ingredient

do not allow direct compression.

15.4.2.3 Direct compressionDirect compression is becoming ever more widely used in the confectionery

industry because it is an easy technique. For good tabletting properties, the mix-

ture of substances must fulfil a number of physical requirements. It must be

free-flowing, it must not be prone to electrostatic charging, its crystals must not

be too brittle, and its compression characteristics must result in tablets of ade-

quate hardness (Bühler, 1993).

15.4.2.4 Types of machines for granulationTwo types of machine are used in the confectionery industry:

• Machines that perform building up: These are the traditional panning machines.

• Machines that perform briquetting: These are stamping apparatuses (rotary

tablet presses).

Compaction by stamping machines will be discussed later; see also Landillon

et al. (2008) and Djuric et al. (2009).

15.4.3 Compression, consolidation and compactionThese three concepts have a close connection with each other:

Compression: The reduction in the bulk volume of a material as a result of the

removal of the gaseous phase (air) by applied pressure.

Consolidation: This involves an increase in the mechanical strength of a material

resulting from particle–particle interactions.

Compaction: The compression and consolidation of a two-phase (solid+ gas) sys-

tem due to an applied force.

The stages of compaction are:

1 Particle rearrangement or interparticle slippage

2 Deformation of particles

3 Bonding or cold welding

4 Deformation of the solid body

5 Elastic recovery or expansion of the mass as a whole

15.4.3.1 Particle rearrangement• This occurs at low pressures.

• It reduces the relative volume of the powder bed.

• Small particles flow into voids between larger particles, leading to a closer

packing arrangement.

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Particle agglomeration: instantization and tabletting 519

As the pressure increases, relative particle movement becomes impossible,

inducing deformation.

15.4.3.2 Deformation mechanisms of materials• Elastic deformation: The shape of the tablet is recovered.

• Plastic deformation: No recovery of shape.

• Brittle fragmentation: During application of the force, the tablet becomes frag-

mented, and after removal of the force, the fragments retain the shape of the

tablet.

15.4.3.3 BondingSolid bridges form directly between particles in the absence of any binding ele-

ments or additives. Intermolecular and electrostatic forces project beyond the particle

surface as small discrete fields with very short-range order.

Under the effect of surface tension and capillary suction, four types of contact

can be established: direct contact, discontinuous contact, contact while saturated

by fluid and contact while enclosed by fluid (the proportion of binding fluid

increases in this sequence).

For the compressive stress in the case of direct contact and globular particles of

equal size,

𝜎D =3.1[(1 − 𝜀)∕𝜀]𝛾x(1 + tan 𝛽∕2)

(15.33)

where 𝜎D is the tensile stress, 𝜀 is the ratio of void volume (0<𝜀< 1),

𝛾 =72 dyn/cm (=72× 10−3 N/m) is the surface tension of water, x is the diameter

of a particle and 𝛽 is the central angle of the fluid bridge.

Example 15.3𝜀 = 0.4, x = 10−3 m, 𝛽 = 60∘, 𝜎D =?

From Eqn (15.33)

𝜎D = 3.1(0.6

0.4

)× 72 × 10−3

10−3 × 1.577= 212.3 Pa

In the case of saturated contact and globular particles of equal size, the following

equation can be applied:

𝜎S = 6[1 − 𝜀

d

]𝛾 (15.34)

where d is the diameter of the granulate. See Tóth (1973, p. 717).

Example 15.4𝜀= 0.4, d=10−3 m, 𝜎S =?

From Eqn (15.34),

𝜎S = 6

[1 − 0.4

10−3

]× 72 × 10−3 = 259.2 Pa

Mechanical interlocking is shape dependent.

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520 Confectionery and chocolate engineering: principles and applications

15.4.3.4 Deformation of the solid bodyAs the pressure increases, the bonded solid is consolidated towards a limiting

density by plastic and/or elastic deformation.

15.4.3.5 RecoveryThe compact is ejected, allowing radial and axial recovery. The elastic character

of the material tends to cause the compact to revert to its original shape.

15.4.4 Characteristics of the compaction processThe steps of the compression cycle are ejection, compression, adjustment of

weight and die filling.

The pressure–volume relationships for this process are shown in Figure 15.6.

The curve A–B–A represents a quasi-static process in which the granules slip

on each other and form a compact structure. Then the shapes of the granules

are deformed; the energy consumption in this period of interfacial connections

between the granules is high. However, the curve A–B–C represents a realis-

tic process in which the tablet dilates (relaxation and recovery). In industrial

practice, tabletting is rather quick, and therefore, the curve A–B–C describes the

actual conditions, and dilatation must always be taken into account.

A typical compression profile is shown in Figure 15.7. Figure 15.8 shows

typical crushing strength versus pressure plots, comparing single and double

compression.

15.4.4.1 Lubricant selectionFigure 15.9 shows plots of ejection force versus compression pressure for use in

choosing a lubricant. The three curves relate to three different lubricants. For any

given value of compression pressure, the curves provide three different values

of the ejection force, and the lubricant that gives the minimum value may be

chosen.

B

A C

Shift of piston

Pre

ssu

re

Figure 15.6 Plot of pressure versus volume in

tabletting.

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Particle agglomeration: instantization and tabletting 521

Fo

rce

(kN

)

00 0.10 Time (s)

0

15

Consolidation

Effective contact time

Dis

pla

ce

me

nt

(mm

)

Figure 15.7 Compression profile: plot of displacement versus time and force versus time.

0

2Double

compressing

Single

compressing

0

Pressure (Mpa)

300

Cru

shin

g s

trength

(M

Pa)

Figure 15.8 Plots of crushing strength versus pressure for single and double compression.

0

1000

0

Compression pressure (Mpa)

400

Eje

ction forc

e (

N)

Figure 15.9 Lubricant selection: plots of ejection force versus compression pressure for three

different lubricants.

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522 Confectionery and chocolate engineering: principles and applications

15.4.4.2 Side-pressure coefficientAn essential characteristic of the tabletting process is the side-pressure coefficient:

side-pressure coefficient (𝜉) =side pressure

tabletting pressure(15.35)

According to Pascal’s law, the pressure in a spreading fluid is the same in every

direction. Consequently, for fluids, 𝜉 =1; for entirely rigid solids, 𝜉 =0. The pres-

sure in a bulk sample of granules cannot spread unchanged in every direction

since, on the one hand, the directions are not equivalent and, on the other hand,

the equalization of pressure differences is hindered; therefore reversibility, which

is an assumption of Pascal’s law, is an unacceptable approximation.

According to Lunyin et al. (1976), for the tabletting of tea,

𝜉 = 1.5 × 10−4W2 + (1.7 × 10−3 + 5 × 10−5W )p + 0.1415 (15.36)

where W is the water content (%) of the tea leaves (values 6–10.7%) and p is

the tabletting pressure (MPa) (values 10–250 MPa).

Example 15.5Let us calculate the value of 𝜉 if W=10% and p=20 MPa and if W= 7% and

p= 150 MPa. From Eqn (15.36),

𝜉(W = 10%, p = 20 MPa) = 0.1965

and

𝜉(W = 7%, p = 150 MPa) = 0.3596

For instant tea and coffee, Nazarov et al. (2006) published the following results:

If p<20 MPa, then 𝜉 ≤0.05.

If p= 20–200 MPa, then 𝜉 = 0.05–0.26 for instant tea and 0.05–0.21 for instant

coffee.

For various praline masses (at p= 0–2 MPa and 36–46 ∘C), Nazarov et al.

(2006) found that, at constant temperature t, if p is increased, 𝜉 also increases

and approaches 1. If both t and p are increased, then 𝜉 increases rapidly. For

example, 𝜉 =0.9 when t=46 ∘C and p=0.15 MPa and when t= 38 ∘C and

p= 1 MPa.

15.4.4.3 Volume modulusAn important characteristic of materials for tabletting is the volume modulus

EV = −p

(ΔVV0

)(15.37)

where p is the pressure (MPa), ΔV is the decrease of volume under the effect of

the pressure p (m3) and V0 is the initial volume of the material tabletted (m3).

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Particle agglomeration: instantization and tabletting 523

15.4.4.4 Change of density under the effect of compressionAccording to Nazarov et al. (2006), the Balshin equation is widely applied to

describe the change of density under the effect of compression:

(𝜌∕𝜌max)m = p∕pmax (15.38a)

where 𝜌 is the density of the material compressed (kg/m3); 𝜌max is the maximum

density of the material (kg/m3), related to the maximum pressure (pmax) of com-

pression; p is the pressure of compression (MPa) and pmax (MPa) is the maximum

pressure.

Taking into consideration the fact that 𝜌max =M/Vmin and 𝜌=M/V (where Vmin

is the volume of the sample when the pressure p is maximum, i.e. pmax, and V is

the volume when the pressure is p), Eqn (15.38a) is an equation of state of solid

matter:

pmax(Vmin)m = pV m (15.38b)

where m is a constant. The logarithmic form of Eqn (15.38a) can easily be used:

mlog10𝜌 = −log10p + log10pmax (15.38c)

Equation (15.38a, b or c) can be applied to describe the density change of refined

sugar (Krivcun et al., 1974), tea leaves (Lunyin et al., 1976) and instant tea and

coffee (Nazarov et al., 2006) during tabletting.

Khvedelidze (cited by Lunyin et al., 1976) studied the tabletting of tea

and determined that in the tabletting mould, the density associated with the

maximum compactness that can be reached is about 340–350 kg/m3. However,

in a quasi-static compression, the final (maximum) density is 1485 kg/m3. An

approximate equation describing the change of density as a function of pressure

and water content is

𝜌 =1485(6.49 − 0.49W + p)

28.46 − 2.13W + p(15.39)

where 𝜌 is the density of the material compressed (kg/m3), p is the pressure in

the tabletting process (MPa) and W is the water content (%).

For instant green tea and instant coffee, the following empirical equation was

recommended by Khvedelidze:

𝜌 = A +p − 10

m + np(15.40)

where 𝜌 is the density (kg/m3), p is the pressure in the tabletting process (MPa)

(values 20–200 MPa) and A, m and n are constants (their values are shown in

Table 15.2).

For recipes for tabletting, see, for example, Bühler (1982) and Johnson (1974),

and for compression of snack foods, see Mazumder et al. (2007).

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524 Confectionery and chocolate engineering: principles and applications

Table 15.2 Values of constants for instant green

tea and instant coffee.

Product A (kg/m3) m N

Instant green tea 716 0.066 0.002

Instant coffee 729 0.117 0.001

Source: Rumpf (1958a). Reproduced with permission

from John Wiley & Sons.

15.4.5 Quality properties of tabletsThe quality properties of tablets are viewed somewhat differently in food produc-

tion than in pharmaceutical production. The common aspects are content unifor-

mity, crushing strength, friability, weight and shape uniformity. For effervescent

mouthwash tablets, such parameters as disintegration time and dissolution time

play an important role too.

For references, see Pfalzer et al. (1973) and Koch and Sommer (1993).

Further reading

Ghosal, S., Indira, T.N. and Bhattacharya, S. (2010) Agglomeration of a model food powder:

effect of maltodextrin and gum Arabic dispersions on flow behavior and compacted mass.

J. Food Eng., 96, 222–228.

Hemati, M., Flamant, G., Steinmetz, D. and Gauthier, D. (2001) Special issue – Euro fluidization

III. Powder Technol, 120 (1–2), 1.

Keleb, E.I. (2004): Continuous agglomeration processes using a twin screw extruder, PhD theses,

Al-Fateh University, Lybia, Laboratory of Pharmaceutical Technology, Gent.

McCarthy, J.J. (2009) Turning the corner in segregation. Powder Technology, 192, 137–142.

Nopens, I., Biggs, C.A., De Clercq, B. and Govoreanu, R. (2006) Advances in population balance

modelling. Special issue. Chem Eng Sci, 61 (1), 63–74.

Pabst, W. and Gregorová, E. (2007) Characterization of Particles and Particle Systems, Lectures, Insti-

tute of Chemical Technology (ICT), Prague.

Pocius, A.V. (2002) Adhesion and Adhesives Technology: An Introduction, 2nd edn, Hanser, Munich.

Salman, A.D. and Hounslow, M.J. (2005) Granulation across the length scales. Second Interna-

tional Workshop on Granulation 22 – 25.June, 2004, The Univ. Sheffield. Chem Eng Sci, 60(14), 3721–4072.

Salman, A.D. and Hounslow, M.J. (2007) Fluidized bed applications. Chem Eng Sci, 62 (1–2),

1–654.

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PART III

Chemical and complexoperations: stability ofsweets: artisan chocolateand confectioneries

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CHAPTER 16

Chemical operations (inversionand caramelization), ripeningand complex operations

16.1 Inversion and caramelization

16.1.1 Inversion16.1.1.1 Hydrolysis of sucrose by the effect of acidsThe hydrolysis of sucrose, or inversion, takes place according to the following

chemical reaction:

C12H22O11(sucrose) + H2O (water) = C6H12O6(glucose) + C6H12O6(fructose)(16.1)

Comment: During this reaction, 342 g dry content of sucrose becomes 360 g dry

content, that is, 18 g water (5 m/m%) is chemically absorbed and accounts for

the increase.

This is a famous reaction because, in 1850, Wilhelmy worked out the prin-

ciples of the kinetics of chemical reactions by studying it; see Erdey-Grúz and

Schay (1954, p. 401). Inversion is stoichiometrically a bimolecular reaction, but

it is kinetically a first order since it takes place in a dilute aqueous solution (the

water is in excess, i.e. the concentration of water remains practically unchanged).

Consequently, Eqn (15.1) can be written in symbols as

AB → A + B (16.2)

and the corresponding kinetic equation is

− d[AB]dt

= k[AB] (16.3)

where k (s−1) is a kinetic constant.

If the yield is denoted by x, Eqn (16.3) can be written as

dxdt

= k(a − x) (16.4)

or, in integrated form,

k =(1

t

)ln

( aa − x

)(16.5)

where a is the initial concentration of sucrose.

Confectionery and Chocolate Engineering: Principles and Applications, Second Edition. Ferenc Á. Mohos.© 2017 John Wiley & Sons Ltd. Published 2017 by John Wiley & Sons Ltd.

527

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528 Confectionery and chocolate engineering: principles and applications

Table 16.1 Catalytic ability of various acids in

inversion, according to Ostwald.

Acid Inversion ability (%)

HBr 111.4

HCl 100

HNO3 100

H2SO4 53.6

H2SO3 30.4

Oxalic acid 18.6

H3PO4 6.2

Citric acid 1.72

Maleic acid 1.27

Lactic acid 1.07

Acetic acid 0.5

In inversion, the hydroxonium ion functions as a catalyst. The catalytic ability

of various acids may be characterized by a scale (Table 16.1).

Comment: The inversion ability is defined as a ratio of kinetic constants related

to hydrochloric acid (HCl) as 100% (Sokolovsky, 1958, p. 160).

In acid-catalysed reactions of first order, the reaction constant k is a sum in

general:

k = k0 +∑

ki[ion]i

(16.6)

where k0 is a constant and ki is the rate constant of the ith ion of concentration

[ion]i.

However, in inversion, k depends exclusively on the activity of the hydroxo-

nium ion (H3O+); thus Eqn (16.6) is valid for inversion in the form

k = kH+ [H3O+] (16.7)

The activity of hydroxonium ions can be determined on the basis of this rela-

tionship (due to Ostwald); see Erdey-Grúz and Schay (1954, p. 536).

Table 16.2 shows the relationship between the logarithm to base 10 of the

inversion ability and pKa (where pKa is the negative logarithm to base 10 of the

dissociation constant). The relatively good correlation (r=−0.9436) of a plot of

the data in Table 16.2 is in accordance with the equation

Δ log k = 𝛼 Δ log Kacid = 𝛼 ΔpKacid (16.8)

where 𝛼 is a constant. See Erdey-Grúz and Schay (1954, p. 538).

Commercially prepared acid-catalysed solutions are neutralized when the

desired level of inversion is reached. Neutralization, however, needs to be done

carefully; if the pH exceeds 7, the colour of the solution rapidly becomes brown

because of the development of so-called reversion products.

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Chemical operations, ripening and complex operations 529

Table 16.2 Relationship between the inversion ability and the dissociation

of inorganic and organic acids.a

Acid Inversion ability (%) Log(inversion ability) pKa

HNO3 100 2 1.2

H2SO4 53.6 1.72916479 1.52

H2SO3 30.4 1.48287358 1.77

Oxalic 18.6 1.26951294 1.42

H3PO4 6.2 0.79239169 1.96

Citric 1.72 0.23552845 3.1

Lactic 1.07 0.02938378 3.82

Acetic 0.5 −0.30103 4.73

a Intercept: 2.414717. Slope: −0.61885. Correlation: r=−0.9436.

Source: Sources of dissociation constants (at 20 ∘C): Erdey (1958, p. 37) and Kaltofen

et al. (1957, p. 270).

It is known that sucrose rotates the plane of polarization of light to the right: its

specific rotation is +66.67∘. Under the effect of acid as a catalyst, glucose, which

rotates the plane to the right (specific rotation +52.74∘), and fructose, which

rotates it to the left (specific rotation −93.78∘), are formed, and because fructose

rotates the plane more strongly to the left than glucose does to the right (and the

amount of sucrose causing a rotation to the right is decreasing by splitting), after a

certain degree of splitting, the solution will rotate the plane to the left by an angle

[𝛼]D = −93.78 + 52.742

= −20.52∘

All of the rotation angles mentioned in the previous paragraph relate to the

D-line of light. The reason for the division by 2 is that two molecules (glucose

and fructose) are formed in equimolar amounts (Maczelka, 1962, p. 37). As a

result, the initial rotation to the right is inverted. Therefore this process is called

inversion and the product is called invert sugar. [Another name for glucose is

dextrose (from dexter, Latin for right), and another name for fructose is laevulose

(from laevus, Latin for left); these are related to the particular optical properties

of these compounds.]

The determination of the reducing sugar content of carbohydrate solutions is a

routine task in the confectionery industry because the reducing sugar content has

proved to be an important quality and consistency parameter for many sweets.

Both iodometric (the Fehling, Schoorl–Regenbogen and Bertrand methods) and

polarimetric methods are used for measuring the reducing content. It should

be mentioned that the cupric→ cuprous reduction, which is the basis of these

methods, is not a stoichiometrically correct reaction since partial oxidation of

the sugar takes place at the same time. However, this problem can be eliminated

by fixing the conditions of the analysis.

High-performance liquid chromatography (HPLC) methods provide a finger-

print of the sugar components.

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530 Confectionery and chocolate engineering: principles and applications

Colorimetric methods are widely applied for the determination of glucose in

human blood. The Somogyi–Nelson micro-method (Morris, 1958) is based on

the blue colour (molybdenum blue) produced by the reaction of cuprous oxide

(Cu2O) and arsenic molybdenate. The cuprous oxide is formed from CuSO4

(from Seignette salt) by the reducing effect of the reducing sugar content.

16.1.1.1.1 Dependence of acidic inversion on temperatureAccording to the Arrhenius law, acidic inversion is catalysed by temperature rise

as well:

k = A exp(−ΔH

RT

)(16.9)

where A (s−1) is a frequency factor (not entirely independent of the temperature

T); ΔH (J) is the activation energy, which is always positive for thermal reac-

tions; R= 8.31434 J/(mol K) (the molar gas constant); and T (K) is the absolute

temperature (see Erdey-Grúz and Schay, 1954, p. 440).

It is known that raising the temperature by 10 K increases the rate of first-order

reactions by two to three times (Lengyel et al., 1960, p. 186). This fact is important

in practice because the majority of sugar confectioneries contain flavouring acids

(citric, lactic, tartaric or, by accident, acetic acid), and the temperature of the

process is rather high (60–100 ∘C). However, the consequences of inversion may

be both advantageous and disadvantageous, depending upon the properties of

the end product; see Chapter 8.

Invert sugar (and fructose) has a lower water activity than sucrose, and as a

consequence, it improves the shelf life of certain products by inhibiting drying

but can make the product surface and consistency sticky. To briefly summa-

rize, control of the inversion of the sucrose content is an essential technological

task.

16.1.1.2 A specific type of acidic inversion: inversion by cream of tartarBesides the edible acids, potassium bitartrate or cream of tartar (C4H5KO6;

M= 188.18) is also used in hard-boiled, pulled and grained sugar confectionery

as an inversion catalyst. The pH value of a saturated aqueous solution of cream

of tartar is 3.577 at 25 ∘C; a solution of 0.01 mol/kg has a pH value of 3.639 at

25 ∘C. (For comparison, a 0.1 N aqueous solution of carbonic acid has a pH of

3.73, that is, it has slightly weaker acidity than a potassium bitartrate solution

of concentration 0.01 mol/kg.)

Potassium bitartrate (KHTa) is formed in wine, from a reaction between the

bitartrate ion (HTa−) from tartaric acid (H2Ta) and the potassium ion (K+) found

in grapes, especially grape skins:

K+ + HTa− ⇄ KHTa (16.10)

Its solubility in water is low: 5.7 g/l at 20 ∘C. However, the solubility of cal-

cium tartrate is lower: 0.1 g/l. Consequently, in the presence of calcium ions,

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Chemical operations, ripening and complex operations 531

a proportion of the dissociated bitartrate ions will be precipitated:

HTa− → H+ + Ta2− (16.11)

Ca2+ + Ta2− → Ca-Ta ↓ (16.12)

One kilogram of sucrose contains about 100 mg of free calcium ions, which con-

sumes

100 mg × 188.1840.08

= 469.6 mg cream of tartar

Assuming that a charge of 100 kg of sucrose needs 0.2 kg of cream of tartar for

inversion, the free calcium ions consume 100×469.6 mg=46.96 g of cream of

tartar, which is a quarter of the total amount of cream of tartar used. Taking into

consideration the fact that the free calcium content of sucrose items is variable,

the technology of inversion by cream of tartar is always accompanied by some

uncertainty. The details of manufacturing hard boiled, pulled and grained sweets

are discussed in Section 2.2.2, page 42–45.

16.1.1.3 Enzymatic inversionSucrose can be hydrolysed by the enzymes α-glucosidase and β-fructofuranosi-

dase, because the glucose part has a glucoside carbon atom of α-configuration

and the fructose part is of β-configuration. The enzyme invertase (E 1103) that

is of industrial importance is produced from yeast and is β-fructofuranosidase.

(The invertase produced from moulds is α-glucosidase.)

The hydrolysis of sucrose is similar to an esterification during which a trisac-

charide is formed (Sumner and Somers, 1953):

Sucrose + enzyme ↔ fructosido-enzyme + glucose

Fructosido-enzyme + sucrose ↔ trisaccharide + enzyme

Trisaccharide + enzyme + H2O ↔ fructose + sucrose + enzyme

Sucrose + enzyme ↔ etc. (′da capo al fine′)

The enzyme activity is dependent on the concentration of the substrate, in

this case sucrose. The activity of invertase increases up to a sucrose concentra-

tion of 5 m/m%; at higher concentrations it decreases (Höber, cited by Tolnay,

1963). The optimal pH interval of yeast invertase is 4.5–5.0 and that for honey

invertase is 5.5–6.6 (Bergmeyer, 1962). The optimal temperature for the func-

tion of invertase is 55 ∘C, according to Bersin (see Tolnay, 1963). However, it can

work well at room temperature, which means that invertase added to a product

continues to cause hydrolysis during storage. (Invert sugar is produced in situ.)

This property is used to soften fondant and marzipan products. With regard to

denaturation, the critical temperature of the function of invertase is about 69 ∘C(Görög, 1964). For further details, see Combes and Monsan (1982).

Székely (1966) studied the application of invertase [Naarden, powder No.

5, activity 5086 Sumner invertase units (SU)/g enzyme] for softening fondant

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532 Confectionery and chocolate engineering: principles and applications

Invert

sugar

(%)

16

14

12

10

8

6

50 5 10 20

Storage (days)

Control: 0%

0.01%

0.025%

0.05% (Deliquesced)

30 45

Figure 16.1 Effect of invertase on the reducing sugar content of fondant products during

storage at 20 ∘C and 50% relative humidity. Source: Székely (1966). Reproduced with

permission of Technical University of Budapest.

products covered with a sucrose crystal layer (kandis) at a level of 6.2 m/m%.

Because of heat sensitivity, the invertase preparation was mixed with the

fondant mass and flavours at a temperature below 60 ∘C. The Somogyi–Nelson

method was applied to determine the invert sugar (reducing sugar) content; see

Morris (1958).

Figure 16.1 shows a storage experiment during which the change of the reduc-

ing sugar content of the fondant was investigated as a function of storage time

at 20 ∘C at a relative humidity of 50%, with different invertase concentrations

(0.05%, 0.025% and 0.01%), and compared with a control (0%). Similar exper-

iments were performed with the same samples at 20 ∘C and a relative humidity

of 70% and at 30 ∘C.

Székely (1966) studied, using a Höppler consistometer (Rod No. 27, diameter

4 mm) and the same samples, the effect of invertase on the softening of fondant.

Figure 16.2 shows the penetration of the consistometer rod into the fondant

product. (The conditions of storage were 20 ∘C and relative humidity 50%.) The

corresponding penetration versus consistency relationship is shown in Table 16.3

(Székely, 1966).

Székely (1966) determined the liquid-phase content of the same samples dur-

ing storage at 30 ∘C. (The temperature of determination was 22 ∘C.) The results

are presented in Table 16.4. The liquid-phase content refers to the centre, with-

out the kandis layer (6.2 m/m%). Under the effect of invertase, the liquid-phase

ratio is slightly increased. The liquid-phase content was determined by centrifu-

gal separation; see Ravasz (1964).

According to Székely (1966), the reducing sugar (invert sugar) content must

not exceed 14–15%, or the fondant product will be liquefied. An invertase con-

centration of 0.01 m/m% (5000 SU/g) can be recommended for softening the

consistency. A fat content of 14 m/m% does not disturb the effect of invertase in

fondant.

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Chemical operations, ripening and complex operations 533

0.025%

Penetr

ation (

mm

)

0

1

2

3

4

5

6

7

8

9

0 10 20

Storage (days)

Control: 0%

0.01%

0.05% (Deliquesced)

35 45

Figure 16.2 Change of penetration under the effect of invertase during storage at 20 ∘C and

50% relative humidity. Source: Székely (1966). Reproduced with permission of Technical

University of Budapest.

Table 16.3 Penetration versus consistency relationship

for stored fondant products that contain invertase.

Penetration (mm) Consistency

0.3–0.45 Semi-hard

0.45–1.00 Soft

1.00–5.00 Very soft

5.00–8.00 Creamy

8.00–9.00 Semi-fluid

Source: Székely (1966). Reproduced with permission of Tech-

nical University of Budapest.

Table 16.4 Variation of liquid-phase content during storage

as a function of invertase content.

Invertase content (%)

Storage (days) 0.05 0.025 0.01 0

1 75.8 75.2 75.7 75.5

5 77.7 77 76.8 75.7

15 79 78.5 77.6 76.4

25 80.1 79.6 78.7 77.1

35 81.2 80.7 79.4 78

45 82 81.2 80 78.9

Source: Székely (1966). Reproduced with permission of Technical

University of Budapest.

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534 Confectionery and chocolate engineering: principles and applications

16.1.2 Caramelization16.1.2.1 Maillard reactionIn the confectionery industry, the concept of caramelization is applied in two dif-

ferent ways: the Maillard reaction (non-enzymatic browning) and sugar melting.

The Maillard reaction, also called the non-enzymatic browning reaction or

amino–carbonyl reaction, is a reaction between compounds containing amino

groups and compounds containing reducing groups such as aldehydes and

ketones. The amino compounds in foods are mostly free or protein-bound

amino acids, and the reducing compounds are reducing sugars. The Maillard

reaction plays a central role in food science. The reaction is very common and

occurs in almost all foods and other systems containing amino acids and sugars

that undergo heat treatment or are subjected to long storage times. Owing to the

complexity of the reaction, it has both positive and negative effects; for example,

the formation of flavour is in most cases positive, while a loss of essential amino

acids is a negative consequence of the reaction.

Although intensively studied, the chemistry of the reaction is not fully under-

stood. Various authors (Hodge, 1953; Ellis, 1959; Reynolds, 1963, 1965, 1969;

Feeney et al., 1975; Mauron, 1981) have reviewed the chemical nature of this

reaction. The classical scheme worked out by Hodge (1953) is still valid in its

description of the main stages of the reaction.

The initial stage is the condensation of the amino and the carbonyl groups,

which can undergo the Amadori rearrangement to give amino-deoxy compounds,

often called Amadori compounds. The Amadori compounds can then react further,

depending on the reaction conditions. These reactions are mainly of three types:

dehydration, degradation and fission. The last stage in the Maillard reaction is the

formation of brown polymers from precursors originating in the previous stages.

The reaction pathways are greatly influenced by the reaction conditions. The

reactants are obviously of great importance. Temperature, water activity, pH and

duration of the reaction are also very important. The formation of the brown

colour is one of the most easily detectable changes caused by the Maillard reac-

tion. The coloured compounds are of high molecular weight, but their structure is

basically unknown. The formation of flavour is another easily detectable change

caused by the Maillard reaction; see Fors (1983), Lingert (1990) and Schieberle

(1990). The flavoured compounds are formed mainly by condensation of the

degradation products. As amino acids are involved in the Maillard reaction, these

are lost during the reaction. The principal amino acid lost in foods is lysine. As

lysine is often the limiting amino acid in proteins, the Maillard reaction can lower

the nutritional quality of proteins (Mauron, 1981). The Maillard reaction can

lead to increased toughness of the food as a consequence of polymerization and

cross-linking of proteins (Labuza et al., 1977).

In the confectionery industry, the Maillard reaction plays an essential role

in manufacturing fudge, toffee, butterscotch (commonly called caramel), milk

chocolate, milk crumb and choco crumb. Fondant mass is often enriched with

sugared condensed milk in order to produce a speciality fondant with a beige

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Chemical operations, ripening and complex operations 535

colour and caramel flavour – the Maillard reaction is similarly important in this

process. This type of fondant mass can be regarded as a kind of caramel too.

Also, sugared condensed milk itself provides a classical example of the Maillard

reaction, which is accompanied by reactions of the milk fat during evaporation.

Naturally, the Maillard reaction takes place in all cases where proteins and

reducing sugars are heated to elevated temperature, for example, in the roast-

ing of cocoa, nuts and coffee, in the alkalization of cocoa nibs or mass, and in

baking. However, the typical operation is a controlled Maillard reaction in the

manufacture of various types of caramels and milk chocolate. A common fea-

ture of these examples is that some kind of fat (mostly butter or cocoa butter)

is present among the reactants. It seems that a fundamental condition for the

typical caramel flavour is the presence of some fat – this is proved by experience

in confectionery practice.

Tressl (1990) has given the principal pathways for the thermal generation of

aromas in foodstuffs and a list of references concerning the Maillard reaction.

The proteins and carbohydrates are transformed into smaller compounds (amino

acids, and monosaccharides and disaccharides, respectively), and then, during

many reactions called early and advanced Maillard reactions (the Amadori trans-

formation, Strecker degradation, etc.), they are terminated by N- or S-containing

heterocycles. The lipids are transformed into fatty acids and then peroxidized and

degraded, and finally the resultant lipid-derived products are transformed into

N- or S-containing heterocycles.

The products of lipid degradation play an important role in the advanced Mail-

lard reactions. This fact is important from the point of view of producing fudges

and toffees; namely, the lipid medium (milk butter) stimulates the generation

of typical milky flavour components. On the other hand, many of the flavour

components are lipid soluble (hazelnut, coconut, etc.); therefore, these types of

flavours are not intense in lipid-poor media. The same applies also to milk pow-

ders and products: the butter-poor products are flavour poor as well.

From the point of view of our objective, two technological parameters are

important if the product composition is fixed: the temperature and the duration

of the effect of heat.

In the production of various types of caramel products, the temperature range

is about 120–130 ∘C (for butterscotch, ca. 145–152 ∘C). The effect of the heat used

in evaporation is sufficient to generate the typical caramel flavour as well.

In the production of milk chocolate, the temperature of conching is about

45–60 ∘C, which is relatively low; however, the effect of heat lasts ca. 12–20 h

in modern conching machine. In the production of milk crumb or choco crumb,

the temperature is higher but the duration of the effect of heat is shorter.

Milk proteins are essential to the generation of caramel flavour, particularly

the whey protein, which is present in an amount of 14–24% (while the casein

proportion is about 76–86%), because the Maillard products of lysine seem to

be the most important factors in the flavour, and the lysine content is higher

(10–12%) in whey protein than in casein (about 8.4%); see Gasztonyi (1979,

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536 Confectionery and chocolate engineering: principles and applications

p. 152). For this reason, whey is a favourite raw material for fudges and toffees,

and it is used also in chocolate production, although whey must not be estimated

as milk content according to EU regulations. Care is needed when whey is used

for chocolate since the microbiological state of whey is often objectionable, and

the temperature of conching is not sufficient to totally destroy its microflora.

Mohos (1982) studied the hydroxymethylfurfural (HMF) content of

caramelized milk powders made by a roll dryer (Vonda type). The pas-

teurized milk used, of pH 6.4–6.9, contained 10% sucrose or dextrose and 20%

milk fat. This solution was condensed up to 40–41% dry content. When this

condensed solution was digested for 1.5–2 h, the flavour of the end product

(milk powder) was excellent. (A longer digestion is not preferable, because the

viscosity of the solution becomes too high for drying.) The optimal HMF content

of caramelized milk powders can be regarded as 15–25 mg/kg. The HMF content

of milk chocolate made from such milk powders is about 10–15 mg/kg, which

shows that a certain part of the final HMF content is also generated during the

chocolate production. If the average ratio of milk powder in milk chocolate is

about 20 m/m%, this results in about 2–3 mg/kg of HMF (10/5–15/5); the other

part (8–12 mg/kg) develops during the production of the milk chocolate.

Many brands of milk chocolate were investigated, and an HMF value of

10–15 mg/kg was determined in general. The HMF value is one of the char-

acteristic properties of the Maillard reaction and the chemical reactions taking

place in molten sucrose. For its determination, see Örsi (1962) and Mohos and

Lengyel (1981). The principle of this method is that HMF results in a colour

reaction with a solution of aniline and barbituric acid in glacial acetic acid.

Barra (2004) deals with rheology of caramel in her doctoral theses and, among

others, also with the Maillard activity as the cooking temperature was changing.

Information about the extent of Maillard reactivity was obtained by the determi-

nation of the isoelectric point using a streaming potential technique. The pH at

isoelectric point was different in each sample and was increasing as the cooking

temperature decreased. The isoelectric point depends on the nature of the pro-

tein, and differences in its value in the samples analysed (arising from the same

formulation) have been attributed to transformations in the chemical structure of

the proteins due to the Maillard reaction. The isoelectric point and pH decreased

as the Maillard reaction developed.

The development of the caramel taste of milk chocolates during conching was

studied by Danzl and Ziegleder (2014).

Paravisini et al. (2014) studied the properties of caramel odour by gas chro-

matography/olfactometry (GC/O) which constitutes an intersection between

physico-chemical and sensory studies by using the human nose as a detector to

evaluate the odour properties of volatile compounds. They determined that the

caramel typicality results from a complex balance between fruity, vegetal, sharp,

nutty and caramel notes arising from the presence of carboxylic acids, aldehydes,

oxygenated heterocyclic compounds, ketones and carbocyclic compounds. This

study brings new clues to understand the contribution of the caramel volatile

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Chemical operations, ripening and complex operations 537

compounds to its odour while proposing a promising experimental approach

to understand the contribution of volatile compounds to the odour of complex

products.

16.1.2.2 Sugar meltingThe Maillard reaction is not the only non-enzymatic browning reaction. The

caramelization reaction is in many ways similar to the Maillard reaction, except

that only sugar compounds take part in the caramelization process.

Brown-coloured products with a typical caramel aroma are obtained by melt-

ing sugar or heating sugar syrup in the presence of acid and/or alkaline catalysts.

The process can be directed more towards aroma formation or more towards

accumulation of brown pigment. The heating of sucrose syrup in a buffered

solution enhances molecular fragmentation and, thereby, formation of aroma

substances. Primarily dihydrofuranoses, cyclopentanolones, cyclohexenolones

and pyrones are formed.

On the other hand, heating glucose syrup with sulphuric acid in the presence

of ammonia provides intensely coloured polymers (sucre couleur, E 150a, b, c, d).

The stability and solubility of these polymers are enhanced by bisulphite anions.

For details of the reactions involved, see, for example, Belitz and Grosch (1987).

These reactions provide the basis for industrial processes for colour production. In

the confectionery industry, a simple method is applied for producing colour: the

intensity of the brown colour of the melted sugar is tailored according to demand

by dissolving it in water, and this aqueous solution is the colour used for colouring

and flavouring.

The other field of application is the manufacture of grillage (Krokant in German)

products. Sugar is melted, and then cut nuts, honey or glucose syrup is mixed

with it. The mixture is cooled and may be shaped.

The melting point of sugar is about 175–180 ∘C, depending on the amount of

non-sucrose ingredients. The temperature range of technological importance is

about 200–210 ∘C. Mohos (1982) and Mohos et al. (1981) studied the operation

of sugar melting. Three steps may be distinguished:

1 The temperature range is about 207–210 ∘C; the colour of the molten sugar

is straw yellow, and its HMF content is about 1.5–2 g/kg. This type of molten

sugar is suitable for covering the so-called Dobos fancy cake (Dobos tart, named

after C. József Dobos, Hungarian confectioner, 1847–1927) because its flavour

is very mild. This temperature range is suitable for producing various grillage

products as well because there is no danger of burning them. The blending of

cut nuts facilitates keeping within this range, since the increase in temperature

is arrested for a short time by the addition of the nuts, which are at room

temperature.

2 The typical temperature range is 210–215 ∘C; the HMF content of the molten

sugar is about 2–3 g/kg; the colour becomes browner, and the molten sucrose

becomes more and more difficult to manage. This product is suitable for man-

ufacturing colour solutions.

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538 Confectionery and chocolate engineering: principles and applications

00 100 150

(a)

Temperature (°C)

(b)

Temperature (°C)

2000

205 210 215

1000

2000

3000

1000

2000

3000

HM

F (

mg/k

g)

HM

F (

mg/k

g)

4000

5000

Figure 16.3 Melting of sugar: variation of hydroxymethylfurfurol (HMF) content of molten

sugar with temperature (a) under laboratory conditions and (b) Sucromelt 3400 machine

(O. Hänsel), by Mohos (1982).

3 The HMF content of the molten sugar is more than 3 g/kg; the colour becomes

deep brown and, finally, black.

Figure 16.3 shows the variation of the HMF content of molten sugar as a

function of the temperature, under laboratory conditions and in the product pro-

duced by the Sucromelt 3400 machine (O. Hänsel); the output of this machine is

80–180 kg molten sucrose/h. Below 210 ∘C, the dependence can be regarded as

quasilinear; however, when the temperature rises above 210 ∘C, HMF production

is accelerated.

Since the temperature is only one of the important parameters in sucrose melt-

ing, in addition to the duration/intensity of heating, the HMF content of sucrose

can be regarded as a reliable characteristic of caramelization. For further results,

see Quintas et al. (2007a,b).

16.2 Acrylamide formation

16.2.1 Acrylamide and carcinogenicityWhile inversion and caramelization are technologically useful chemical processes

to a certain limited extent, acrylamide formation during food technology seems

unambiguously to be detrimental to health; see Joint FAO/WHO Consultation

(2002). Nevertheless, some link between the Maillard reaction and acrylamide

formation is probable (Stadler et al., 2002).

Acrylamide (or acrylic amide, IUPAC name: prop-2-enamide; see Fig. 16.4)

was discovered accidentally in foods in April 2002 by scientists in Sweden (see

Tareke et al., 2002) when they found the chemical in starchy foods, such as potato

chips (potato crisps), French fries and bread that had been heated to temperatures

higher than 120 ∘C (248 ∘F) (production of acrylamide in the heating process was

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Chemical operations, ripening and complex operations 539

Figure 16.4 Structural formula of acrylamide.

HH

H

C C C

NH H

O

shown to be temperature dependent). It was not found in foods that had been

boiled or in foods that were not heated.

Acrylamide levels appear to rise as food is heated for longer periods of time.

Although, researchers are still unsure of the precise mechanisms by which acry-

lamide forms in foods, many believe it is a by-product of the Maillard reaction.

In fried or baked goods, acrylamide may be produced by the reaction between

asparagine and reducing sugars (fructose, glucose, etc.) or reactive carbonyls at

temperatures above 120 ∘C (248 ∘F).

Later studies have found acrylamide in black olives, prunes, dried pears and

coffee. Acrylamide also is found in cocoa powder and chocolate, formed during

cacao bean roasting. Cigarette smoking is a major acrylamide source; it causes a

threefold greater increase in blood acrylamide levels than any dietary factor.

Already in the year of the first observations, the report of the Joint FAO/WHO

Consultation (2002) provided the acrylamide levels measured in different foods

and food product groups from Norway, Sweden, Switzerland, the United King-

dom and the United States (Table 16.1).

Recently acrylamide is considered to be a probable human carcinogen, based on

studies in laboratory animals given acrylamide in drinking water. However, tox-

icology studies have shown differences in acrylamide absorption rates between

humans and rodents; thus the evidence from human studies is still incomplete.

16.2.2 Investigations on acrylamide formationSome recent studies relate to acrylamide formation: Segtnan and Knutsen

(2011) studied the analytical issues of acrylamide determination. Jin et al.

(2013) provided a review on the relationship between antioxidants and acry-

lamide formation. Van Der Fels-Klerx et al. (2014) studied the acrylamide and

5-hydroxymethylfurfural formation during baking of biscuits, in addition to the

effect of NaCl and temperature in processing biscuits.

The EU Commission (2011) document provides recommendation on inves-

tigations into the levels of acrylamide in food. The scientific report of EFSA

(2011) deals with the result on acrylamide levels in food from monitoring

years 2007–2008 and exposure assessment. The CAOBISCO document (2008)

contains a review on acrylamide mitigation in fine bakery wares and crisp bread.

It deals with measures recommended in the CIAA Toolbox, but not confirmed by evidence

from this survey and validated as commercially viable: crop selection for lower

asparagine, rework reduction, calcium and amino acids, fermentation extended

time and dough resting time reduction. It informs on the results or partial results

of approaches: ammonium bicarbonate replacement, fructose/reducing sugar

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540 Confectionery and chocolate engineering: principles and applications

replacement, applications of asparaginase, thermal input and colour end point,

moisture specification change, low free asparagine (ASN) cereals, dilution and

agronomy and innovative processing. Finally, it refers to the health impact of

the mitigation methods which is often doubtful, for example, the increased

intake of sodium substituting ammonium ion.

16.2.3 Strategies to reduce acrylamide levels in foodAnese (2012) summarizes the strategies to reduce acrylamide levels in food

which are mitigation by agronomical and technological approaches, as well

as removal by technological approach. A brief survey of these strategies is as

follows:

Technological strategies based on physical approach: Acrylamide formation is dramat-

ically influenced by the heating temperature and the time as well as by the

modality of heat transfer during processing. Maintaining the relative humid-

ity high during baking proved to be effective in reducing acrylamide levels in

bakery products; namely, as long as the water evaporates (the temperature

does not exceed 100 ∘C), no acrylamide is detected in bakery products. On the

contrary, the lower the moisture in the product, the more acrylamide is formed

at a given temperature. A lower amount of acrylamide in bakery products can

also be achieved by combining conventional and radio frequency heating.

Technological strategies based on chemical approach: Among others it is to be men-

tioned that organic acids (citric, acetic, L-lactic acid), calcium and sodium salts

effectively reduce acrylamide formation in the final product. However, substi-

tution of ammonium carbonate or bicarbonate with the corresponding sodium

salts leads to finished products often unacceptable (!) for consumption.

Strategies based on a biotechnological approach: Asparaginase pretreatment of raw

potatoes and dough has been claimed to reduce effectively acrylamide levels

without altering the appearance and taste of the final product. The biotech-

nological approaches for acrylamide reduction involve fermentation by yeast

and lactic acid bacteria.

Mogol (2014) studied the possibilities for mitigation of thermal process con-

taminants by alternative technologies.

16.3 Alkalization of cocoa material

16.3.1 Purposes and methods of alkalizationThe cocoa substance (cocoa nibs, the cotyledon) contains many acidic com-

ponents, which have a harsh flavour; see Rohan and Stewart (1963, 1964a,b,

1965a,b, 1966a,b) and Bonar et al. (1968). Also, flavonoids play an important

role in the development of cocoa powder. The purposes of alkalization, first

applied by Van Houten in 1828, are:

• To neutralize acidic components

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Chemical operations, ripening and complex operations 541

• To bring about chemical changes in flavonoids in order to develop the deep

brown colour of cocoa powder

• To bring about swelling and solubilization of the cellulose and hemicellulose

components of the nibs to improve the flotation properties of the cocoa parti-

cles in solution

• To increase the proportion of free cocoa butter by opening the cells of the nibs

Alkalization has to be finished by evaporation in order to reduce the mois-

ture content of the cocoa mass below 1%, which is a principal requirement for

pressing. The most frequently applied methods of alkalization (often called prepa-

ration) are:

• The Dutch process: alkalization of nibs

• The German process: alkalization of cocoa liquor (cocoa mass)

16.3.2 German processAlkalization is discussed in detail in classical publications, for example, Fincke

(1965) and Minifie (1999). Here only the German process will be briefly

described (Fig. 16.5), in order to emphasize an interesting aspect: phase

inversion.

In alkalization, by any method, the pH is increased to about 7–8 (in extreme

cases, up to 9.5) by using aqueous alkali, mostly a solution of potassium car-

bonate (potash) or bicarbonate. The characteristic concentrations are as follows:

100 kg of cocoa mass is stirred with 10 kg of water containing about 1–3 kg of the

potassium compound. (If more potash is added, alkalization is terminated by the

addition of citric acid in order to lower the pH to neutral.) The potash solution is

continuously stirred into the cocoa liquor for about 8 h at ca. 110–115 ∘C to allow

the continuous evaporation of water. In contrast, if the potash solution is added

to cocoa liquor in one block, the cocoa liquor, of W/O type emulsion, is inverted

into an O/W-type emulsion, and as a consequence, the rheological properties

change drastically: the power requirement of the stirrer is strongly increased.

Also, the mixture takes on a mud-like appearance and is violet brown in colour.

Cocoa

Adds

Fla

vons

Cellu

lose

Hem

icellu

lose

(Free)

Butter

(Bound)

Diffusion

Aqueous alkali

Condensation

Neutralization

Swelling

and partial

solubilization

Figure 16.5 Changes during alkalization (German process).

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542 Confectionery and chocolate engineering: principles and applications

However, this method of alkalization is radical, and the cocoa liquor–potash

solution mixture needs very robust machinery for kneading and evaporation.

Evaporation is the last operation of alkalization which finally re-established the

original W/O emulsion state of cocoa liquor. In this state the viscosity of cocoa

liquor is sufficiently low for pressing.

16.4 Ripening

In food production, the collective designation for most of the enzymatic processes

that take place is ripening. However, in confectionery manufacture the concept

of ripening is used also for processes that occur as a result of diffusion. A typical

example is Ostwald ripening, which can be manifested as coagulation of very

small particles in an emulsion or dissolution of crystals of very small size.

From the point of view of thermodynamics, ripening is a process of stabilization,

that is, the first step is to bring about an unstable state, which then changes

spontaneously into a stable state in a certain time (e.g. during storage).

Some processes of ripening are practically complete before the product leaves

the factory; however, many carry on in the consumers’ home, for example,

transcrystallization of cocoa butter. These phenomena point to the fact that a

definition of food stability is necessary that is in conformity with the understand-

ing of thermodynamics and takes into account the fact that in certain cases the

technological aim is to create an unstable state; see Chapter 18.

16.4.1 Ripening processes of diffusionFondant ripening is a typical case of Ostwald ripening. A well-known experience

is that if fondant mass is allowed to rest overnight before shaping, its consistency

will be entirely changed to its advantage (e.g. such a fondant, when blended with

other ingredients, is not so apt to dry). However, modern technologies operate

continuously and do not allow the new fondant mass to rest.

Fondant ripening was studied by Maczelka and Gyorbíróné (1958), who deter-

mined that the optimal size interval of the sucrose crystals was 5–20 μm; crys-

tals larger than 30 μm can be perceptible in the mouth. Karácsony and Pentz(1955a,b) determined that very small crystals (ca. 1 μm) were dissolved after leav-

ing the fondant machine, and about 24 h was necessary for the development of

a stable state in the crystalline bulk of the fondant mass. Consequently, calcula-

tions of the liquid phase based on the chemical composition of the fondant can be

regarded as an approximation only, because the solubility values are dependent

on the crystal size; however, this effect cannot be calculated.

For crusted liqueur bonbons/pralines, an aqueous sucrose solution of boiling

point 112.5 ∘C is made (schwach pflug, weak blow), and then ethyl alcohol and

flavouring (rum, brandy etc.) are blended with it; finally, this flavoured alco-

holic solution is cast into moulds made of starch, and the surface of the centres

is dusted with starch. After 10–12 h, the palettes are turned. The entire period

of crystallization takes about 24 h, during which a continuous sucrose crust,

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Chemical operations, ripening and complex operations 543

including the diluted liqueur, is formed. After the centres have been carefully

undusted, they may be packed or covered by chocolate. Traces of acid are the

killer of this technology because inversion hinders the crystallization of sucrose.

The following types of grained sweets can be distinguished:

• Hard-boiled sweets grained by humidity of filling. The trick of the technology is that

crystallization in a sugar mass needs a certain water content and a suitably

low reducing sugar content (a dry sugar mass of about 13–14%). In the case of

hard-boiled sugar bonbons with an aqueous filling (e.g. fruit jellies), this con-

dition means that the water content of the filling can start the crystallization

(graining) of the sucrose in the sugar mass. As a result, the sugar mass becomes

entirely grained and slightly whitened: the consistency of a hard-boiled sugar

bonbon becomes soft.

• Hard-boiled sweets grained by pulling (forced crystallization). In Section 2.2.2, the

technology of crystalline grained drops was discussed. Both the cream of tar-

tar and the glucose syrup technology result in a sugar mass that is suited

to crystallization because of its low reducing sugar content. When the sugar

mass is pulled, a forced crystallization starts in the sugar mass, which takes

some days.

The effect of pulling is wide ranging: small, thin tubes are formed by it. At the

beginning, the volume of the pulled mass increases (the density of the sugar mass

decreases from 1.5 to ca. 0.9 in 6–7 min); later the small tubes break, which causes

an increase in the density of the sugar mass; see Sokolovsky (1951, p. 103) and

Figure 2.18. The pulling induces, if the composition of the sugar mass is correct,

a slow crystallization that extends step by step over the entire volume of the

product.

The warm, wet air of the store room promotes crystallization of the unpacked

product. If the product is packed promptly after leaving the cooling tunnel, crys-

tallization will be slower.

• Sweets grained by addition of fondant (fudge). In fudge, crystallization originates

from sucrose crystals added to the fondant mass. The process of crystallization

starts quickly but continues slowly for about half an hour after the product has

left the production line. The structure is entirely homogeneous because of the

thorough mixing.

• Sweets grained by spontaneous crystallization (grained caramels). Crystallization is

generated by the correct high ratio of sugar to glucose syrup (i.e. a low reducing

sugar content). The usual method of shaping such grained caramels is casting

into moulds of starch dust. The crystalline structure of the centres develops

slowly during solidification in the moulds (3–4 h), and it has a certain inho-mogeneity: the external part of the centres is more solid than the internal part,

which is slightly creamy. This peculiar consistency is preferred.

16.4.1.1 Dissolution of fondant in cherry liqueur pralinesThe preparation of the fruit involves preserving washed sour cherries in an aque-

ous solution of ethanol of ca. 70 V/V% until the end of diffusion (4–6 weeks) at

12–15 ∘C.

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544 Confectionery and chocolate engineering: principles and applications

For the production of pralines, the cherries are placed in chocolate shells and

then covered by fondant mass. The cooled, solid fondant layer is then covered

with chocolate. The praline pieces need intensive cooling for demoulding; there-

fore, a slow, step-by-step warming up is necessary to avoid cracking them. It is

reasonable to couple this warming up (6–8 ∘C→15–16 ∘C) period with the ripen-

ing of the pieces, which takes approximately overnight.

During ripening, the change of temperature induces high tensions in the pra-

line pieces because the dilatations of the chocolate shell and the centre are dif-

ferent (Zs. Szabó-Forrás, Confectionery Research Laboratory, Budapest, 1970,

personal communication).

In addition, during this period the osmotic pressure differences between the

fondant mass and the cherries start to be balanced. Consequently, the fondant is

dissolved by the aqueous alcoholic solution, which diffuses from the cherry into

it. The effect of diffusion is that the filling becomes thinner and thinner, and the

solution can easily bubble through cracks. The high tensions, the cracking and

the thinning of the filling together may cause considerable problems if ripening

is neglected, and the pieces are packed promptly after demoulding.

16.4.1.2 Humidity balance between cookies and fillings (toughening)A rule of thumb may be applied in this relationship (here the term cookie refers to

any sweets made of flour): the cookie and the filling have to be contrary from the point of

view of hygroscopicity, that is, a cookie with hydrophilic properties (e.g. wafers and

biscuits of low fat content) needs a fatty filling, and a cookie with hydrophobic

properties (e.g. linzer and others of high fat content) needs a hydrophilic filling

(e.g. fruit jelly or jam).

If the cookie is hydrophilic, the use of a fatty filling hinders the toughening of

the cookie. If the cookie is hydrophobic (short pastry), the water content of the

filling migrates to a certain extent into the cookie, which makes its consistency

short. (The effect of air humidity is similar.)

Thus, a cookie with hydrophilic properties must be protected from humidity

(=fatty filling), while a cookie with hydrophobic properties needs some humidity

for an optimal consistency (=aqueous filling).

16.4.1.3 Ripening of dough before shapingRelaxation is recommended because during it beneficial processes take place in

the dough, which are driven by diffusion in general. Naturally, in the case of a

yeast dough, ripening means both fermentation and diffusion. For further details,

see Section 16.5.4.

16.4.1.4 Tempering of chocolate mass and polymorphismThe aim of the tempering of chocolate mass is to generate the 𝛽(V) modification

of cocoa butter, the transcrystallization of which into the 𝛽(VI) modification is

sufficiently slow to produce a product of stable quality. At the same time, during

tempering, the crystals of the very unstable 𝛽(IV) modification are melted.

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Chemical operations, ripening and complex operations 545

Cooling and storage have to provide the correct conditions to prolong the

𝛽(V)→ 𝛽(VI) transcrystallization of cocoa butter as long as possible. Conse-

quently, tempering generates an unstable state, the stabilization of which is

controlled both in production and in storage.

Polymorphism is discussed in Section 10.9.1.

16.4.2 Chemical and enzymatic reactions during ripeningOnly acidic and enzymatic inversions have been mentioned here, because a

detailed discussion of the processes that take place in baking, in the development

of flavour, is beyond the scope of this book.

16.5 Complex operations

16.5.1 Complexity of the operations used in the confectioneryindustry

Foods are systems consisting of many ingredients, and the ingredients themselves

are complex systems as well. Consequently, any operation exerts a wide range

of effects on them. This complexity of operations means an essential difference

compared with chemical operations.

The various fields of confectionery engineering are typical from this point of

view: many raw materials are blended, and many operations are used to process

them. In Sections 16.5.2 and 16.5.4, structure theory (see Appendix 5) is used

to take this complexity of operations into account when conching and dough

preparation are discussed.

16.5.2 ConchingConching is one of the most studied fields of chocolate manufacture. The first

steps in studying the conching process were taken by Zipperer (1924), Fincke

(1936), Aasted (1941), Taubert (1954), Heiss (1955) and Rohan (1965). Fincke

(1965), Minifie (1999) and Marshalkin (1978) discussed the conching process in

detail.

According to Fincke (1956b) and Acker and Diemair (1956), the fat-free cocoa

material has a strong anti-oxidative effect, which protects cocoa butter from oxi-

dation. Bartusch and Mohr (1966) determined that a decrease in the water and

acid contents of chocolate mass took place together during conching. Although

the tendencies of both processes may be described by a decreasing concentra-

tion versus time curve, this curve actually consists of concentration minima and

maxima, which become fewer and fewer as time progresses. The reason for this

phenomenon may be explained by briquetting of the chocolate particles during

the refining process, which is a consequence of the pressing performed by the

rollers. During conching, the small briquettes are comminuted step by step, and

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546 Confectionery and chocolate engineering: principles and applications

humidity and acid vapours are evaporated from the surface of the briquettes. But

the regeneration of the evaporation surface is not continuous, and this causes

fluctuations of the concentrations of about 0.1%.

Sommer (1973) studied the change of the concentration deviation in the pro-

cess of homogenization of a 1 : 1 mixture of cocoa butter and sugar powder.

Tscheuschner et al. (1992a,b, 1993a,b) experimentally demonstrated that

dry conching may lead to aggregation or de-aggregation of chocolate particles,

depending on the temperature, the water content and the shear rate generated

by the conching machine. These phenomena are highly influenced by the types

of sugars and milk solids. A high temperature and a low-to-medium intensity of

shearing promote aggregation, whereas intensive shearing and long conching

diminish the size of the aggregated particles in chocolate. The aggregation of

particles during dry conching of milk chocolate is a complex process in which

amorphous lactose and the humidity play an essential role.

For details of the physico-chemical relations of the polymorphism of lactose,

see King (1965).

In the initial step of aggregation, the free humidity, sugar and other hydrophilic

ingredients are in contact. As a result, a soft aggregate is formed, which may be

dissolved by the effect of a high shear rate. In contrast, the aggregate may solidify

when the humidity decreases. For this reason, it is important that the humidity

of the chocolate, which became free during roll refining, is rapidly decreased at

the beginning of conching. Free humidity is absorbed by amorphous lactose and

is needed for lactose crystallization. In the process of lactose crystallization, there

is free water at the start. If this water is not quickly eliminated, it dissolves a small

portion of the sugar content, which is sufficient to start aggregation. The process

of lactose crystallization is dependent on temperature, and it starts below about

30% relative humidity if the temperature is higher than about 60 ∘C.

For further details, see Mohos (1979), Tscheuschner et al. (1992a,b, 1993a,b),

Winkler and Tscheuschner (1998), Scheruhn et al. (2000), Tscheuschner (2000),

Franke et al. (2001, 2002), Franke and Heinzelmann (2006) and Gray (2006).

In brief, the technological procedure consists of the following steps. The

chocolate mass is refined by five rollers; a total fat content of ca. 26–27 m/m%

is necessary for refining. After refining, the chocolate, of powder consistency, is

transported to the conche machines, where it is liquefied by adding 1–2% cocoa

butter and kneading strongly. According to practical observations, intensive

kneading of chocolate mass of high viscosity is very beneficial from the point

of view of quality. This period is called dry conching and takes some hours. Dry

conching is followed by wet conching, in which a 1–2% amount of cocoa butter

is added to the chocolate mass again. Finally, half an hour before the end of the

process, ca. 0.3–0.4% of lecithin is added to the chocolate mass to emulsify the

residual water content of the mass in the suspending cocoa butter phase. The

use of lecithin is very financially advantageous because it causes a decrease in

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Chemical operations, ripening and complex operations 547

Aroma

development

(Maillard reaction,

oxidation,

etc.)

Change of

flow properties by

kneasing and

emulsification

Steam

distillation

(decrease of

acid content)

Figure 16.6 Triangle model of conching.

viscosity equivalent to that caused by about 7% cocoa butter (Fincke, 1965).

Thus, the final cocoa butter content of the chocolate mass for bars can be

relatively low, about 30–33% (for couverture, the value is higher, 35–38%).

When conching was first used, the duration was very long, ca. 3 days for dark

chocolate and 1 day for milk chocolate, because the conche pot (Langreiber in Ger-

man) was unable to provide sufficiently intensive kneading and aeration for the

removal of the water and acid content. Later, as a result of many developments,

the alternating motion of the rollers agitating the chocolate in the conche pot

was replaced by a rotating motion, and several different solutions have also been

developed for intensifying the aeration (e.g. the use of vacuum and blowing-in

of warm, dry air).

In the last 30–40 years, compact conching solutions have been developed, the

common property of which is that refining, kneading and aeration are cou-

pled together either in one machine or in a closed transport circle of machines.

Although opinions on the quality of the chocolate produced with such com-

pact machines differ, they have many advantages (saving of space, simplicity of

operation, cheapness, low repair costs, etc.). In addition, these solutions have

contributed to the demystification of conching.

16.5.2.1 Batch conchingMohos (1982) developed a qualitative model (the triangle model) of batch conch-

ing by the application of structure theory as shown in Figure 16.6.

The quantitative model (Fig. 16.7) consists of the following parts (the conserved

substantial fragments that the calculation refers to are given in parentheses).

The set of conserved substantial fragments:

1 Dry, fat-free cocoa material (7 kg)

2 Cocoa butter (dry) (26 kg)

3 Sucrose (dry)+milk dry material (62 kg)

4 Oxygen

5 Water (1 kg)

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548 Confectionery and chocolate engineering: principles and applications

Gas phase

Chocolate

mass

Chocolate

massConched

Liquid phase

a3 = 4 5

a5 = 4 5

a6 = 3

a4 = 1 4 5

a1 = 1 2 3 5

a2 = 1 2 3 5

1 2 3 4 5

Figure 16.7 Quantitative conching model based on conserved substantial fragments. For

example, a3 = |4|5| means a material flux consisting of oxygen and water.

The set of material fluxes:

a1 the chocolate mass at the start of conching

a2 the dry ingredients of the chocolate mass conched (without Maillard

product or lecithin)

a3 the humidity and oxygen of the air entering the conche machine

a4 the humidity and oxygen of the air leaving the conche machine, enriched

by acid content from the cocoa material

a5 the water content and amount of oxygen bound in the chocolate mass by

oxidation

a6 M (the product of the Maillard reaction)

The chocolate mass that is conched is a union of three material fluxes: a2, a5

and a6.

The set of technological changes (where t is the time coordinate):

Evaporation of acids, s= s(t): the amount of acid evaporated

Maillard reaction, M=M(t): the amount of Maillard reaction product

Oxidation, y= y(t): the amount of oxygen that reacts with the cocoa material

Evaporation of water, w=w(t): the amount of water evaporated

The set of phases:

G= gaseous

L= liquid

We can express the value of a2 as follows, taking into account the set of tech-

nological changes:

a2 = (7 − s − y) + 26 + (62 − M) + (1 − v) (16.13)

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Chemical operations, ripening and complex operations 549

Let us study the elements of the set of technological changes in order to obtain

the value of every material flux at the end of conching.

Evaporation of acids. According to Bartusch and Mohr (1966), the changes of

the water and acid contents of the cocoa mass parallel each other, that is, we

may write

s0 − st = k1(w0 − wt) (16.14)

where s0 and st are the acid contents of a2 when t= 0 and t= t, respectively; w0

and wt are the water contents of a2 when t=0 and t= t, respectively; and k1 is

the rate constant (1/time).

Maillard reaction. For the rate of the Maillard reaction, it is assumed that

Mt − M0 = k2(w0 − wt) (16.15)

where M0 and Mt are the amounts of the conserved substantial fragment (3) in

a2 that participate in the Maillard reaction when t= 0 and t= t, respectively.

Oxidation. For the rate of oxidation, it is assumed that

yt − y0 = k3(w0 − wt) (16.16)

where y0 and yt are the amounts of (1) in a2 that are oxidized when t= 0 and

t= t, respectively.

We introduce the simplifying notation (w0 −wt)≡w. It may be assumed that

ΔY = k4(y0 − yt) = k3k4w

where ΔY is the loss of oxygen in the input air. Thus,

a5 = ΔY + (y0 − yt) = k3w(1 + k4) (16.17)

a3 = L + k5L = L(1 + k5) (16.18)

where L is the oxygen content of the input air and k5L is the water content of

the input air if p and V are constant. The value of k5 is 10.76×10−3 kg/0.2314 kg

dry air at t= 35 ∘C and relative humidity 30%. (The increase in the proportion

of nitrogen in the air that accompanies the decrease in the amount of oxygen is

neglected.)

a4 = L(1 + k5) + w(1 + k1 − k3k4) (16.19)

a6 = (M0 − Mt) − k2w (16.20)

The value of a2 at the end of conching (see Eqn 16.13) is

a2 = (7 − k1w − k3w) + 26 + (62 − k2w) + (1 − w) = 96 − (1 + k1 + k2 + k3)w(16.21)

Evidently, the task has been simplified to a drying task because

1 + k1 + k2 + k3 = constant (16.22)

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550 Confectionery and chocolate engineering: principles and applications

A drying process may be most easily modelled by a first-order kinetics:

ddt(w0 − wt) = k0(wt − w∞) (16.23)

where w∞ is the water content of the chocolate mass after very long conching

(≈0.3%). (The value of w0 is ≈1.3–1.5%). After integration,

wt = (w0 − w∞) exp(−k0t) + w∞ (16.24)

The halving time can be obtained from

𝜏1∕2 = ln 2k0

(16.25)

The value of the halving time 𝜏1/2 can be regarded as a measure of the effec-

tiveness of a conching machine. In order to obtain comparable results for conche

machine effectiveness, either the value of w∞ should be given together with 𝜏1/2

(e.g. 𝜏1/2 =8 h; w∞ = 0.3%) or a value of w∞ should be defined (standardized) by

the industry.

The kinetic constant k0 and, therefore, also the value of the halving time are

dependent on the amount of charge, that is, the way to correctly characterize a

conche machine is as 𝜏1/2 =X hours (referring to Y tonnes of chocolate). Since Y

tonnes means a characteristic property of the construction of the machine, every

amount of charge has its own characteristic halving time.

Example 16.1In a conching machine of volume 5 m3, w0 = 1.4% and wt =0.8% when t=6 h

and w∞ =0.3%. (This is a very effective conche.) Let us calculate the halving

time 𝜏1/2.

From Eqn (16.24),

wt − w∞

w0 − w∞= exp(−k0 × 6) = 0.8 − 0.3

1.4 − 0.3

that is,

exp(k0 × 6) = 1.10.5

= 2.2

K0 × 6 = ln 2.2 = 0.7885 …

k0 = 0.1314 …

and

𝜏1∕2 = ln 20.13142

= 5.274 h

Checking: the half-value is (1.4+ 0.3)%/2= 0.85%, that is,

1.4% → 0.85% ↔ (0 → 5.274 …) h

0.85% → 0.8% ↔ (5.274 … → 6) h

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Chemical operations, ripening and complex operations 551

If conching is continued, the water content after 2× 𝜏1/2 (2×5.274 h=10.548 h) will be (0.85+ 0.3)%/2= 0.575%.

An approximate calculation of the values of rate constants. Rohan and Stewart (1963,

1964a,b, 1965a,b, 1966a,b) and Bonar et al. (1968) studied the change of acid

content of chocolate during conching. They determined that the loss of acid con-

tent of cocoa mass during conching for 48 h was about 0.14%. If the loss of water

content is approximated by a value of 0.8% and the ratio of cocoa mass in milk

chocolate is R, then, from Eqn (16.14), the value of k1 is

k1 = RΔsΔw

= R × 0.14% acid0.8% water

= R × 0.175% acid∕% water

If the value of R is 0.12, then

k1 = 0.12 × 0.175 g acid∕g water = 0.021 g acid∕g water

Mohos (1982) studied the change of the hydroxymethylfurfural content of

milk chocolate during conching, and the following equation was obtained:

HMF = [2.25 + 0.674(T − 45∘C)∕∘C + 0.1723t∕h](mg∕kg milk chocolate)(16.26)

where T is the temperature of conching (∘C) (interval studied 45–60 ∘C) and t

is the duration of conching (h) (interval studied 0–20 h). (The values of r were

0.9954 at 45 ∘C, 0.9673 at 50 ∘C, 0.9384 at 55 ∘C and 0.9781 at 60 ∘C.)

Evidently, the quantitative description of conching sketched earlier can be

regarded as only approximate, because Eqn (16.24) is linear in t; however, Eqn

(16.15) leads to an exponential function of t. Nevertheless, this linear kinetics

is uncommon, and therefore first-order kinetics will be applied in the following

treatment; further studies are necessary to clear up this question.

Regarding the exactness of such an approximation, the following Taylor series

can be considered:

C exp(kt) = C + Ckt +(C

2

)(kt)2 + · · ·

where C and k are constants and t is the time. In the present case,

C = [2.25 + 0.674(T − 45 ∘C)∕∘C](mg milk chocolate)

k = 0.17232.25 + 0.674(T − 45 ∘C)∕∘C

(h−1)

The greatest error is for T=45 ∘C because at this temperature the value of k is

highest (the rounded values are k= 0.0766 and C= 2.25).

For convergence, kt<1 is needed, that is, t< (1/0.0766) h→ t< 13.055 h. Con-

sequently, if an exponential function is applied instead of a linear function (Eqn

16.26), as time passes, this approximation becomes more and more inaccurate,

and when t≥ 13.055 h, it is not usable at all.

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552 Confectionery and chocolate engineering: principles and applications

According to Mohos (1982), in dry conching of milk chocolate, the tempera-

ture must not be higher than 60 ∘C; the optimum is about 55 ∘C, and this period

is recommended until the HMF content reaches 10–15 mg/kg. For storage of milk

chocolate, a maximum temperature of 45 ∘C is recommended. Rheological mea-

surements (Mohos, 1966a) show that above 45 ∘C the viscosity of milk chocolate

starts to increase, and the mass shows the phenomenon of rheopexy, which is

related to structural changes. Rheopexy is greater in milk chocolates produced

with milk crumb than with milk powder.

According to Gray (2006), the viscosity of chocolate is high below 40 ∘C,

although such temperatures are essential for masses using monohydrate sugar

alcohols (and, according to Mohos, also dextrose monohydrate). Above 60 ∘C,

white chocolate will darken and its flavour will be affected. Above 75 ∘C, milk

chocolate may caramelize, depending upon its recipe – this is often desirable.

Above 85 ∘C, milk chocolate can start to burn, which introduces a bitter note.

Again, this may be desirable. The temperature range 50–100 ∘C is suitable for

dark chocolates. At the end of conching, the mass must be cooled to 40–45 ∘Cfor storage or immediate use. White chocolate should be stored at the lower end

of this range.

For estimation of an average value of k2, we assume that T= 50 ∘C, t= 20 h and

the loss of water content is 0.7%. Then,

ΔM = 2.25 + 0.674(50 − 5) + 0.1723 × 20 = 9.066 mg HMF∕kg milk chocolate

k2 = −ΔMΔw

= −9.066 mg HMF∕7 g water = −1.291 mg∕HMF∕g water

The negative sign means that while the water content of the chocolate mass

is decreasing, the HMF content of it is increasing. In Eqn (16.21), k2 and k3 are

of negative sign because an increase in HMF content (and in the amount of oxi-

dation product) means a loss similar to evaporation of water and volatile acids;

however, from the viewpoint of kinetics, the rate constants k0 and k1 are nega-

tive, and k2 and k3 are positive.

Lipscomb (1954) determined that 100 g of cocoa mass absorbs about 12.3 mg of

oxygen in 16 h, that is, 1 kg of milk chocolate of 12% cocoa mass content absorbs

0.123 g× 0.1= 0.01476 g of oxygen. If the loss of water content is approximated

as 0.6%, then

k3 = −Δy

Δw= −14.76 mg oxygen∕6 g water = −2.46 mg oxygen∕g water

The results may be summarized by a matrix equation:

(ddt

)⎡⎢⎢⎢⎢⎣

w

s

M

y

⎤⎥⎥⎥⎥⎦

=

⎡⎢⎢⎢⎢⎣

−k0 0 0 0

0 −k0k1 0 0

0 0 k0k2 0

0 0 0 k0k3

⎤⎥⎥⎥⎥⎦

×

⎡⎢⎢⎢⎢⎣

w

s

M

y

⎤⎥⎥⎥⎥⎦

(16.27)

The stability matrix (see Section 18.4) is regular (its determinant is not zero),

but its two positive elements (k0k2 and k0k3) show that the Maillard reaction and

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Chemical operations, ripening and complex operations 553

the oxidation cannot be controlled. These processes are theoretically unstable:

the increase in the amounts of Maillard and oxidized products is unlimited in an

infinite time, although these possibilities have no practical importance.

If linear kinetics are supposed in the cases of the Maillard reaction and oxida-

tion, then the correct form of Eqn (16.27) is

dwdt

= −k0w,dsdt

= −k0k1s,dMdt

= k0k2,dy

dt= k0k3 (16.28)

Also in this case, the system is unstable, although the increase of M and y is

slower.

The development of aroma in chocolate is a very complicated process, and the

present discussion has been limited to modelling the decrease of the volatile acid

content and the increase of the Maillard reaction product. Besides these factors,

many others need to be taken into account, but a discussion of them is beyond

the scope of this book.

Similarly, the change of consistency during conching is an important topic (see

Chapter 4).

16.5.2.2 Modelling a continuous conching process with high shear rateFranke and Tscheuschner (1991) developed a model of a high-shear-rate conch-

ing process, applying the Danckwerts one-dimensional dispersion model (Danck-

werts, 1953). It is assumed that the materials move axially at a mean rate w in

the conching equipment, which is a double-mantled tube of length L, and the

chocolate mass and the cooling water flow in countercurrent on the two sides of

the mantle. To this motion a turbulence produced by inserts and by an air feed

is added, which is shown by the axial diffusion coefficient Dax:

𝜕m𝜕t

= −w𝜕m𝜕x

+𝜕(Dax𝜕m∕𝜕x)

𝜕x(16.29)

where x is the coordinate in the axial direction (m), 0≤ x≤ L; w is the mean speed

(m/s), assumed to be constant in the steady state; dm/dt is the rate of change of

the quantity of chocolate mass in a considerable space (kg/s); −w 𝜕m/𝜕x is the

convective transport at a mean rate w; Dax is the axial diffusion remixing (m2/s);

and 𝜕(Dax 𝜕m/𝜕x)/𝜕x is the mass transport by axial diffusion.

The model assumes linearity of Dax(x) as a function of x:

Dax(x) = Dax.0 + xDax.1 (16.30)

where Dax.0 and Dax.1 are constant. By using this assumption, the equation of

continuity (Eqn 16.29) is

dmdt

= (Dax.1 − w)𝜕m𝜕x

+ (Dax.0 + xDax.1)𝜕2m𝜕x2

(16.31)

The heat balance can be written by applying the following assumptions:

1 Heat conduction between layers within the chocolate mass is neglected.

2 The possible state transitions of cocoa butter are neglected.

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554 Confectionery and chocolate engineering: principles and applications

3 Heat exchange with the environment of the conching equipment is neglected.

4 Steady-state conditions are assumed, that is, the heat balance for a chocolate

layer of width dx is zero:

− dH′back − dH′

ch − dH′w + dH′

D = 0 (16.32)

where dH′back

is the enthalpy change due to diffusion back mixing (W), dH′ch

is the

convection enthalpy change of the chocolate mass (W), dH′w is the heat exchange

by the cooling water (W) and dH′D is the heat dissipated from the power input

by the shearing devices (W). The primes ′ mean derivatives with respect to time,

that is, d( )/dt.

The terms of Eqn (16.32) can be expressed as

dH′back =

(Dax.0 + xDax.1

Dax.1 − w

)m′

chcp.ch

(𝜕2Tch

𝜕x2

)dx (16.33a)

The model uses an approximation

− dH′back =

(Dax(x)

w

)m′

chcp.ch

(𝜕2Tch

𝜕x2

)dx (16.33b)

Moreover,

dH′ch = m′

chcp.chdT ′ch (16.34)

where m′ch

is the mass flow of chocolate (kg/s), cp.ch is the specific heat capacity

of the chocolate (J/kg K) and dTch is the temperature change of the chocolate

mass (K):

dH′w = (d 𝜋 dx)kw(Tch − Tw) (16.35)

where d𝜋 dx is the area of the heat transfer surface (m2), d is the inner diameter of

the tube (m), kw is the (resultant) heat transfer coefficient between the chocolate

mass and the cooling water (W/m2 K) and Tch and Tw are the temperatures of

the chocolate mass and cooling water, respectively (K):

dH′D = PD(x) dx (16.36)

where PD(x) is the position-dependent power dissipated per unit length input by

the shear elements of the conching equipment.

Substituting Eqns (16.33)–(16.36) into Eqn (16.32), a common linear

second-order differential equation results, which describes the temperature

profile (Tch vs x) of the chocolate mass along the length of the conching

equipment:

[Dax(x)

w

]m′

chcp.ch

(𝜕2Tch

𝜕x2

)+ m′

chcp.ch

(dT ′

ch

dt

)+ (d𝜋)kw(Tch − Tw) − PD(x) = 0

(16.37)

In Eqn (16.37), Tw is unknown and can be calculated from the energy balance

around a thin layer of the cooling jacket of the conching equipment.

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Chemical operations, ripening and complex operations 555

To calculate the temperature profile of the cooling water:

1 A steady-state process of cooling is assumed, that is, dH′w∕dt = 0 (the enthalpy

flow of the cooling water is constant).

2 Back mixing within the cooling water is neglected.

These assumptions result in the equation

m′wcp.w

(dT ′

ch

dx

)+ (d𝜋)kw(Tch − Tw) − (dout𝜋)ken(Tw − Ten) = 0 (16.38)

where m′w is the mass flow of cooling water (kg/s), cp.w is the specific heat capacity

of the chocolate (J/kg K), dout is the outside diameter of the cooling jacket (m), ken

is the heat transfer coefficient between the cooling water and the environment

(W/m2 K) and Ten is the temperature of the environment (K).

The system of coupled differential equations (16.37) and (16.38) represents

the Franke–Tscheuschner process model. The variables included are

Process variable∶ m′ch,m′

w;

A geometric variable∶ x;

Thermodynamic variable∶ cp.ch, cp.w, kw, ken

Transport variables∶ w,Dax.0,Dax.1

These variables can be determined for any particular conching equipment in

order to calculate the process model.

The variable that cannot be simply determined is the dissipated power per unit

length, PD(x), because both dissipation and diffusion take place in the chocolate

mass in parallel. It is assumed that the total power required, Ptotal(x), can be

separated into two parts:

Ptotal(x) = PD(x) + PD(x)str (16.39)

where PD(x)str is the power used for the structural modification of the choco-

late mass.

By using the notation for the ratio PD(x)/Ptotal(x)≡ 1− zstr(x), we assume the

linearity of zstr(x):

zstr(x) = zstr.0 + xzstr.1 (16.40)

where zstr.0 is a constant (the initial value at x= 0) and zstr.1 is a constant (the

variation of zstr(x) along the length of the equipment). The linear model repre-

sented by Eqn (16.40) has been validated by the fact that there is good agreement

between real measured temperatures and the temperatures calculated from the

process model using the parameter zstr(x).

By varying the chocolate mass flow m′ch

, a plot of w versus m′ch

, is constructed,

which can be approximated by a quadratic function f, that is, w= f(m′ch

); further-

more, a plot of Dax.0 versus m′ch

is constructed, which can be approximated by a

quadratic function g, that is, Dax.0 = g(m′ch).

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556 Confectionery and chocolate engineering: principles and applications

To describe the variation of the power input with time, P(t), an exponential

approximation is applied:

P(x) = P0 exp(− t𝜏

)(16.41)

where P0 is the starting value of the power input (W) and 𝜏 is a time constant

(s) describing the decrease of power input with increasing shearing time. When

plots of P0 versus T and 𝜏 versus T for different amounts of chocolate mass are

constructed, the types of approximate equation obtained are

P0 = −A + Bm − C(mT) (16.42)

𝜏 = D − Em − FT + G(T) (16.43)

where m is the amount of chocolate in the container (kg), T is the temperature

(K) and A (W), B (W/kg), C (W/kg K), D (s), E (s/kg), F (s/K) and G (s/kg K) are

positive constants.

According to Franke and Tscheuschner’s experiments, the fraction of the

power input required to modify the structure of the chocolate mass varies from

60% to 85%, and with increasing throughput, the fraction used for this modi-

fication of the chocolate mass decreases while the dissipative fraction increases,

that is, the efficiency of the equipment deteriorates. No significant correlation

between the conching temperature and the percentage of structural modification

was identified. For further details, see Franke and Tscheuschner (1991).

16.5.2.3 Conching degreeThe conching degree (CD) can be defined qualitatively as a noticeable effect of

conching on the taste of chocolate. A high CD means a harmonious, intense

chocolate flavour in sensory terms. The CD can be measured (Ziegleder et al.,

2003; Ziegleder, 2004) and can be calculated as the reciprocal values of chosen

markers (benzaldehyde and tetramethylpyrazine). These volatile marker com-

pounds are obtained by fractional short-time steam distillation and then iden-

tified and quantified by the GC-MS technique. The analytical values and the

sensory results are in good correlation.

16.5.3 New trends in the manufacture of chocolateIn the second half of the last century, many studies aimed at simplifying chocolate

manufacture focused on the following targets:

• To cut the duration of the conching process

• To improve the efficiency of certain unit operations, for example, comminution

and aeration of the chocolate mass

• To cut the costs and space requirements of the machinery (compact plant)

The most easily damaged parts of the machinery are eight- and five-roll refin-

ers. Substitution of eight-roll refiners was the easiest task: the comminution of

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Chemical operations, ripening and complex operations 557

cocoa nibs to cocoa mass can be performed by a disc mill, an agitated ball mill,

a beater blade mill or a combination of these. A logical idea was to substitute a

five-roll refiner by an agitated ball mill, which is a relatively cheap machine with

a small space requirement and high efficiency.

At the beginning of modern chocolate production, the melangeur was used as

a machine for homogenization – and for conching too! This tradition offered a

practical solution to the problem of finding a machine that could unify homog-

enization and conching.

The development of the conching process resulted in many types of conche

machines that used intensive circular motion instead of alternating motion (as in

the old longitudinal conche, the Langreiber) and intensive aeration. The typical

conche machine of today is a circular container with a rotating kneader, plus

strong ventilation.

Table 16.5 lists the relationships between the raw materials processed and the

unit operations in chocolate manufacture. It is evident that the sugar, milk dry

content and cocoa nibs need to be comminuted; however, there is a question of

which combinations of them would be the most efficient or whether separate

comminution would be preferred. This question, among others, was discussed

by Simon (1969a,b) and Ubezio (1976).

Processing using separate unit operations is one of the trends. For comminu-

tion of cocoa nibs by a combination of a disc mill, agitated ball mill and beater

blade mill, see Niediek (1973, 1978), Bauermeister (1978), Samans (1978), Gory-

acheva et al. (1979), Bertini (1989), Taylor and Zumbe (2000) and Alamprese

et al. (2007). For evaporation of cocoa mass and cocoa butter by a thin-layer evapo-

rator (for pre-conching), see Schmitt (1974, 1986, 1988), Heemskerk and Komen

(1987) and Bäucker (1974).

Separate production of milk crumb (milk+ sugar) or choco crumb (milk+ sugar+cocoa mass) in order to focus on the Maillard reaction is another trend. Both

types of crumb are produced by evaporation, condensation, kneading and drying

to ca. 4% of final water content. For further details, see Bouwman-Timmermans

and Siebenga (1995), Aguilera and Stanley (1999), Minifie (1999, pp. 144–148),

Table 16.5 Relationships between raw materials and unit operations carried out in chocolate

manufacture.

Homogenization Comminution Evaporation Maillard Rheology

Sugar Yes Yes No Yes Yes

Milk dry content Yes Yes Yes Yes Yes

Cocoa nibs Yes Yes Yes No Yes

Cocoa butter Yes No Yes No Yes

Lecithin Yes No No No Yes

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558 Confectionery and chocolate engineering: principles and applications

McCarthy et al. (2000), Beckett (2003), Lim and Barigou (2004), Edmondson

(2005) and Aguilera (2005).

Universal conching machines achieve all operations at the same time in the

same space. Continuous kneading machines have been well proven for

homogenization, and, consequently, agitated ball mills seemed to be an obvious

solution for coupling homogenization and comminution. An extreme case

of such a solution is when all the unit operations of chocolate manufacture

are implemented in a single machine of special construction: comminution is

performed by a tailored device using a knife, as in the MacIntyre and Lloveras

machines. All the other unit operations are automatically done during com-

minution. For further details, see Riedel (1991) for the MacIntyre technology,

and see the Lloveras technical documentation for the Lloveras Universal refiner

conche.

Some of the various nontraditional chocolate technologies are discussed in the fol-

lowing; however, it is nearly impossible to achieve completeness, and so instead

we cite the following references:

• LSCP (Lindt & Sprüngli Chocolate Process): see Kleinert (1971, 1973) and Coc-

colo (1973).

• Wiener process: see Karoblene et al. (1981) and Tadema (1988).

• EMA plant: see Heemskerk and Komen (1987).

• Konticonche: see Tscheuschner et al. (1981a,b) and Tscheuschner and Winkler

(1997).

In the first step (preparation of cocoa mass) of the Tscheuschner chocolate process,

a portion of the sugar (1–2%), dissolved in water, is added to the cocoa mass,

which is warmed to 80 ∘C in order to induce the Maillard reaction. Then the

water content of the cocoa mass is evaporated to a value of 0.3% by insuffla-

tion of conditioned air. The time and temperature conditions of preparation are

controlled and fitted to the quality requirements.

In the second step, this prepared cocoa mass is refined together with sugar. The

agglomeration in the refining is small after such a preparation, and, as a result

of intensive shear during conching for 10–20 min, the agglomerated particles are

reduced in size. Because a decrease in moisture content and a sufficient amount

of Maillard reaction, which are the usual requirements in the traditional conch-

ing process, have already been provided in the preparation step, the conching

time may be drastically reduced.

A similar preparation of milk powder is done before using any of the following:

• The NETZSCH process: see Harbs and Jung (2005).

• The Carle & Montanari system: see Anonymous (1985).

• The BFMIRA process: see BFMIRA (1970).

Further references are Perry (1968), Dunning and Dannert (1970), Hofmann

and Tscheuschner (1976), Billon (1984), Ritschel et al. (1985), Ley (1988),

Aguilar et al. (1995), Ziegler and Aguilar (1995, 2003), Müntener (1997, 2007),

Kuster (2000), Jolly et al. (2003) and Blakemore (2006).

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Chemical operations, ripening and complex operations 559

16.5.4 Modelling the structure of dough16.5.4.1 The phases of dough productionThe various kinds of dough are produced from flours (wheat, rye, etc.), water,

milk, various emulsions and suspensions, as well as additives. These ingredi-

ents are thoroughly mixed by special machinery (Z-blade kneader) in tempered

conditions. The dough production is a complex physical, chemical, colloidal and

microbiological process. Three phases of it can be theoretically distinguished:

16.5.4.1.1 HydrationThe flour as a hydrophilic xerogel is capable of adsorbing about 30 m/m% water

in relation to its own amount by its polar groups. The cereal skin, bran, etc.

become wet on surface only, without any thorough change. The water-soluble

ingredients (sucrose, proteins, minerals, etc.) become partly or entirely dissolved

to a colloidal solution. In this phase the most important proteins of flour, the

gliadin and glutenin, hardly change still, only a little amount of water is adsorbed

on their surface.

16.5.4.1.2 Swelling and development of glutenIn this phase the structure of gluten, a typical component of the dough net-

work is developed. The gluten proteins adsorb considerable amount of water

and swell to liogel. In the beginning of water adsorption, the protein fraction

of small molecule becomes dissolved, and in the micelles, the osmotic pressure

increases. While the pressure in the micelles and the outer osmotic pressure of

the colloidal solution are not balanced, the invasion of solution into the micelles

is carrying on.

In the first minutes of dough production, the volume of flour particles is

expanded as a consequence of the swelling of the gluten proteins. The measure

of swelling is determined by the stability of the protein molecules. In the case

of strong protein binding (strong gluten), the swelling is limited. However, the

binding is weak, and the swelling is unlimited; that is, the proteins of gluten

become partly peptidized. Also in the case of strong gluten, some peptidization

takes place but it does not play any role.

The gluten can be regarded as a complex macromolecular system con-

sisting of many peptide chains. In the peptide chains the amino acids

are linked by (—CO—NH—) peptide binding. In the peptide bindings, two

alpha-amino-carbonic acids are coupled. The disulphid bindings are devel-oped by oxidation of sulphydryl groups of cysteines of the peptide chains

(—SH+HS—) that results in cross-bindings between the peptide chains. The

hydrogen bindings in the gluten proteins are developed between carbonyl-,

amino-, amide- and thiol-groups.

The mechanical properties of gluten are essentially influenced by the types of

binding and the water content. Among the ingredients, the sucrose, the fats/oils

and the emulsifiers influence the development of gluten. The larger amount of

sucrose decreases the swelling through hydration. The fats/oils partly or entirely

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560 Confectionery and chocolate engineering: principles and applications

adsorb on the hydroxyl groups of flour particles, hindering the water adsorption

of gluten; a larger amount of them hinders the coupling of gluten proteins to

each other and, finally, the development of gluten network. The hydrophilic

surface-active substances increase the hydration and strengthen the peptidizing

effect of the disperse medium. The hydrophobic surface-active substances stimulate

the development of bindings between the colloidal particles, resulting in a

dough of more flexible, stronger structure. In the presence of emulsifiers, the

amount of ingredients of hydrating effect (e.g. carbohydrates) can be increased

to a certain extent without any unbeneficial effect on the rheological properties

of the dough.

16.5.4.1.3 Development of dough structureThe swelling of the gluten proteins into hydrogel is finished. The gluten micelles

develop a protein network that includes the solid disperse medium consisting of

the wet molecular-dispersed starch and the wet skin/bran particles. The devel-

opment of dough structure is essentially influenced by the quality of flour (the

amount and quality of gluten, particle distribution of flour), the amount of water

added and the intensity of kneading.

Figure 16.8 shows a triangle model of the structure of dough that consists of

three elements: (mono-, di-, oligo- and poly) carbohydrates, proteins and lipids. The

set of technological changes may be constructed from these elements as follows:

• Homogenization (kneading or solution)

• Emulsifying (by using egg or lecithin)

Yeast

or

baking

powder

Poly-

Carbohydrates

Emulsifiers

(egg, lecithin)

Emulsifying

Proteins

(gluten)

Swelling

gelation

foaming

Lipids

Hyd

roph

ilic

Hyd

roph

ilic

Mono-, di-

oligo-

Swelling

gelationDissolution

Inhibition

Inhib

itionIn

hib

ition

Maill

ard

reaction

(Non-e

nzym

atic b

row

nin

g)

Gas

dev

elop

men

t

Figure 16.8 Triangle model of the structure of dough: model of processes in aqueous medium.

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Chemical operations, ripening and complex operations 561

• Swelling of gluten

• Gelation of polycarbohydrates and/or proteins

• Foaming of polycarbohydrates and/or proteins

• Gas development under the action of chemical agents or fermentation by yeast

• Change of consistency

• Maillard reaction, of small extent

This enumeration cannot aim for completeness. The set of conserved substan-

tial elements is determined by the set of technological changes, the same refers

to the set of elements of machinery as well.

16.5.4.2 Relaxation and fermentationAfter kneading the dough, technological relaxation/ripening process is needed

for assuring the optimal conditions of shaping. The duration of ripening depends

on the kinds of products. During ripening microbiological, enzymatic and colloidal

changes are taking place which are strongly determined by the composition of

dough.

The microbiological changes are produced by yeast and acid-producing bacteria.

The previous causes a loose structure of dough by gas production; the latter par-

ticipate in the development of the product flavour. The leaving effect of carbon

dioxide produced by yeast (mostly Saccharomyces cerevisiae) in beneficial condi-

tions (water content, soluble nutritive matter for yeast, optimal pH and tem-

perature) is essential; the developing alcohol as by-product plays some role in

increasing the hydrophilic behaviour of the flour particles. Also other species

of yeast belonging to the flour microflora appear in the dough, and in nor-

mal case they do not play any role in the microbiological processes. Among the

acid-producing bacteria, the role of the lactic acid bacteria is essential in the micro-

biological processes of dough which produce lactic acid or lactic and acetic acid

from sugars at relatively higher temperature. As a result of the microbiologi-

cal processes, further substances such as acids, alcohols, esters, aldehydes and

ketones are developed as well which are important from the point of view of the

flavour character.

Among the enzymatic processes, the starch hydrolysis and the splitting of the pro-

tein bindings are essential. The beta-amylase plays the most important role in the

starch hydrolysis. It changes some part of starch to maltose that is an essen-

tial nutritive material to the yeast bacteria; namely, the starch contains a very

small sugar for fermentation originally. In certain cases special enzyme prepa-

rations (malt extraction, Aspergillus oryzae-extraction) are added to the dough

which contains also alpha-amylase for intensifying the starch hydrolysis.

Among the main ingredients of starch, the beta-amylase entirely splits the

amylose, however, only the half of the amylopectin. If the dough contains

both enzymes, the alpha-amylase continues to split the amylopectin to smaller

molecules called dextrins, and the beta-amylase finishes to split these dextrins,

that is, the starch will be entirely hydrolysed in a short time.

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562 Confectionery and chocolate engineering: principles and applications

The protein-splitting enzymes (proteases) split the chemical links of gluten. This

loosing effect essentially influences the physical properties of dough; therefore,

only a limited splitting is beneficial and only in the case of certain products (e.g.

biscuits). It is well known that in the case of strong gluten, the biscuit pieces may

be strongly deformed during baking, and this hinders their compact packaging.

For destroying the strong gluten, protease enzymes are used.

However, if the protease hydrolysis is of extreme measure, the gluten loses its

flexibility and its capability for reserving gas.

In the freshly produced dough, the swollen protein molecules are of unordered

position that disadvantageously affects on the physical properties of dough. The

colloidal processes of ripening can be characterized by the changes during which

the swollen, unordered protein molecules slowly become ordered more or less

parallel to each other. On the effect of ripening being optimal in temperature

and time, the dough becomes easily deformable; namely, the parallel arranged

molecular chains can easily slip on each other, which assures a flexible consis-

tency. On the other hand, ripening is beneficial for processes of diffusion such as

balancing the distribution of particles, of water and so on. All these processes are

necessary for the available shaping behaviour of dough.

The leavening effect may be reached by baking powders producing mostly car-

bon dioxide, ammonia and so on (chemical leavening) or by addition of whipped

protein ingredients (physical leavening with, e.g. eggs yolk/white) as well. This

latter method results in a more complex effect since the whipped ingredients con-

tain – besides different gases (air, nitrogen, etc.) – components which participate

in the development of the product structure and taste.

16.6 Drying/frying, baking and roasting

These three operations are discussed together; in spite of similarities there are

considerable differences among them.

Drying is carried through at temperatures which do not exceed 100 ∘C practi-

cally.

Frying is drying of chips and snacks in hot oils/fats, that is, at high temper-

atures≥ about 180 ∘C, that is accompanied by special flavour-developing pro-

cesses.

Baking is a typical operation of manufacturing products of flour (e.g. biscuits);

the typical interval of temperature is about 150–200 ∘C.

Roasting is a thermal operation typically used for cocoa, coffee and nuts in the

temperature interval of about 150–220 ∘C.

A detailed discussion of machinery relating to these operations exceeds the

volume of this book.

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Chemical operations, ripening and complex operations 563

16.6.1 Drying/frying16.6.1.1 DryingA detailed discussion of these operations regarding the theoretical principles and

the technical solutions can be found in any handbook of food engineering, for

example, Valentas et al. (1997), Earle and Earle (2004), Heldmann and Lund

(2006), Mujumdar (2006, Chapters 21, 52), Smith (2011) and Barbosa-Cánovas

(2014). Here we deal with the confectionery peculiarities of drying process only.

Drying means – in limited sense – the partial or complete removal of humid-

ity from the material at a temperature below 100 ∘C, that is, the boiling point of

water at normal atmosphere. In a broader sense, also frying, baking and roasting

which are carried through at higher temperatures can be regarded as drying pro-

cesses. But we remain at the limited sense, except frying which is a characteristic

of snacks and chips in the confectionery industry only.

The drying machinery in the confectionery industry may be drying room and

drying oven, but in the manufacture of panning articles, it is an organic part

of the panning machinery. In each case, filtered, conditioned air flow of fitted

temperature and relative humidity has to be used. The drying ovens are usually

multifunctional machines being available both for drying and baking. The drying

rooms serve to relax (e.g. Ostwald ripening) the semi-products as well.

16.6.1.1.1 ChocolatesChocolate bars that are unfilled do not need any drying since their surface is

hydrophobic and normally is not wet. The surface of filled chocolate bars and of

pralines may be wet in the case wherein the filling is hydrophilic (e.g. cream of

fondant basis) and the shell is cracked. Such products must not be packed because

of quality defect. Drying the wet surface does not mean a solution; moreover, the

cracked pieces have to be separated.

16.6.1.1.2 Soluble cocoa powdersDrying the mixture of the cocoa powder and sugar-containing ingredients is an

essential unit operation of processing that is generally made by fluidization.

16.6.1.1.3 Hard-boiled sugar confectioneriesA traditional surface covering (in German: Ballieren, i.e. packing) is made by

sprayed, saturated aqueous solution of sucrose in panning kettle. After the sur-

face having been wetted, it is dried by air flow of not too warm temperature.

The purpose of this operation is to defend the hard-boiled sugar confectioneries

from the air moisture in the case wherein the reducing sugar content of sugar

mass is too high (e.g. more than 16 m/m%) and the packaging material of the

product does not provide a sufficient closing against air humidity. This method

generally becomes unnecessary nowadays as a result of the development both

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564 Confectionery and chocolate engineering: principles and applications

in the confectionery technology and in the packaging technique (e.g. packaging

per piece, laminated foils, etc.).

16.6.1.1.4 Fondant productsAn old method is to cover the fondant pieces by sucrose crystals (candying, candis

layer). The technology is very awkward since the crystal layer gets easily damaged

before setting. The setting process needs drying without any sudden moving or

shaking. In order to set, after the candis solution has been drained, the fondant

pieces are cautiously overthrown (in German: Stürzen: overthrowal) from the

candis boxes onto a drying belt or trays where the dry air of about 30 ∘C achieves

the setting.

Table 16.6 shows the usual conditions of candying – the temperature of the

room where the drying of the sugar-covered fondant pieces is carried through is

the same as that of candying in general.

A description of the candying technology can be found, for example, in Mein-

ers et al. (1984, Vol 2, 4.17.3, pp. 415–416).

To the best of my knowledge, there is no continuous technology for candying

fondants. The usual continuous method is to cover the surface of fondant pieces

by chocolate or compound mass.

The various types of caramel are continuously packed after shaping and cool-

ing – no surface handling is necessary.

16.6.1.1.5 Jellies• A big amount of jellies is produced by Mogul methods, that is, by casting

into starch moulds. In starch the water content of jelly decreases from about

23–25 m/m% till 20–21 m/m% during about 4–6 h (pectin jellies) and 12–24 h

(e.g. agar jellies), respectively. This period of drying makes the separation of

articles from starch possible. After this step the starch has to be dried (condi-

tioned) and to filter out the pieces of the broken jellies.

The water content (m/m) of the dried (corn or rice) starch is about 8–10

which increases up to 13 on the effect of contacting the jellies.

• The surface covering of jellies can be made by chocolate/compound mass

or big sucrose crystals. This latter process (in German: panieren, i.e. to

Table 16.6 Duration of sugar crystal coating (candying) depending on the concentration of the

candying solution and the temperature.

Concentration(g, sugar/kg solution)

Boiling point(∘C)

Hours at20 ∘C

Hours at30 ∘C

Hours at40 ∘C

740 107.8 2.4 1.9 1.3

730 107.2 2.7 2.4 1.4

720 106.6 3.4 3.1 2.4

710 106 3.9 4.5 6.1

700 105.5 5.3 7.7 –

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Chemical operations, ripening and complex operations 565

bread, to crumb) starts with wetting the surface by sucrose solution of about

70–75 m/m% in panning kettles and then is continued by a drying process

with dry air flow. There are continuous solutions presently.

16.6.1.1.6 Dragées

Drying is essential if soft or hard sugar dragées are produced. The sugar con-

tent of the wetting solution may be about 65–82 m/m, and each layer has to be

dried after wetting in order to get a solid layer. For drying conditioned air has to

be used, and the relative air humidity and temperature have to be fitted to the

quality requirements of the product.

16.6.1.1.7 Honey cakes

The usual way to protect honey cakes against drying is by covering the surface

with chocolate (by fat mass in case of cheaper products) or saturated aqueous

sugar solution, that is, candying.

16.6.1.1.8 Lozenges

An essential step of manufacturing lozenges is drying in a drying oven (about

90–100 ∘C) or drying rooms (30–50 ∘C). The final water content of the article is

usually below 5, mostly 2–3 m/m. The aim of drying process is to solidify the

binding agent (e.g. gum arabic or gum tragacanth) which expresses its effect in

wetted, jelly condition.

16.6.1.1.9 Compressed and granulate products

In direct compression no drying process has to be used since the components get

no wetting or similar preparation for assuring the available adhesive properties

of surface.

In the case of indirect compression, the surface of the components has to be

prepared before compression. The most effective way of such preparation is flu-

idization during which, on the one hand, the components are thoroughly mixed,

while on the other hand, their surface is activated by aqueous, mostly sucrose

solution. The binding agent can express its effect in aqueous medium, and finally

in fluid bed the drying process can be effectively carried through.

The final water content of the article is usually below 5, mostly 2–3 m/m.

The manufacture of granulates is done perhaps exclusively by fluidization, and

the drying process is carried out, for example, in fluid bed (see following text).

16.6.1.2 FryingThe operation frying (baking in fat or oil) develops particular organoleptic prop-

erties in the product, for example, crispy consistency and specific flavours. A

considerable amount of the aroma substances is lipophilic (fat soluble), and thus

the less or more amount of oil absorbed by the product during frying increases

the effect of aroma.

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566 Confectionery and chocolate engineering: principles and applications

Two types of frying are usually distinguished:

1 If only a thin layer of oil is sprayed on the surface of the product (e.g. crackers),

and then baked; this operation is called toasting. It is favoured also in cookery,

for example, toasting in wok.

2 If the product is dipped into hot oil, this operation is called deep-frying. The

chips and snacks, instant pastas and so on are produced by deep-frying.

In the case of (deep-)frying, the heat transferring medium is hot oil (mostly

peanut, soya, coconut oil). During frying the amount of free fatty acids (FFAs)

increases as a result of hydrolysis; however, in order to get the correct taste, it

must not exceed 0.3 m/m% in the frying oil.

During the frying process, the development of acrylamide in hot oil cannot be

avoided but it is necessary to hold under control. For further details see Section

16.2.

An essential requirement concerning the frying process is continuously to lead

away the deliberated vapour in order to avoid its condensation, namely, the con-

densed vapour sets into reaction with the oil, and causes hydrolysis, that is, the

development of FFAs.

• Potato snacks: The snack pieces have to be dried before frying. In both sides of

conveyor, ventilators dry the transported snack pieces, the decrease of water

content (m/m) in this phase is about 1–2, and the optimal value of the snack

pieces is 12 when the pieces are fried. The duration of frying is regularly 2 min.

The available – not too high – water content is beneficial in the viewpoint of

hydrolysis in the hot oil.

• Corn chips: The first step of technology is producing Masa/Mehl which consists

of cooked corn, water and fluid slaked lime (if Zea mays var. indentata Bailey is

used). Its water content is about 50 m/m%. After a washing operation which

clears away the lime and the physical impurities, corn material will be dried

and grounded. Finally, the corn chips will be toasted in hot oil.

The Tortilla chips are manufactured from Masa/Mehl which, after washing,

will be dried into sheet or various thin figures (triangle, square, rhombus, etc.)

between cylinders, and finally fried at 400–480 ∘C during 12–18 s.

The final water content of both types of corn chips is about 1–1.2 m/m%, the

final oil content (m/m) of corn chips is about 37 and that of Tortilla chips is about

23 – these values may alter ±3–4%.

For further details see Gould (1994).

16.6.2 Baking16.6.2.1 Preparation of baking: shapingThe shaping of dough connected with the weighing of the one-piece amount

always goes before baking and essentially influences the conditions of baking.

The shaping operation would deserve an original chapter as well; however, such

a study exceeds the volume of this book. Mohos (1983) found that the Euler

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Chemical operations, ripening and complex operations 567

characteristic as topological invariant (see, e.g. Spanier, 1982) can be regarded a

key in the relation between the product shape and the kind of shaping machinery

(some Euler characteristics related to various shapes: disc: 1; sphere: 2; torus: 0;

double torus: −2; triple torus: −6). As it is well known, dough shaping is a usual

demonstrative example of topological invariants.

Baking solidifies the shape of dough and develops the taste of the product. The

product-specific topics are separately discussed as well.

16.6.2.2 The Phases of bakingDuring baking various physico-chemical and colloidal changes take place in the

dough. The dough is a capillary-porous material, inside of which oriented heat

and moisture migration start on the effect of heat. The temperature difference in the

dough increases in Phase 1, and then after a short decreasing period, it remains

constant. However, if the heating continues, the temperature difference in the

dough can be highly increased.

Parallel to the temperature change, essential moisture change takes place as

well. The process of moisture decrease can be divided into three phases according to

the rate – constant, then decreasing, and finally constant again:

• In Phase 1 of baking, the temperature difference increases; therefore, the mois-

ture vapour diffuses from the outer layers to the inner layers and warms them.

Although the temperature difference decreases in the end of Phase 1, the

decrease of moisture content in the outer layers is carrying on. Finally, when

the moisture movement in the dough is stopped, the moisture content is bal-

anced and constant in the inner layers.

• In Phase 2 of baking, the moisture content of dough starts to decrease with a

constant rate, and the evaporation zone spreads over from the surface also

to the inner layers. As a result, the volume starts to increase, and the pres-

sure difference developed by the volume increase induces internal moisture

movement.

• In Phase 3 of baking, the evaporation zone reaches the inner layers as well, and

the moisture starts to move in the capillaries to the outer layers. In this phase

typically not the free but the bound water leaves away.

16.6.2.3 Factors effecting on the heat and moisture migrationAs in the space of baking the temperature is increasing, and the duration of bak-

ing is decreasing, the moisture transfer becomes more intensive, and relative

air humidity increases. As a result, vapour will be condensed on the surface of

dough.

The duration of baking is quasi-proportional to the layer width of dough as a

consequence of the heat resistance of dough. A loose structure of dough needs a

much shorter duration of baking than a compact structure. However, the smaller

pieces, because of their high specific surface, need shorter duration of baking.

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568 Confectionery and chocolate engineering: principles and applications

The moisture migration is more intensive in the layers of dough which contain

less bound, more free water.

16.6.2.4 Changes during bakingAccording to Mowbray (1981), the changes during baking are as follows:

In the first third part of baking, the temperature is increased up to 100 ∘C. In

this period the gas production is completed, and the steady-state drying starts. In

detail (approximate temperature values):

30–40 ∘C: the fats are melted; 50 ∘C: gluten softens; 75–80 ∘C: gluten coagu-

lates; 55–60 ∘C: starch begins to take up water; 75–80 ∘C: starch is gelatinized;

55–60 ∘C: yeast is killed; 60–65 ∘C: maximum enzyme activity; 80–85 ∘C:

enzymes are inactivated.

In the second part of baking, the temperature is increasing up to about 180 ∘C. In

detail:

110 ∘C: yellow dextrins form; 125–130 ∘C: caramelization starts; 145–150 ∘C:

outer surface gets skin; 160 ∘C: brown dextrins form.

In the development of dough structure, the proteins and starch play the most

important role. Due to the effect of heat, the gluten proteins will be denatured

and lose a larger amount of their water content taken up by swelling. Due to the

thermal effect, starch becomes very much swollen and starts to get sticky but not

entirely because of the insufficient amount of water being present. The porous

network developed by the denatured proteins and the sticky starch of the fat

components can be easily adsorbed.

As a consequence of moisture migration, the outer layers of dough lose consider-

able amount of water; therefore, a thin crust develops on the dough surface. This

crust influences the expansion of dough volume which has to be held under con-

trol by the temperature and relative air humidity in the baking space in order to

assure the optimal phase of the volume expansion.

After the inner layers of dough have been warmed up, the heat decomposition

of baking powder produces a considerable amount of gases, and in addition, the

water content of dough starts to evaporate. This double effect induces the expansion

of dough volume.

The gas production of yeast starts at room temperature already and gets inten-

sive in the period of 30–45 ∘C during warming up. Higher water content produces

more vapour and, consequently, more intensive increase of volume.

On the thermal effect, the development of dextrins in starch takes place to a

large extent, and the water-insoluble part of starch very much decreases. The

water-soluble dextrin derivatives are mostly maltose and glucose which form con-

densation substances of brown colour in Maillard reaction.

In the dough the amount of albumin, globulin, gliadin and mostly glutenin will

decrease by their decomposition into amino acids which react with maltose and

glucose in Maillard reaction, resulting in melanoidine compounds (see previous

text).

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Chemical operations, ripening and complex operations 569

Since the inner layers of dough lost water, their hydrophilic behaviour gets

weaker, and this is advantageous for the uniform distribution of fats in the dough.

For more details see Manley (1998a,b,c,d), Chapter 38 and Mogol (2014).

16.6.2.5 Machinery of bakingA detailed discussion of the machinery of baking is beyond the volume of

the present work; the reader is referred to the manufacturers of the biscuit

oven-heating systems.

In general, the length of ovens is about 60–150 m; the usual width (mm) of

the oven band is 800, 1000 or 1200, but may be different as well. Its usual form

may be steel band, perforated steel band or wire band of various (so-called wire,

continental or heavy) mesh.

16.6.2.6 Direct fired ovens• In direct gas fired (DGF) ovens, many strip or ribbon burners are situated above

and below the baking band. The top of the baking chamber is usually low and

the burners are as near to the baking band as is practicable. Turbulence of air

may be to improve the rate of heat transfer.

• Electric fired ovens are similar to DGF ovens but each burner is electric.

• Forced convection direct-fired ovens: each zone of the oven has one large

burner. The forced convection ovens allow more uniform temperature and

heat transfer conditions across the width of the baking chamber.

• Convectoradiant fired ovens: hot gases from the burner in a zone pass through

tubes above and below the baking band. The first tubes radiate heat to the

biscuits, and then the released air gives convection currents of air.

16.6.2.7 Indirect fired ovensThey are similar to the direct-fired forced convection ovens, but a heat exchanger

near the zone burner heats the air that passes through all the chambers in the

baking place. In the Cyclotherm system, the hot gases pass through tubes above

and below the baking band and circulate back to the burner.

16.6.2.8 Hybrid ovensThese are a combination of two of the aforementioned types. In the first, baking

period maximum power and radiant heat are to be used; in the second, drying

period of the convected heat is dominant.

For further details see Manley (2000).

The radio frequency (RF) and microwave heating are spread in baking tech-

nology although they can be used together with the traditional firing systems

only. For the theoretical principles, see Section 3.8.1. The RF energy eliminates

the excess moisture from the product rapidly and efficiently, without causing

overbaking (excessive browning) of the surface.

For the temperatures of baking, see Figure A6.24 (semisweet biscuit and crack-

ers), Figure A6.25 (short-dough biscuits) and Figure A6.26 (Lebkuchen, i.e. honey

cakes).

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16.6.3 Roasting16.6.3.1 Cocoa beansThe roasting of cocoa beans develops the typical flavour properties, removes the

substances of offensive odour and taste, destroys the harmful microflora, looses

the shell of beans and develops the physical properties of nibs for comminution.

Two phases of roasting are distinguished in general:

1 Drying: The temperature increases to about 110 ∘C, and the water content of

the cocoa beans decreases below 3 m/m%.

2 Roasting: The temperature maximum remains between 115 and 135 ∘C,

depending on the aimed strength of roasting. The water content of raw beans

is 6–8% which decreases to 1.5–2.5% in the end of roasting. Some choco-

lates, particularly milk chocolate, require lower roasting temperatures, and

some cocoa powders, if red shades are required, also need low-temperature

roasting. In some batch roasters, temperatures may rise to 150 ∘C or higher.

Some chocolates, particularly milk chocolate, require lower roasting tem-

peratures, and some cocoa powders, if red shades are required, also need

low-temperature roasting. To produce mild-flavoured cocoa butters, very

low temperatures are best, and when using the expeller press, unheated raw

beans may be used (Minifie, 1999, pp. 37–38).

One of the essential aroma-developing processes is the Maillard reaction

between the amino acids and reducing sugars which is increased by the presence

of water, high temperature and during roasting. The roasting includes also a

pasteurizing phase in that the majority of microflora of beans (Salmonella and

various pathogens) is destroyed. In certain cases this pasteurizing phase of about

100 ∘C is carried through in a separate machine. The roasting causes a small loss

in cocoa butter as well which diffuses into the shell.

The roasting of beans is the most widespread process of cocoa roasting.

For the processes of roasting, some references are as follows:

Nazaruddin Ramu et al. (2006) discuss the influence of roasting conditions on

volatile flavour of roasted Malaysian cocoa beans; Gu et al. (2013) compared the

cocoa beans from China, Indonesia and Papua New Guinea regarding the con-

ditions of roasting. Jinap and Dimick (1991) studied the effect of roasting on

acidic characteristics of cocoa beans, and Krysiak (2011) discusses the effects

of convective and microwave roasting on the physico-chemical properties of

cocoa beans and cocoa butter extracted from this material. Frauendorfer and

Schieberle (2008) studied the moisture, colour and texture changes in cocoa

seeds during superheated steam roasting. Farah et al. (2012) dealt with the opti-

mization of cocoa beans roasting process. Zzaman and Yang (2013) studied the

moisture, colour and texture changes in cocoa seeds during superheated steam

roasting.

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Chemical operations, ripening and complex operations 571

16.6.3.2 The mass balance (kg) of cocoa bean roastingIf M is the amount of the cocoa bean lot before, and m after roasting, the mod-

elling of process is as follows:

M → m + W (ater) ↑ +D(ecomposed organic substances) ↑

Then it holds

M = m + W + D (16.44)

and

W = M∗X–m∗x (16.45)

where X and x are the mass rate of water in the cocoa bean lot before and

after roasting, respectively. This calculation supposes that during determination

of the water content of cocoa beans, the decomposition of organic substances can

be neglected; for example, at the drying box method, the temperature does not

exceed 103–105 ∘C.

Example 16.2The amount of lot before roasting is M= 560 kg, and its water content is X= 0.0;

these data after roasting are m=515 kg, x= 0.02. Let us calculate the size of D.

The total mass loss is (560− 515) kg= 45 kg.

The amount of eliminated vapour is W= (560*0.07− 515*0.02) kg= 28.9 kg.

The amount of decomposed organic substances is D= (45−28.9) kg=16.1 kg.

16.6.3.3 Cocoa nib (cotyledon) and cocoa massAfter cleaning the cocoa beans are dried usually by shock heat which is developed

either by infra radiation or hot air in fluid bed. This process is used mostly in the

case of flat or thick-shelled beans. The drying is followed by winnowing and

classifying of the beans, and finally the roasting of the nibs. The nib roasting

makes possible for furthering the development of aroma precursors, for example,

by addition of glucose solution to promote the Maillard reaction.

After the nib roasting the water content of nibs is about 5%; therefore, they are

not available for comminution, and the microbiological properties are not accept-

able as well. A further roasting is necessary for which special machinery (vacuum

evaporators and thin-layer evaporators) is used. The cocoa mass roasting is a very

effective method which, on the one hand, provides a certain pre-conching and,

on the other hand, guarantees the available microbiological conditions (Minifie,

1999, p. 46):

Plate count <100 per gram

Enterobacteria <per gram

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572 Confectionery and chocolate engineering: principles and applications

Escherichia coli none

Salmonella none

Spores <100 per gram

16.6.3.4 Roasting machines16.6.3.4.1 Batch roastersThe batch roasters are bowl (Sirocco type) or drum (Thermalo or Tornado type)

shape. The roasting metal drum is rotating and is heated by conduction from

outside.

The Tornado roasters work with conduction and forced convection; that is,

the hot air gets in the rotating vessel moved. This way of heating is intensive. In

the Sirocco roaster the heater protrudes into the vessel, and the hot air is drawn

through the beans. The air is heated by gas or oil burners, and cyclones are used

to extract the dust from the exit air. The vessel is coupled with a balance that

stops the roasting when the weight loss of batch is sufficient.

16.6.3.4.2 Continuous roastersIn these machines the drying, the heating and the cooling are solved in zones of

the current of cocoa beans, but in the zones the temperature is held at prescribed,

controlled values (e.g. Lehmann Roaster). Many designs of continuous roasters

are now available, and these have shown great economies in fuel consumption

and also result in fewer broken beans and less transfer of cocoa butter from the

nib to the shell. In the fluid bed roaster, the beans are heated by convection in a

current of hot air. In the Probat roaster the beans are pre-warmed, roasted and

cooled entirely by convection. The NARS process (nibs, alkalizing, roasting and

sterilizing) is described by Mayer-Potschak (1983). For more details see Kleinert

(1966) and Minifie (1999, Chapter 2).

The roasters are always joined with a cooling machine which has to be ready

for working before the beginning of roasting in order to prevent the combustion

of cocoa beans or other nuts.

Figure 16.9 shows the equilibrium relative humidity (ERH) as the function

of the moisture of cocoa beans which is quasilinear: ERH (%)= 9.58 M+ 5.811

(R2 = 0.976); M: moisture (%).

16.6.3.5 Roasting of nuts, cereals and cereal coffee raw materialsThe cocoa roasters are available for roasting various nuts (hazelnut, peanut,

etc.), cereals and cereal coffee raw materials. However, here we are obliged to

limit this discussion only for providing some references: Burdack-Freitag and

Schieberle (2010, 2012), Kiefl and Schieberle (2013), Pelvan et al. (2012), Donno

et al. (2013), Smyth et al. (1998), Environment Australia (1999), Ogunsanwo

et al. (2004), El-Badrawy et al. (2005), Brown et al. (2001) and Małgorzata et al.

(2013).

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Chemical operations, ripening and complex operations 573

80

70

60

50

40

30

20

10

00 2 4 6

Moisture (%)

ER

H (

%)

8

Figure 16.9 The ERH as the function of the moisture of cocoa beans. Source: Minifie

(1989a,b). Reproduced with permission of Springer.

16.6.3.6 Coffee roastingCoffee is one of the most popular beverages in the world. A good quality cup of

coffee depends on many factors, such as the quality of green beans, the roasting

conditions, the time since the beans are roasted and the type of water used for

brewing. More than 800 volatile compounds have been identified in roasted cof-

fee, whereof around 30 compounds are responsible for the main impression of

coffee aroma (Baggenstoss et al., 2008).

Yeretzian et al. (2002,b), Ciampa et al. (2010), Jokanovic et al. (2012), Wang

(2012) and Sualeh et al. (2014) provide detailed descriptions on the roasting

process and the physico-chemical changes of coffee beans during roasting, for

example, on the effect of roasting on the formation of chlorogenic acid (Farah

et al., 2005) which is an essential component of coffee beans. Roasting of coffee

beans typically takes place at 200–240 ∘C for different times depending on the

desired characteristics of the final product. Events that take place during roast-

ing are complex, resulting in the destruction of some compounds initially present

in green beans and the formation of volatile compounds that are important con-

tributors to the characteristic of coffee’s aroma.

In the roasting process four phases can be distinguished:

In Phase 1 (drying) the majority of water evaporates, and the proteins start to be

denaturized. The uniform increase of temperature is essential to prevent the

beans from bursting into pieces on the effect of evaporation.

In Phase 2 (about 160–165 ∘C), the roasting process is starting. The volume of

the beans highly increases, the carbohydrates become caramelized and partly

melanoidins and the insoluble carbohydrates become soluble. The majority

of coffee fibres such as cellulose, hemicellulose and lignin substances remain

insoluble in water. First the structure of cellulose shrinks but later highly

swells. The colour of the beans is light brown.

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574 Confectionery and chocolate engineering: principles and applications

In Phase 3 (180 ∘C), the thermal decomposition of organic substances (carbo-

hydrates, proteins) becomes intense, and, as a result, the typical aromas of

coffee are developing. The moisture loss is little but the development of carbon

dioxide is intense. The volatile substances are alcohols, aldehydes, ketones,

ethers, heterocyclic compounds, sulphides and nitrides. The caramelization of

carbohydrates is carrying on which results in a deepening brown colour. The

pentosans change to sulfurol.

In Phase 4 (200–250 ∘C), the roasting is finished, and the final temperature

depends on the consumers’ habit (see following text). A large portion of caf-

feine (330–40%) gets sublimated, and 10–15% of trigonelline is decomposed.

As a result of caramelization of carbohydrates and decomposition of carbonic

acids, about 2% carbon dioxide is developed, a majority of which is adsorbed

on the surface of the roasted beans. The adsorbed carbon dioxide plays an

essential role in the shelf life of roasted coffee since it hinders the autoxidation

of the coffee oil containing a lot of unsaturated fatty acids.

The roasting process can be characterized by the colour changes of beans and

typical sound phenomena (cracks) – the latter are studied by acoustic method as

well (Wilson, 2014).

As temperature increases to about 100 ∘C, coffee beans undergo moisture loss

from 8% to 12% in green coffee beans to about 5% in the roasted coffee beans.The smell of the beans changes from herb-like green bean aroma to bread-like,

the colour turns from green to yellowish and the structure changes from strength

and toughness to more crumbly and brittle.

When the internal temperature of beans reaches 100 ∘C, the colour is darkened

slightly for about 20–60 s due to the vaporization of water.

A rough temperature profile of roasting is as follows:

135–149 ∘C: the beans seem more green.

165–174 ∘C: the beans are going to become yellow.

182 ∘C: light sunlit colour.

188 ∘C: moderate sunlit colour.

190 ∘C: brownish sunlit colour.

196 ∘C: light brown colour.

196–199 ∘C: first crack.

204–207 ∘C: the entire batch is cracking.

210–215 ∘C: pleasant brown colour.

225 ∘C: the beginning of the second crack.

240 ∘C: the end of the second crack.

The degrees of roasting and the corresponding denominations follow the cus-

tomer’s habit in the United States and Europe.

16.6.3.6.1 Light roast196 ∘C (385 ∘F): Cinnamon roast

A very light roast level, immediately at first crack. Light brown, toasted grain

flavours with sharp acidity.

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Chemical operations, ripening and complex operations 575

205 ∘C (401 ∘F) New England roast or half city

Moderate light brown but still mottled in appearance, sharp acidity. This is

a preferred roast of products for trading in the United States.

16.6.3.6.2 Medium roast210 ∘C (410 ∘F): American roast

Medium light brown, developed during first crack. Original character is still

completely preserved. This is an American speciality.

219 ∘C (426 ∘F): City roast

Medium brown, common for most speciality coffee.

16.6.3.6.3 Dark or full roast225 ∘C (437 ∘F): Full city roast

At the beginning of second crack. Medium dark brown with occasional oil

sheen.

230 ∘C (446 ∘F): Vienna roast

In the middle of second crack. Moderate dark brown with light surface oil, more

bittersweet, caramel flavour acidity muted. Any original characteristics have

become eclipsed by roast at this level.

240 ∘C (464 ∘F): French roast

At the end of second crack. Dark brown, shiny with oil, burnt undertones and

acidity diminished. Roast character is dominant, and the original aromas of

coffee are eliminated.

245 ∘C (473 ∘F): Italian roast

Very dark brown and shiny, burnt tones become more distinct and acidity

almost gone.

250 ∘C (482 ∘F): Spanish roast

Extremely dark brown, nearly black and very shiny and charcoal and tar

tones dominate.

After finishing the roasting, a quick cooling is essential which can be done by

available cooling machinery and additionally by spraying some water into the roasting

drum. The water content of finished product has to remain below 4% together

with the sprayed water because too much water causes stale flavour and des-

orption of carbohydroxide, that is, decreases the shelf life. After roasting and

cooling a destoner machine has to be used before grinding the roasted coffee by cylin-

der refiners.

16.6.3.7 Coffee roastersBecause of the versatility of roasters, for study we can recommend mostly the

technical brochures provided by the manufacturers of coffee roaster. Here the

principles of Probat coffee roasters are shown only (see Fig. 16.10).

16.6.3.7.1 Drum roaster (see Neptune)Roasting coffee in a drum turning on a horizontal axis is the oldest method still

commonly in use and the traditional form of slow roasting. The variable drum

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576 Confectionery and chocolate engineering: principles and applications

Neptune

drum roaster

Jupiter

tandential roaster

Saturn

centrifugal roaster

Figure 16.10 Principles of various machinery solutions of roasting by Probat.

rotation speed enables shorter cycle times; the special shovel mechanism ensures

gentle and optimal mixing; and the effective cooling system provides you with

even greater assurance of consistent product quality.

16.6.3.7.2 Tangential roaster (see Jupiter)In the tangential roaster the beans move on circular path and contact the hot air

tangentially. The combination of controlled roast supply air and the mechanically

moved coffee beans ensures an ideal heat transfer between the bean surface and

the bean interior. Not only that, it also delivers maximum colour and moisture

consistency.

16.6.3.7.3 Centrifugal roaster (see Saturn)The rotation on the vertical axis and the combination of roasting bowl and

lamella ring ensure an especially homogeneous and gentle mixing of the roasting

product in the medium roasting range. The centrifugal roaster boasts minimum

heat loss, an especially energy-saving and environmentally friendly operation

and automatic regulation of cooling times.

16.6.3.7.4 Continuous roasterThis allows an efficient product change without any need to stop the roasting

process. Green coffees with a greater tendency for breakage can be processed

easily. The process is ideal for roasters that roast similar products over longer

runs. The heat transfer is achieved almost exclusively via convection. The hot

air is blown into the individual chambers via nozzles and, in combination with

the rotation of the drum, ensures that the roasting product is mixed thoroughly.

Dust and chaff separation is achieved by cyclones.

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Chemical operations, ripening and complex operations 577

16.6.3.8 Air pollution in connection with roastingRoasting causes air pollution inevitably; however, presently the solutions of mit-

igation have become essential. Schmidt (2008, 2009) comprehensively discusses

this topic in connection with coffee-roasting plants. The important sections of the

coffee plant which uses all the necessary solution of air pollution mitigation and

of reduction of energy consumption are the afterburner exploiting heat energy

from the cyclone-exhausted air by burning the dust, and recycling the hot air from

the afterburner through a heat exchanger for preheating the air which is fed to the

burner.

Further reading

Aasted. Technical brochures.

Almond, N. et al. (1991) Biscuit, Cookies and Crackers, Elsevier Applied Science, London.

Barbosa-Cánovas, G.V., Fontana, A.J. Jr., Schmidt, S.J. and Labuza, T.P. (eds) (2007) Water Activ-

ity in Food, Fundamentals and Applications, IFT Press, Blackwell Publishing.

Barbosa-Cánovas, G.V., Zhang, Q.H. and Tabilo-Munizaga, G. (2001) Pulsed electric fields in

food processing, in Nonthermal Processing Technologies for Food, Technomic Publishing Co. Inc.

Bauermeister (Probat Group). Technical brochures.

Beckett, S.T. (ed.) (1988) Industrial Chocolate Manufacture and Use, Van Nostrand Reinhold, New

York.

Beckett, S.T. (2000) The Science of Chocolate, Royal Society of Chemistry, Cambridge.

Beckett, S.T., Francesconi, M.G., Geary, P.M. et al. (2006) DSC study of sucrose melting. Carbo-

hydrate Research, 341, 2591–2599.

Bessiêre, Y. and Thomas, A.F. (1990) Flavour Science and Technology. Sixth Weurman Symposium,

Wiley, Chichester.

Biscuit and Cracker Manufacturers Association (1970) The Biscuit and Cracker Handbook, Biscuit

and Cracker Manufacturers Association, Chicago.

Cakebread, S.H. (1975) Sugar and Chocolate Confectionery, Oxford University Press, Oxford.

Catterall, P. (2011) Cakes and biscuits; I know what I mean!. New Food, 14 (3), 39–42.

Chung, B.Y., Iiyama, K. and Han, K.-W. (2003) Compositional characterization of cacao (Theo-

broma cacao L.) hull. Agricultural Chemistry & Biotechnology, 46 (1), 12–16.

Eiarsson, H. (1987) Antibacterial Maillard reaction products. Doctoral thesis. University of Göte-

borg.

Ellis, P.E. (ed.) (1990) Cookie and Cracker Manufacturing, Biscuit and Cracker Manufacturers Asso-

ciation, Washington, DC.

Faridi, F. (ed.) (1994) The Science of Cookie and Cracker Production, Chapman and Hall, New York.

Gaonkar, A.G. and Anulkumar, G. (1995) Ingredient Interactions: Effects on Food Quality, Dekker,

New York.

Gisslen, W. (2005) Professional Baking, 4th edn, John Wiley & Sons, Inc.

Guttiérez-López, G.F., Barbosa-Cánovas, G.V., Welti-Chanes, J. and Parada-Arias, E. (2008) Food

Engineering: Integrated Approach, Springer Science+Business Media, LLC.

Haque, M.K., Kawaib, K. and Suzuki, T. (2006) Glass transition and enthalpy relaxation of

amorphous lactose glass. Carbohydrate Research, 341, 1884–1889.

Heldmann, D.R. and Lund, D.B. (eds) (2007) Handbook of Food Engineering, 2nd edn, CRC Press.

Hodge, D.G. and Wade, P. (1968) Investigation of the baking of semi sweet biscuits, Part I.

C&CFRA (FMBRA) Report 14.

Hui, Y.H. (2005) Handbook of Food Science, Technology, and Engineering – 4 Volume, Blackwell Pub-

lishing.

Hurtta, M., Pitkänen, I. and Knuutinen, J. (2004) Melting behaviour of D-sucrose,D-glucose

and D-fructose. Carbohydrate Research, 339, 2267–2273.

Ibarz, A. and Barbosa-Cánovas, G.V. (2003) Unit Operations in Food Engineering, CRC Press LLC.

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578 Confectionery and chocolate engineering: principles and applications

Kasapis, S., Al-Marhoobi, I.M. and Mitchell, J.R. (2003) Testing the validity of comparisons

between the rheological and the calorimetric glass transition temperatures. Carbohydrate

Research, 338, 787–794.

Kempf, N.W. (1964) The Technology of Chocolate, The Manufacturing Confectioner Publishing Co.,

Glen Rock, NJ.

Kulp, K. (ed.) (1994) Cookie Chemistry and Technology, American Institute of Baking, Kansas.

Lehmann. Technical brochures.

López-Gómez, A. and Barbosa-Cánovas, G.V. (2005) Food Plant Design, Taylor & Francis Group,

LLC.

MacFarlane, I. (1989) Measurement of Oven Conditions and Types of Ovens Used in the Biscuit Industry,

Biscuit Seminar, ZDS Solingen, Germany.

Meursing, E.H. (1983) Cocoa Powders for Industrial Processing, 3rd edn, Cacaofabriek de Zaan, Koog

aan de Zaan.

Mujumdar, A.S. (2014) Handbook of Industrial Drying, 4th edn, CRC Press.

NETZSCH. Technical brochures.

Oracz, J. and Nebesny, E. (2014) Influence of roasting conditions on the biogenic amine content

in cocoa beans of different Theobroma cacao cultivars. Food Research International, 55, 1–10.

Paravisini, L., Septier, Ch., Moretton, C. et al. (2014) Caramel odor: contribution of volatile

compounds according to their odor qualities to caramel typicality. Food Research International,

57, 79–88.

Pratt, C.D. (ed.) (1970) Twenty Years of Confectionery and Chocolate Progress, AVI Publishing, West-

port, CT.

Rotstein, E., Singh, R.P. and Valentas, K.J. (eds) (1997) Handbook of Food Engineering Practice,

CRC Press LLC.

Seo, J.-A., Kim, S.J., Kwon, H.-J. et al. (2006) The glass transition temperatures of sugar mix-

tures. Carbohydrate Research, 341, 2516–2520.

Silke Elwers, S., Zambrano, A., Rohsius, Ch. and Lieberei, R. (2009) Differences between the

content of phenolic compounds in Criollo, Forastero and Trinitario cocoa seed (Theobroma

cacao L.). European Food Research and Technology. doi: 10.1007/s00217-009-1132-y

Smith, W.H. (1972) Biscuit, Crackers and Cookies, Applied Science Publishers, London.

Smith, J.S. and Hui, Y.H. (2008) Food Processing Principles and Applications, Blackwell Publishing.

Sollich. Technical brochures.

U.S. Department of Agriculture (2003) USDA Database for the Flavonoid Content of Selected

Foods.

Vieira, J. and Sundara, V.R. (2011) Chocolate aeration-art or science? New Food, 14 (4), 65–69.

Wade, P. (1988) Biscuit, Cookies and Crackers, Elsevier Applied Science, London.

Wade, P. and Bold, E.R. (1968) Investigation of the baking of semi sweet biscuits. Part I, C&CFRA

(FMBRA) Report 14.

Whiteley, P.R. (1971) Biscuit Manufacture, Applied Science Publishers, London.

Wieland, H. (1972) Cocoa and Chocolate Processing, Noyes Data Corp., Park Ridge, NJ.

Wollgast, J. (2004) The contents and effects of polyphenols in chocolate: qualitative and quanti-

tative analyses of polyphenols in chocolate and chocolate raw products as well as evaluation

of potential implications of chocolate consumption in human health. PhD Theses. University

of Giessen, Germany

Yanniotis, S. (2008) Solving Problems in Food Engineering, Springer Science+Business Media, LLC.

Zhang, Q.H., Barbosa-Cánovas, G.V., Balasubramaniam, V.M. et al. (eds) (2011) Nonthermal Pro-

cessing Technologies for Food, Blackwell Publishing Ltd.

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CHAPTER 17

Water activity, shelf life and storage

17.1 Water activity

17.1.1 Definition of water activityThe term water activity (aw) describes the (equilibrium) amount of water avail-

able for hydration of materials; a value of unity indicates pure water, and zero

indicates the total absence of free water molecules; the addition of solutes always

lowers the water activity.

The water activity aw is the equilibrium vapour pressure that the water in a

food exerts (pw) divided by the vapour pressure of pure water (p0). The water

activity can also be defined as the relative humidity of air (RH%) at which a food,

if held, would neither gain nor lose moisture:

aw = 𝛾wxw =pw

p0

= RH%100

(at a given temperature) (17.1)

where 𝛾w is the activity coefficient of water, xw is the mole fraction of water in

the aqueous fraction, p is the partial pressure of water above the material and p0

is the partial pressure of pure water at the same temperature. The water activity

is strongly dependent on temperature. The value of the water activity coefficient

is often calculated, but it is only a rough approximation in most cases and holds

only in a narrow region of concentration.

For a given food, different amounts of water are held or bound at differ-

ent water activities. The relationship is called the water sorption isotherm, since

it defines the moisture content m in equilibrium with different values of aw at

constant temperature. Figure 17.1 shows typical water sorption isotherms.

Equation (17.1) can be written in another form:

aw =(RH%)air

100=

(ERH%)food

100(17.2)

where (ERH%)food is the equilibrium relative humidity of the food. The value of

ERH% is, by definition, equal to the water activity of the food and is defined by

the relative humidity of the air in equilibrium.

Confectionery and Chocolate Engineering: Principles and Applications, Second Edition. Ferenc Á. Mohos.© 2017 John Wiley & Sons Ltd. Published 2017 by John Wiley & Sons Ltd.

579

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580 Confectionery and chocolate engineering: principles and applications

Non-hygroscopic

100

50

00 10 20 30

Hygroscopic

Rela

tive h

um

udity (

%)

Typical S-shaped profile

(e.g. foodstuffs, paper)

Water content (m/m%)

Figure 17.1 Typical water sorption isotherms.

The water activity aw usually increases with temperature and pressure. For

small temperature increases (T1 → T2) at low aw, an often used relationship is

ln a(T1)a(T2)

=(ΔH

R

)(1T1

− 1T2

)(17.3)

where a(T1) and a(T2) are the water activities at temperatures T1 and T2 (K),

respectively, ΔH is the enthalpy change (J/mol) (e.g. the enthalpy change of

absorption or mixing) and R= 8.31434 J/mol K is the universal gas constant.

Differences in water activity may cause water migration between food com-

ponents.

17.1.2 Adsorption/desorption of waterIn order to understand the essential role of the concept of water activity and

ERH%, let us consider the physical phenomena taking place in a food. Two

extreme cases can be differentiated (where RH is a characteristic of the air in

the room, and aw =ERH is a characteristic of the food):

1 Mass of air≫mass of food. This is the case when an unpacked substance (e.g.

food) is stored in a large room with free space (e.g. a storehouse). The phe-

nomena are as follows:

If RH> aw → adsorption (the food becomes wet)

If RH< aw → desorption (the food becomes dry)

If RH= aw → equilibrium, that is RH=ERH

It should be emphasized that during both adsorption and desorption, the

food changes; the original state of the food is preserved only when the RH of

the air is equal to the ERH, which is an essential characteristic of the food.

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Water activity, shelf life and storage 581

2 Mass of air≪mass of food. This case is characteristic of a packed food: the air

space above the product is tiny, and thus the process RH (of air space) →

ERH (of product) is characteristic of this state. This state will be disturbed

(slowly or quickly) by the migration of air (if it is possible at all) through the

packaging material if the RH of the outside air is very much different from the

RH of the inside air. Evidently, in such a case the water activity (=ERH) of the

food determines the microbiological, physico-chemical and other processes

taking place in the food during storage as well. If the ERH of the food is high

enough to reach the region where microbiological deterioration is probable,

a packaging that does not permit continuous water loss from the product may soon

cause microbiological defects (e.g. mould). (At the same time, this water loss from

the product must remain above a minimum water content defined by the

requirement for a fair quality until the shelf life expires.)

17.1.3 Measurement of water activityMany techniques, both direct and indirect, are available for the measurement

of water activity. The oldest technique, that of the hair hygrometer, was in fact

reported by Leonardo da Vinci. A hair, being basically protein, will absorb water

and change in both weight and length as the humidity increases. The hair can be

tied to a pointer to indicate the degree of saturation of the vapour space in terms

of relative humidity. The device is very inaccurate below 30% and above 80%

RH but is used (usually with synthetic fibres) in home air-conditioning units for

humidity control. It is not accurate enough for research purposes.

A very accurate technique, which cannot be applied to the measurement of aw

of small samples, is wet bulb psychrometry. The method involves spinning two ther-

mometers, one of which is immersed in a wet wick, in the vapour space. Based on

the properties of the air, the relative humidity can be determined. It is still used

in the measurement of the RH in large warehouses, such as storehouses where

there is a large air volume. The method is fast but cannot be applied to small

samples. However, a dew point device employing the same principle can be used.

In this case, a surface is cooled and the temperature at which water condenses

is measured optically. This can then be related to aw. The instruments available

have an accuracy of ±3% RH. In relation to this topic, see Section 10.9.4 and

Example 10.5.

Example 17.1Let us prepare a table using Eqns (10.143) and (10.144):

Td = b𝛼a − 𝛼

𝛼 = aTb + T

+ ln(RH)

if T (temperature of air, ∘C)= 15, 20, 25 and 30, Td (the measured dew point,∘C)= 6, 8, 10 and 12, a= 17.27 and b=237.7 K.

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582 Confectionery and chocolate engineering: principles and applications

Table 17.1 Evaluation of relative humidity of air at various temperatures by measuring the

dew point.

Temperature (∘C) Dew point (∘C)

6 8 10 12

15 0.548848 0.629508 0.720425 0.822693

20 0.400467 0.459321 0.525658 0.600278

25 0.295728 0.339189 0.388176 0.44328

30 0.22087 0.25333 0.289917 0.331072

The procedure of calculation is as follows. From Eqn (10.143),

Td → 𝛼 =17.27Td

237.7 + Td

→ 𝛼

From Eqn (10.144),

(𝛼;T) → ln RH = 𝛼 − 17.27T237.7 + T

→ RH

The results are shown in Table 17.1. For example, if the dew point of air at

20 ∘C is 8 ∘C, then the RH of the air is 0.459.

One of the best direct measurements of aw is the direct measurement of the

vapour pressure of water in the space surrounding the food by manometric tech-

niques. In addition, electrical devices, for example, the Sina-Scope, should be

mentioned; of these, the most often used devices are relative humidity sensors

based on electrical resistance, with an accuracy of ±0.5 RH%.

For measurements of high-aw systems (low solute concentration), the mea-

surement of freezing-point depression provides a suitable method; it is used by

microbiologists for studies of microbiological growth as a function of aw. This

method is based on Raoult’s law being valid for dilute solutions, according to

which the freezing-point depression behaves as follows:

• It is equal to Δt=−1.86 K if 1 mol of substance is dissolved in water (this is the

so-called molal freezing-point depression)

• It is proportional to the Raoult concentration (molality) of the dissolved sub-

stance.

If the Raoult concentration of the solute (denoted by a subscript 2) is m2, then

the freezing-point depression is

Δtf = −1.86m2(K) (17.4)

If A2 g of solute is dissolved in A1 g of water, then the numbers of moles are

n1 =A1

M1

and n2 =A2

M2

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Water activity, shelf life and storage 583

and the Raoult concentration of the solute is

m2 =n2

1000=

A2

1000M2

(17.5)

Supposing that the activity coefficient of water 𝛾1 = 1, then

aw = 𝛾1x1 = x1 =n1

n1 + n2

(17.6)

To simplify the calculations, we write

aw = x1 =1000∕18

(1000∕18) + m2

= 55.5655.56 + m2

(17.7)

and m2 (the Raoult concentration) is calculated from the freezing-point depres-

sion (see Eqn 17.4).

The value of the freezing-point depression (Δtm.f) for a given solvent is deter-

mined by the Clausius–Clapeyron equation,

Δtm.f =R(Tf)2

1000 Lf

(17.8)

where Tf is the freezing point of the pure solvent (K), Lf is the latent heat of

freezing/melting of the solvent and R=Nk is the molar gas constant, equal

to 8.31434 J/mol K (N= 6.022× 10−23 mol−1 is the Avogadro number and

k= 1.38062×10−23 J/K is the Boltzmann constant). For example, Δtm.f for

benzene is 5.12 K.

If Tev is the boiling point of the pure solvent (K) and Lev is the latent heat of

boiling of the solvent, then the Clausius–Clapeyron equation gives the elevation

of boiling point for the given solvent:

Δtm.ev =R(Tev)2

1000Lev

(17.9)

Both the freezing-point depression and the boiling-point elevation depend

exclusively on the type of solvent and not on the dissolved substance.

Example 17.2Let us calculate the theoretical values of Δtm.f and Δtm.ev according to the

Clausius–Clapeyron equation:

R = 8.31434 J∕molK

Freezing-point depression: Tf =273 K and Lf = 334.9 J/g:

Δtm.f =8.314 × 2732

1000 × 334.9= 1.85K (measured value∶ 1.86 K)

Boiling-point elevation: Tev = 373 K and Lev = 2260.87 J/g:

Δtm.ev = 8.314 × 3732

1000 × 2260.87= 0.51K (measured value∶ 0.52 K)

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584 Confectionery and chocolate engineering: principles and applications

Table 17.2 Water activity of sucrose solutions.

Sucrose (m/m%) Water activity aw =ERH

5 0.999

10 0.994

20 0.993

40 0.96

60 0.89

Source: Labuza (1975). Reproduced with permission from

Springer.

Example 17.3Let us calculate the water activity of an aqueous sucrose solution of concentration

20 m/m%, although it is questionable whether this solution could be regarded

as dilute. If 20 g of sucrose is dissolved in 80 g of water, then (1000/80)×20 g of

sucrose is dissolved in 1000 g of water. Since M1 = 342 for sucrose,

m2 = 100080

× 20342

= 0.731

and

Δtf = −1.86m2 = −1.36K

According to the aforementioned method of measuring the water activity, the

freezing-point depression is measured, and from its value (assumed here to be

Δtf =−1.36 K), the water concentration of the sucrose solution (20 m/m%→ x1)

is deduced:

x1 =n1

n1 + n2

=80∕18

80∕18 + 20∕342= 0.9871

Values of the water activity of aqueous sucrose solutions of various concen-

trations, according to Labuza (1975), are shown in Table 17.2. It can be seen

that the measured (0.993) and calculated (0.9871) values are slightly different.

If the sucrose concentration is increased, the difference increases. In general, the

molar mass of the solute is not known and the Raoult concentration of it must

be calculated from the freezing-point depression caused by the solute; then Eqn

(17.7) is used.

Example 17.4The water concentration of a culture medium is 90 m/m% and the measured

freezing-point depression of it is −1.2 K. Let us calculate the water activity of this

solution:

m2 = 1.21.86

= 0.645

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Water activity, shelf life and storage 585

This means that in 1000 g of water, the number of moles of the solute is 0.645.

Consequently, the mole fraction of water (see Eqn 17.7) is

aw = x1 =1000∕18

1000∕18 + m2

= 55.55655.555 + 0.645

= 0.9885

Moreover, by using Eqn (17.5), an average molar mass for the culture medium

can be calculated, taking into account the fact that A2 = 10 g:

m2 = 0.645 =A2

1000M2

=10 g

1000M2

(17.10)

and from Eqn (17.10), M2 =645 g.

Measurement of the freezing-point depression is a common tool for determin-

ing the molar mass of a solute.

An indirect method uses a chamber system in which aw can be directly con-

trolled by some means. The moisture content after equilibrium is then measured

rather than the water activity, as this can be done by a much simpler technique.

The basic technique is the use of a saturated salt solution slurry. In a desiccator,

various salts at saturation give a definitive value of aw, which varies little with

temperature. Table 17.3 lists some of the more common salt systems (see Labuza,

1975, p. 204).

For further details, see Labuza (1975).

Table 17.4 shows calculated water activity data for three saturated salt solu-

tions. The calculation for LiCl⋅H2O is

M = 1000100

× 82.842.4

= 19.53

Table 17.3 Equilibrium relative humidity (ERH) of

salts used in chamber system.

Salt Water activity aw =ERH

Desiccant <0.001

LiCl⋅H2O 0.11

MgCl2 0.33

K2CO3 0.49

Mg(NO3)2 0.55

NaNO3 0.65

NaCl 0.76

CdCl2 0.82

K2CrO4 0.88

KNO3 0.94

Na2HPO4 0.99

Source: Labuza (1975). Reproduced with permission from

Springer.

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586 Confectionery and chocolate engineering: principles and applications

Table 17.4 Calculated water activity data for three saturated salt solutions.

Salt Solubility at 20 ∘C (g/100 g water) Molar mass Water activity aw, calculated

LiCl⋅H2O 82.82 42.4 0.7399

NaNO3 88.27 85 0.843

KNO3 31.66 101.1 0.947

Source: Data from Kaltofen (1957).

aw = 55.5655.56 + 19.53

= 0.7399

If it is (rightly) supposed that LiCl is entirely dissociated, then

xw = 55.5655.56 + 2 × 19.53

= 0.587

Furthermore, the measured water activity coefficient is 𝛾w =0.19, and thus

aw = 0.19 × 0.587 = 0.11

which is the actual water activity of a saturated LiCl solution.

It can be seen from Tables 17.3 and 17.4 that the measured and calculated val-

ues differ strongly for LiCl⋅H2O and NaNO3, which proves that the assumptions

𝛾w =1 and aw ≈ xw cannot be accepted.

In the confectionery industry, the minimum concentrations of carbohydrates

used are about 60 m/m% because only more concentrated solutions are sta-

ble against microbiological deterioration. As the concentration of carbohydrates

increases, the accuracy of Eqn (17.7), based on Raoult’s law, becomes unreliable.

17.1.4 Factors lowering water activityThe basic factor that lowers aw is association of solutes with water to form a

hydration shell. Depending on the amount present, the availability of the vapour

pressure of water is decreased from x1 = n1/n1 =1, according to Eqn (17.6), to

aw = 𝛾1x1 ≈ x1 =n1

n1 + n2

(<1 if n2 >0).

Most solutes, especially as the concentration is increased, behave non-ideally

and bind or structure water more than predicted. This is true for solutes (e.g.

carbohydrates and hydrocolloids) of importance in the confectionery industry

as well.

With any solid system, a second important factor that lowers aw is the capil-

lary effect. According to the equation, the vapour pressure or activity of a liquid

present in a capillary is reduced as the radius of the capillary decreases:

aw = exp

(−2𝛾V cos 𝜃

rRT

)(17.11)

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Water activity, shelf life and storage 587

where aw is the water activity if the liquid is water, 𝛾 is the surface tension of the

liquid in the capillary, V is the molar volume of liquid, 𝜗 is the contact angle, r is

the radius of the capillary, R is the universal gas constant and T is the temperature

(K). The capillary effect becomes important only in capillaries of radius less than

0.1 μm, as the following calculation shows.

For simplicity, let us approximate Eqn (17.11) in the form

aw = 1 − 2𝛾V cos 𝜃

rRT

Substituting the values 𝛾 =73 dyn/cm, V= 18 cm3/mol, cos 𝜗= 1, r=10−5 cm,

R= 8.31 erg/mol and T=300 K, we obtain aw = 1−0.01= 0.99.

If r= 10−6 cm, then aw = 1− 0.1=0.9 and so on. The exact values must be cal-

culated according to Eqn (17.11) because the approximation applied becomes

incorrect for higher values of the exponent.

Bluestein and Labuza (cited in Labuza, 1971) have shown that most of the

capillaries in foods are larger than 10 μm but after having removed the water from

these capillaries, the water present in small capillaries (r< 0.1 μm) comprises a

significant amount of the total water. Thus, these capillaries do partially control

the lowering of aw.

The third factor responsible for lowering aw can account partially for the

fact that hysteresis occurs (Fig. 17.2). A different path is followed depending on

whether or not the isotherm is approached by adsorption or desorption.

The most important factor controlling the vapour pressure is the interaction

of water with solid surfaces and with high-molecular-weight colloidal systems.

Water molecules usually interact with the polar groups on surfaces and are held

5

00.0 0.1 0.2 0.3

A

Adsorption

Desorption

Solvent and

free water

Strongly bound

monolayer

Less strongly bound

water layer and

capillary absorbed water

B

0.4 0.5 0.6 0.7 0.8

Water activity (aw)

Wate

r conte

nt (%

)

0.9 1.0

10

15

20

25

Figure 17.2 Adsorption/desorption of water on the surface of foods – data for information

only. The middle region Less strongly bound water layer and capillary absorbed water has

boundaries at about A=0.33 and B= 0.75.

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588 Confectionery and chocolate engineering: principles and applications

very tightly. The energy required to remove these water molecules is greater than

the energy required to vaporize a water molecule from the surface of pure water.

Many aspects of a food system cause a lowering of the availability or activity

of water. Many people have tried to quantify the degree to which water is bound

or free in a food; however, as shown by Labuza et al. (1970) and Labuza (1971),

water even below aw = 1 still has the properties of bulk water: this water can

still dissolve solutes, act as a medium for their mobilization, allow reactions to

occur within the structure itself and be available as a reactant for reactions such

as hydrolysis.

17.1.5 Sorption isothermsMany theories have been developed to describe the shape of sorption isotherms

from both theoretical and mathematical standpoint. The mostly commonly used

equations are the following:

• The Kelvin equation (Eqn 17.11)

• The BET isotherm:aw

m(1 − aw)= 1

m0c+

(c − 1)aw

m0c(17.12)

where m is the moisture content at given aw, m0 is the monolayer value and c

is a constant

• The Harkins–Jura isotherm:

ln aw = B − Am−2 (17.13)

• The Henderson isotherm:

ln(1 − aw) = AmB (17.14)

• The Kuhn isotherm:

m = Aln(1∕aw)

+ B (17.15)

• The Labuza isotherm:

m = Baw (17.16)

• The Oswin isotherm:

m = A

(aw

1 − aw

)B

(17.17)

• A statistical equation:

aw = A + mB + m

(17.18)

where A and B are constants.

For details, see Labuza (1975).

The profile of a sorption isotherm is characteristic of the hygroscopicity of a

product, the sorption behaviour of a product being dependent on temperature.

Sandoval and Barreiro (2002) studied the water sorption isotherms of

non-fermented cocoa beans at 25 ∘C, 30 ∘C and 35 ∘C in the water activity region

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Water activity, shelf life and storage 589

aw = 0.08− 0.94. The best fit was shown by the BET equation when aw < 0.50

(r=0.986) and by the Harkins–Jura model when aw ≥0.50 (r=−0.986). An

average value of the sorption enthalpy of 1.81± 0.10 kcal/g mol was obtained

for the temperature range studied.

17.1.6 Hygroscopicity of confectionery productsThe fact that sucrose is a typical non-hygroscopic material under certain

conditions plays an important role in products covered by sucrose crystals, for

example, candied and crystallized confectioneries. The sucrose crystals may

effectively restrict the porosity on the surface of the centre, through which

the migration of moisture in or out is strongly hindered until the ambient air

humidity reaches the region RH=50–70%. Above RH=70% sucrose starts to

become hygroscopic, and consequently the product may become wet. [Below

RH= 50%, the product slowly dries; see later sections and Minifie (1999, Group

5 of confectioneries).]

17.1.6.1 Non-hygroscopic materials (ERH>60%)Among the non-hygroscopic materials, sucrose is the first that we shall mention.

The isotherm of sucrose (at room temperature) is shown in Figure 17.3.

The water content of sucrose must not exceed 0.1 m/m%, which relates to

an ERH≈ 80% (!) as the isotherm of sucrose shows. For refined sucrose, the

prescription is usually maximum of 0.08 m/m% (↔ ERH≈ 75%). When the

100

90

80

70 Intensive wetting

of sucroce

Practically no wetting

of sucroce

Critical region60

50

Re

lative

hu

mid

ity (

%)

40

30

20

10

00.02 0.04 0.06

Water content (m/m%)

0.08 0.10 0.12 0.14

Figure 17.3 Isotherm of sucrose.

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590 Confectionery and chocolate engineering: principles and applications

sucrose is stored in a silo, the upper limit of the water content is 0.02–0.04 m/m%.

The higher values are tolerable for storing sucrose in sacks because the moisture

slowly evaporates through the sack material, although the released water may

stick the sucrose particles together, and the consequence of such a process is

the development of a crust on the sack material (e.g. paper). However, in a

silo, the moisture cannot leave. Therefore, wetting zones are formed in the

bulk of the sucrose, which promote the compression of hard lumps of sucrose.

When the water content increases, osmophilic mould fungi on the surface of

the sucrose particles may produce invert sugar, which causes intensive sticking

(caking) of the sucrose particles. Accordingly, the condition of the air in silos is

essential.

The isotherm of sucrose shows that the maximum relative humidity of

the air in a storehouse for sucrose must not exceed 70% (↔ water con-

tent≈ 0.03 m/m%), otherwise the sucrose stock starts to get wet. However,

the region of RH=0.6–0.7% may also be critical because of traces of several

impurities. In this region, bulk sugar is liable to agglomeration under the effect

of own weight both in the sack and in the silo.

The relatively non-hygroscopic behaviour of sucrose plays an essential role

in fondant products covered by a sucrose crust (Kandisschicht): up to RH=70%,

the sucrose crust provides a barrier against the diffusion of humidity in and out,

which blocks both drying and wetting of the product. If this crust is damaged

(cracked), the protective effect is lost.

According to Csajághy (2001), the water content of sucrose is dependent on

the size of the sucrose crystals as well. There is an (average) optimal crystal size of

sucrose (region II)≈ 0.5–0.77 mm. In this region, the curve of water content ver-

sus crystal size has a minimum (Fig. 17.4). The explanation of this phenomenon

is that

• The surface area of very small crystals (region I) is very high, and this surface

absorbs a rather large amount of water.

• If the sucrose particles are too large (region III), many large conglomerates

come into being, which may enclose a large amount of water.

Size of sucrose crystals (mm)

I II

0.3 0.5 0.7 0.9 1.1

III

Mo

istu

re c

on

ten

t

Figure 17.4 Moisture content of sucrose as a function of size of sucrose crystals.

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Water activity, shelf life and storage 591

Fats and oils are other non-hygroscopic materials that should be mentioned.

If the continuous dispersion phase is a lipid, outwardly the product behaves

non-hygroscopically. The best example of this is sweets covered by chocolate

(or fat mass): the relationship between the product and its environment is

determined by the non-hygroscopic behaviour of chocolate (if the chocolate

coating is not damaged).

17.1.6.2 Less hygroscopic materials (ERH=40–60%)Many confectionery products can be classified into this group. The essential mat-

ter is to ensure that the product in question has properties that guarantee that

its ERH remains in this relatively narrow range. In this way, the properties of a

product to a certain extent can buffer the effect of the RH changes of air in the

storage room. The risk is double: if the ERH sinks below 40% (too much invert

substance), the product will be sticky; however, if the ERH rises above 60% (too

little syrup and too much sucrose), the product will be hard and dry and possibly

grained.

Figure 17.5 shows an isotherm for cocoa powder at room temperature

(Meursing, 1976). It can be seen why the critical value of 8 m/m% is the upper

limit prescribed in product specifications: this moisture content corresponds

to ERH=60% and, at higher ERH values, microbiological deterioration will

start. Cocoa powder is not a hygroscopic material, since its moisture content does

not rise steeply in the region RH= 20–60% as the relative humidity of the air

increases (Fig. 17.5).

20

18

16

14

12

10

Mois

ture

conte

nt (m

/m%

)

8

6

4

2

00 10 20 30 40 50 60

ERH (%)

70 80 90 100

Figure 17.5 Isotherm of cocoa powder at room temperature. ERH= equilibrium relative

humidity. Note that this figure is for information only. Source: Reproduced with permission

from ADM Cocoa (1998).

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592 Confectionery and chocolate engineering: principles and applications

Table 17.5 Approximate equilibrium relative humidity (ERH) for confectionery products.

Class of confectionery products or raw materials ERH (%)

1. Water cookies (freshly baked), roast nuts, fresh cereals (cornflakes) 15–25

2. Hard candy, aerated high boilings, hard toffee, butterscotch 25–30

3. Hard caramels, hard nougats (ungrained), soft cookies, milk crumb 35–50

4. Gums, pastilles, low-moisture jellies, liquorice pastes, soft caramels 50–60

5. Soft fondants, marzipan, pastes, fudge 60–56

6. Soft marshmallows, Turkish delight, some fondants, fruit jellies, soft nougats (grained) 65–75

7. Chocolate coatings, compound coatings, lozenge pastes, dragees See text

Source: Minifie (1989a,b). Reproduced with permission from Springer.

17.1.6.3 Hygroscopic materials (ERH<40%)As the appropriate isotherm shows, even low values of the relative humidity of the

air may cause a rapid increase in the moisture content of a strongly hygroscopic substance.

Typical hygroscopic substances in the confectionery industry are fructose, invert

sugar, sorbitol and glycerine. The order of hygroscopicity and solubility is the

same: glucose< sucrose< invert sugar< fructose, that is, the hygroscopicity and

solubility rise in parallel.

Minifie (1999) has given approximate ERH intervals for several confectionery

products (Table 17.5). Group 7 needs some comment. The hygroscopicity of these

products, the moisture content of which is mostly about 1 m/m%, is dependent

on their ingredients. Dark chocolate will start to absorb moisture at RH= ca. 85%

and milk chocolate at ca. 78%. The water activity of normal chocolate is about

0.1–0.2 – these low values accord with the fact that the continuous dispersion

phase of chocolate is cocoa butter (see Section 17.1.6.1).

17.1.7 Calculation of equilibrium relative humidityof confectionery products

The basic assumption of this calculation is that the dry content of a substance can

be divided into two parts: sucrose and others. The non-sucrose part of the dry

substance is taken into account as an additional value of sucrose sA, and the values

for several types of substances are calculated by the use of special factors.

According to Grover (1947), the additional value of sucrose sA is calculated

from

sA = 1.994 − 0.339 (g + i) + 0.038(g + i)2 (17.19)

where sA is the content of non-sucrose ingredients (g/g of water), g is the content

of glucose (g/g of water) and i is the content of invert substances (g/g of water).

The special factors for calculating sA for various kinds of non-sucrose substances

are sucrose=1; invert sugar, gelatine, milk protein, sorbitol=1.3; glucose, glu-

cose dry content, pectin and other jellifying materials= 0.8; and fruit acids= 2.5.

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Water activity, shelf life and storage 593

It can be seen that the typical hygroscopic substances are taken into account

with a factor greater than 1. The non-hygroscopic substances that are less hygro-

scopic than sucrose are calculated with a factor less than 1.

The next step in the calculation is

sT = s + sA (17.20)

where s is the content of sucrose in formula g/g of water, and sT is the content of

calculated total sucrose (g/g of water).

Finally, aw (=ERH/100%) is calculated according to Eqn (17.1). Völker (1968)

studied the applicability of the Grover equation (Eqn 17.19) in detail.

Cakebread (1969, 1971, 1972) studied the ERH properties of confectionery

products and modified the Grover equation, since, according to Eqn (17.19), the

solubility should increase after a decrease if sT increases:

sA = 1.9941 + 0.1775 (g + i)

(17.21)

Applying Raoult’s law, Money and Born (1951) suggested the following equation

for calculating ERH:

ERH = 1001 + 0.27N

(17.22)

where N is the number of moles dissolved in 100 g of water.

Example 17.5Let us consider hard-boiled drops of the following composition (%):

Water, 1.5

Sucrose, 65.6

Glucose syrup, 35.0

Citric acid, 0.9

Using the Grover equation (Eqn 17.19),

g = 35 × 0.8

1.5= 18.67, i = 0.9 × 2.5

1.5= 1.2, g + i = 19.87

sA = 1.994 − 0.339(g + i) + 0.038(g + i)2

= 1.994 − 0.339 × 19.87 − 0.038 × 19.872 = 10.25

sT = s + sA = 65.61.5

+ 10.25 = 53.98

The (modified) Raoult concentration of sucrose is

m2 = 10001.5

× 53.98342

= 105.2 (moles of sucrose∕1000 g of water)

According to Eqn (17.7),

aw = 55.5655.56 + m2

= 55.5655.56 + 105.2

= 0.3456

ERH=34.56%.

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594 Confectionery and chocolate engineering: principles and applications

Table 17.6 Calculation of equilibrium relative humidity

(ERH) for hard-boiled drops according to several models.

Principle N ERH (%)

Grover equation 34.56

Cakebread equation 39.2

Money–Born equation

(According to Grover) 10.5 26.04

(According to Cakebread) 8.61 30.12

Using the Cakebread equation (Eqn 17.21),

sA = 1.9941 + 0.1775(g + i)

= 1.9941 + 0.1775 × 19.87

= 0.44

sT = s + sA = 65.61.5

+ 0.44 = 44.17

m2 = 10001.5

× 44.17342

= 86.1

aw = 55.5655.56 + m2

= 55.5655.56 + 86.1

= 0.392

ERH= 39.2%.

Let us calculate ERH using the Money–Born equation (Eqn 17.22):

ERH = 1001 + 0.27N

(17.22)

where N is the number of moles dissolved in 100 g of water.

According to Grover, N=10.52 and ERH= 100/(1+0.27×10.52)= 26.04%.

According to Cakebread, N=8.61 and ERH= 100/(1+ 0.27× 8.61)=30.12%.

The results of these calculations are summarized in Table 17.6.

According to Minifie (1999), the ERH of hard-boiled drops is 25–30%, with

which the values calculated earlier according to the Money–Born equation are

in good agreement.

Minifie (1999) gave methods for determining the water activity of confec-

tionery products and raw materials. Further references are Mansvelt (1962),

Jansen (1969), Lees (1972) and Thieme (1972).

17.2 Shelf life and storage

17.2.1 Definition of shelf lifeThe shelf life is the period of time that starts at the moment a food has been made

and up to end of which the quality of the food remains faultless. Shelf life covers

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Water activity, shelf life and storage 595

all parts of the period, such as storage in the factory, in trading, in storehouses

and finally in the home of the consumer.

The shelf life and the stability of foods are concepts closely connected to each

other. The shelf life is defined by the concept of marginal (or Lyapunov) stability

(see Appendix 6 for details).

In order to understand the optimal conditions of storage, let us consider the

factors influencing shelf life.

17.2.2 Role of light and atmospheric oxygenLight and oxygen promote destabilization reactions of fats/oils (autoxidation),

proteins and sugars, and consequently the conditions of storage and the proper-

ties of the packaging have to be chosen to isolate foods from the effect of light

and oxygen.

17.2.3 Role of temperatureThere is an optimal interval of temperature for every food, which is dependent on

its specific quality properties. For example, in the case of chocolate, the micro-

biological aspects are usually not a priority, but the melting properties of the

cocoa butter in it (e.g. polymorphism) must be taken into account. In contrast,

marzipan is sensitive to macrobiological (yeast) infections, and therefore the tem-

perature of storage is important from this point of view. This means that a rise in

temperature may cause problems. On the other hand, a decrease in temperature

may also be damaging: if dew condenses from the ambient air onto the surface

of the food, moulding may start. Thus the effect of temperature on the humidity

of air is an important aspect of storage.

Finally, it should be mentioned that temperature differences in food induce

water migration and the equalization of mechanical stresses.

17.2.4 Role of water activityThe main types of deterioration related to the water activity of a medium are as

follows:

• In the interval of water activity aw = 0.2–0.4, lipid oxidation is relatively slow;

at lower and higher values, it is stimulated.

• Non-enzymatic browning starts at about aw =0.2 and reaches its maximum at

about aw = 0.8.

• Enzymatic activity starts at about aw = 0.3, mould growth starts at about aw =0.75,

yeast growth starts at aw = 0.8 and bacterial growth starts at aw = 0.9 – all these

four types are stimulated by an increase in aw.

17.2.5 Role of enzymatic activityEnzymatic activity may be important in products containing lauric acid (e.g.

coconut confectioneries and compounds made with hydrogenated coconut oil

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596 Confectionery and chocolate engineering: principles and applications

or palm kernel oil) because of saponification. It is well known that if the mois-

ture content of coconut products exceeds 3–4 m/m%, the risk of saponification

becomes high.

Enzymatic activity is closely connected with the microbiological state of the

raw materials and with infections during production. The measures prescribed

by good manufacturing practice and hazard analysis of critical control points and

so on should be taken into account to prevent such problems.

An everyday problem is the defence of products against moulding if the water

activity exceeds aw =0.75. Conditions in which this high value of water activity

can develop may originate from the following:

• Ambient air (supposing that the packaging does not defend the product against

wetting):

– If the climate is hot and wet

– If the ambient temperature is low (air humidity is condensed on the pack-

aging)

• The packaged product:

– If the water activity of the product is higher than 0.75, the RH of the small air

space above the product becomes equal to this high value since the packag-

ing does not allow the humidity to escape through it (the product becomes

stuffy).

– If the product continuously releases its water content because of syneresis,

which is a common phenomenon in, for example, jellies. If the packaging

material is not capable of permitting continuous water diffusion of appro-

priate extent, the product will be stuffy.

Both phenomena become more pronounced when the product is

cooled.

Non-enzymatic browning is important in confectionery practice (see Chapter 16).

In conclusion, it can be established that packaging plays an important role in

shelf life.

17.2.6 Concept of mould-free shelf lifeThe concept of the mould-free shelf life (MFSL) is connected to the important

role of moulding, which may reduce the shelf life of food. A method has been

worked out that takes into account the permeability of the packaging material,

and the length of time during which the water activity of the food reaches a

critical value can be calculated in this way.

A unique use of isotherm equations and a storage stability map has been

made by a research group from MIT for the prediction of the shelf life of foods

stored in semipermeable films (see Mizrahi et al., 1970a,b; Simon et al., 1971;

Labuza et al., 1972a,b; Quast and Karel, 1972; Quast et al., 1972). In these stud-

ies, it was shown how the reaction kinetics of deterioration as determined under

steady-state conditions could be applied to a condition where moisture was being

slowly transported into a package.

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Water activity, shelf life and storage 597

Let us take the case of moisture adsorption in a package of a food (Labuza,

1975, pp. 214–217). One limiting acceptability factor is the critical water activity

mcrt at which mould will grow, or at which the product will lose its crispness (e.g.

for wafers) or the surface will become sticky (e.g. for sugar bonbons).

The rate at which a package of food picks up water is modelled by a first-order

reaction:dwdt

=(

kx

)A(Pout − Pe) (17.23)

where t is the duration of storage (hours, days or months), w is the weight of

water gained by the package (kg), k is the permeability of the package to water

(kg/m h), x is the film thickness (m), A is the film area (m2), Pout is the outside rel-

ative water vapour pressure (%/100%), assumed constant, and Pe is the relative

vapour pressure of water in equilibrium with the food (%/100%).

If the assumption is made that the limiting resistance to water vapour flow is

the film, then the water in the package should equilibrate rapidly, that is, Pe ≈ Pt,

where Pt is the instantaneous relative vapour pressure of water in equilibrium

with the food (%/100%) as a function of the time t. Thus, Pt can be determined

from the isotherm. In the simplest case, a linear isotherm is assumed:

mout − mt = C(Pout − Pt) (17.24)

where mout is the outside equilibrium moisture content (%/100%), mt is the

instantaneous moisture content of the food (at time t) (%/100%) and C is the

constant of the linear isotherm. If wS is the weight of dry solids in the food, then

(dw∕dt)wS

= dmdt

=(

kx

)(AwS

)(Pout − Pe) =

(kx

)(AwS

) (mout − mt)C

(17.25)

that is,dmt

dt=(

kx

)(AwS

) (mout − mt)C

= K(mout − mt) (17.26)

where w/wS =mt, and K= (k/x)(A/wS)/C is a constant.

After integrating Eqn (17.26) from t= 0 to t= tcrt,

tcrt =( 1

K

)ln

[mout − m0

mout − mcrt

](17.27)

where tcrt is the shelf life of the food investigated (hours or days), m0 is the initial

moisture content of the food (at t=0) and mcrt is the critical water activity in

the food.

The procedure for the determination of shelf life is demonstrated in

Figure 17.6.

If the outside humidity is lower than the instantaneous water activity of the

food, the water content of the food will decrease, that is, the food will dry. In this

case, Eqn (17.23) can be applied in the form

dwdt

= −(

kx

)A(Pe − Pout) (17.28)

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598 Confectionery and chocolate engineering: principles and applications

Changing water activity

of food

mout

mcrt

tcrt

(Shelf life)

tTime (h)

m0

00

Wa

ter

activity

Outside relative humidity

Critical water

activity

Figure 17.6 Determination of shelf life of foods.

The corresponding differential equation is

dmt

dt= −K(mt − mout) (17.29)

The change in the water activity of the food is shown by a curve similar to that

in Figure 17.6 but reflected in the line mout, that is, in this case mout <m0. The

integration of Eqn (17.29) (from t=0 to t= tcrt) gives

tcrt =( 1

K

)ln

[m0 − mout

mcrt − mout

](17.30)

In both cases (see Eqns 17.27 and 17.30), mt =mout when t→∞, that is,

after an infinite time the water activity of the product reaches the water

activity (relative humidity) of the environment. Note that in Eqns (17.26)

and (17.29) the coefficient of mt is negative – this fact makes possible the

stabilization of both hydration (Eqn 17.36) and dehydration (Eqn 17.39) of the

product.

Example 17.6A filled wafer (m0 = 3.0%) is packed and stored under the following conditions:

the air humidity is Pout =mout =80% and the critical water activity of the prod-

uct is mcrt =5.0%. The size of the package is 210×100× 15 mm, and the solid

content of the product is 150 g (the total mass of the package is 160 g). The

thickness of the packaging film is x= 2.5×10−5 m. The permeability of the film

is k=3.75× 10−6 kg/(m×month).

Two points (%) of the linear isotherm of the wafer m (%)=CP (%) are (m= 8.0,

P= 90) and (m= 2.0, P= 20), from which C= (8.0−2.0)/(90− 20)= 6/70. The

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Water activity, shelf life and storage 599

equation of the linear isotherm is

m − 2 =( 6

70

)(P − 20)

m =( 6

70

)(P − 20) + 2

and therefore

mout =( 6

70

)(Pout − 20) + 2 =

( 670

)(80 − 20) + 2 = 7.143%

tcrt =( 1

K

)ln

[mout − m0

mout − mcrt

](17.30)

where K= (k/x)(A/wS)/C.

From the geometry of the product,

A = 2(0.21 × 0.1 + 0.21 × 0.015 + 0.1 × 0.015) m2 = 0.026 m2

ln

[mout − m0

mout − mcrt

]= ln

[7.143 − 3.07.143 − 5.0

]= 0.6592

K =(k∕x)(A∕wS)

C=(

3.75 × 10−6

2.5 × 10−5

)(0.0260.15

)(706

)= 0.3033 month−1

tcrt =(0.6592

03033

)months = 2.17 months

From the isotherm, the value of Pcrt corresponding to mcrt can also be calcu-

lated:

5 =( 6

70

)(Pcrt − 20) + 2 → Pcrt = 55%

This value of air humidity is lower than the boundary of the risk of moulding

(RH= ca. 75%) but is necessary for preserving the crispness of the wafer.

This example demonstrates that a high humidity in the storehouse cuts the

shelf life of a product.

Another formula for calculating the MFSL assumes that during storage the

water activity of the food does not change and, principally, the lower the water

activity is, the longer the MFSL will be:

log10MFSL(days) = 7.91 − 8.1aw (17.31)

at 21 ∘C. Table 17.7 shows the values of MFSL calculated for some values of water

activity from Eqn (17.31). It can be seen that an increase in water activity radi-

cally (exponentially) decreases the value of the probable MFSL.

Minifie (1999) has given data on the water vapour permeability (WVP) of

some packaging materials (Table 17.8).

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600 Confectionery and chocolate engineering: principles and applications

Table 17.7 Calculated values of mould-free shelf

life (MFSL).

aw log10(MFSL) MFSL (days)

0.2 6.29 1949844.6

0.5 3.86 7244.3596

0.7 2.24 173.78008

0.9 0.62 4.1686938

Table 17.8 Water vapour permeability (WVP) of some

packaging materials.a

Material WVP (g/(m2 ×24 h))

Cellulose film 300 P (30 g/m2) 1000

Cellulose film 300 MS (33 g/m2) 18

Cellulose film 330 XS (33 g/m2) 5

Polyamide 6 (Capran) 220

Polyamide 11 (Rilsan) 55

EVA (ethyl vinyl alcohol) 36

PVC (plasticized) 35

PVC (non-plasticized) 35

Polyester 22

Polyethylene LD 22

Polyethylene MD 6

Polypropylene (bioriented) 8

PVDC (extruded) 5

Aluminium foil (25 μm) 0.05

Aluminium foil (12 μm) 1.5

Aluminium foil (9 μm) 4

aGauge of all materials: 25 μm unless otherwise specified.

Source: Minifie (1989a,b). Reproduced with permission from Springer.

The relationship between the WVP given by Minifie and k is

WVP[g∕(m2 × 24 h)] = 30 WVP × 10−3[kg∕(m2 × month)]

= k∕(25 × 10−6 m) → k[kg∕(m × month)]

= 30 × 25 × WVP × 10−9 = 0.75 × WVP × 10−6.

For example, if WVP= 5, then k= 3.75× 10−6 kg/(m×month).

The actual shelf life of confectionery products should be experimentally deter-

mined in each case – none of the theoretical and empirical equations, although

they are indicative, predicts with sufficient accuracy the behaviour of products

with respect to flavour/off-flavour, odour, brightness, crispness and so on.

For more details, see Minifie (1999) and Man and Jones (2000).

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Water activity, shelf life and storage 601

17.3 Storage scheduling

Fuzzy logic seems to be suitable for describing the properties of a stored product

that has a definite value of shelf life. During the time interval up to the end of the

shelf life, the quality properties of the product are changing, and although this

period can be partitioned with the help of qualitative characteristics, picking out

the quantitative thresholds of such parts may be open to dispute. The essence of

the matter is that every lot with the same shelf life is a little different, and during

storage the differences are likely to become more evident. However, a trader has

no means to check them to decide how to manage the lot in terms of shelf life.

Fuzzy logic can handle this vagueness phenomenon. The model presented in

Figure 17.7 is proposed.

In the example shown in the figure, the shelf life of a product is 12 months,

which is partitioned into four parts: Fresh, Good, Medium and Fair. These labels

qualitatively characterize the product over 12 months.

The membership function m(xi) measures the truth related to the given

quality property, for example, m(x1) measures the change of freshness, which

is maximum (=1) at the start (month= 0) and is minimum (=0) at the end of

the third month. The corresponding membership functions of the model are as

follows:

For the interval Fresh:

m(x1) = 1 −x1

3if 0 ≤ x1 ≤ 3 (17.32)

For the interval Good:

m(x2) =x2 − 2

2if 2 ≤ x2 ≤ 4 (17.33)

and

m(x2) =6 − x2

2if 4 ≤ x2 ≤ 6 (17.34)

Membership Shelf life

1

0

0 3 6

Months

GoodFresh

x1 x2 x3 x4

x5

Sta

le

Medium Fair

9 12

Figure 17.7 Model for storage scheduling by fuzzy logic.

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602 Confectionery and chocolate engineering: principles and applications

For the interval Medium:

m(x3) =x3 − 5

2if 5 ≤ x3 ≤ 7 (17.35)

and

m(x3) =7 − x3

2if 7 ≤ x3 ≤ 9 (17.36)

For the interval Fair:

m(x4) =x4 − 8

2if 8 ≤ x4 ≤ 10 (17.37)

and

m(x4) =10 − x4

2if 10 ≤ x4 ≤ 12 (17.38)

For the interval Stale:

m(x5) =x5 − 11

2if 11 ≤ x5 ≤ 12 (17.39)

Both the shelf life and the partitioning of it must be adapted to the given task.

The fuzzy approach provides doubly covered time intervals ({2; 3}, {5; 6}, {8; 9},

{11; 12} in the present example), which show the manager that a new period will

be starting soon. The simplest way of applying this approach is to generate a signal

by a clock in the store documentation system that links a colour to each period.

For example, the numbers showing the amount of products Fresh may be green

(and Good may be represented by blue, Medium by yellow, Fair by orange and Stale

by red), and the doubly covered time intervals may be linked to intermediate

colours (e.g. green → blue).

Further reading

Barbosa-Cánovas, G.V., Fontana, A.J. Jr., Schmidt, S.J. and Labuza, T.P. (2007) Water Activity in

Foods, IFT Press, Blackwell Publishing, Oxford, UK.

Buck, D.F. and Edwards, M.K. (1997) Anti-oxidants to prolong shelf life. Food Tech Int, 2, 29–33.

Coles, R., Dowell, D.M. and Kirwan, M.J. (2003) Food packaging technology, Blackwell Publishing

Ltd.

Cooper, R.M., Knight, R.A., Robb, J. and Seiler, D.L.A. (1968) The Equilibrium Relative Humidity

of Baked Products with Particular Reference to the Shelf Life of Cakes. FMBRA Report 19.

Duckworth, D. (1975) Water Relations of Foods, Academic Press, London.

Fabbri, A., Cevoli, Ch. and Troncoso, R. (2014) Moisture diffusivity coefficient estimation in

solid food by inversion of anumerical model. Food Research International, 56, 63–67

Food Safety Authority of Ireland (2011): Guidance Note No. 18: Validation of Product Shelf-Life

(Revision 1), Abbey Court Lower Abbey Street, Dublin, ISBN 1-904465-33-1.

Labuza, T.P. (1984) Moisture Sorption: Practical Aspects of Isotherm Measurement and Use, American

Association of Cereal Chemists, St Paul, MN.

Leistner, L. (1970) Bedeutung des pH-Wertes, des Redox-potentiales und der Wasseraktivitaet

fuer die Praxis des Fleischwarenherstellung. Arch Lebensmittelhyg 21: 121–126; Einfluss der

Wasseraktivitaet auf Vermehrungsfaehigkeit von Mikroorganismen. Arch Lebensmittelhyg, 21,

264–267.

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Water activity, shelf life and storage 603

Manley, D. (1998) Biscuit, Cookie and Cracker Manufacturing Manuals (Vol. 1: Ingredients; Vol. 2:

Biscuit Doughs; Vol. 3: Biscuit Dough Piece Forming; Vol. 4: Baking and Cooling of Biscuits; Vol. 5:

Secondary Processing in Biscuit Manufacturing; Vol. 6: Biscuit Packaging and Storage), Woodhead

Publishing, Cambridge.

Oswin, C.R. (1983) Package Life Theory and Practice, The Institute of Packaging, UK.

Institute of Food Science and Technology (1993) Shelf-Life of Foods – Guidelines for Its Determination

and Prediction, Institute of Food Science and Technology, London.

Reade, M.G. (1970) Hygrometry of confectionery products. Ingredients and methods for testing.

Confect Prod, 36 (2), 94–99, 116.

Reade, M.G. (1970) Hygrometry of cocoa and chocolate products. Confect Prod, 36 (8), 475–478,

494.

Reade, M.G. (1970) Hygrometry of cocoa and chocolate products. Confect Prod, 36 (9), 557–562.

Reade, M.G. (1970) Hygrometry of cocoa and chocolate products. Confect Prod, 36 (10), 619–625.

Sieler, D.A.L. (1978) The Microflora of Cake and Its Ingredients. Cake and Biscuit Alliance Tech-

nologists’ Conference.

Sieler, D.A.L. (1984) Preservation of bakery products. Proc Inst Food Sci Technol, 17 (1), 31.

Steele, R. (2004) Understanding and Measuring the Self-Life of Food. Woodhead Publishing Limited.

Wedzicha, B.L. and Quine, D.E.C. (1983) Sorption of water vapor by wafer biscuits. Lebensm

Wiss Techn, 16, 115.

Wolf, W., Speiss, W.E.L. and Jung, G. (1989) Sorption Isotherms and Water Activity of Food Materials,

Science and Technology Publishers, London.

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CHAPTER 18

Stability of food systems

18.1 Common use of the concept of food stability

The use of the concept of stability in food science does not entirely agree with

its use in physics and chemistry because the word stable is used to mean reliable,

correct or sound. However, one of the essential aims of the technology is to pro-

duce an appropriately unstable food structure; for example, fresh bread is rather

unstable but dry bread is close to a stable state. Another provocative example

is that the processes of deterioration lead to stable states that are not wanted.

In addition to deterioration, several types of ageing (Ostwald ripening, brown-

ing phenomena, hydrolysis, inversion, etc.) can be mentioned as well. These are

well-known facts.

On the other hand, the concept of a stable state has a very real meaning in

relation to food processing and storage: it relates to a well-defined system of

conditions, among them that the food product must be preserved. One of the

essential technological targets is to establish the characteristics of a food that meet

the requirements of food safety and food quality (laid down in the specification

of the product) during a specified period of storage (called the shelf life).

How is the concept of stability used in food engineering?

18.2 Stability theories: types of stability

18.2.1 Orbital stability and Lyapunov stabilityStability theory was founded by Lyapunov (1892) and Poincaré at the end of the

19th century. Poincaré dealt with orbital stability, concerning the cyclic motion

of orbits (the three-body problem). His investigations led to the foundation of per-

turbation theory. Since orbital stability seems to be uninteresting from our point

of view, however, it is not discussed in the following.

Lyapunov worked out the mathematical principles of stability and methods for

deciding whether a system is stable or unstable. His theory includes definitions of

the types of stability, their characteristics (Lyapunov numbers), and functions for

deciding the existence of stability. These Lyapunov functions simplify the descrip-

tion of the behaviour of a system in a similar way to the potential function for a

central force field.

Confectionery and Chocolate Engineering: Principles and Applications, Second Edition. Ferenc Á. Mohos.© 2017 John Wiley & Sons Ltd. Published 2017 by John Wiley & Sons Ltd.

604

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Stability of food systems 605

18.2.2 Asymptotic and marginal (or Lyapunov) stabilityLet us characterize a system by a point P on a trajectory x that has n parameters

as follows:

P1×n(x) =

⎡⎢⎢⎢⎢⎣

x1

x2

⋮xn

⎤⎥⎥⎥⎥⎦

That is, P(x) is described by a column vector x of n dimensions, where the param-

eters x are functions of the time t. (P has 1 column and n rows, as the usual

designation 1×n shows.) The evolution of this system can be described by the

trajectory P(x; t):P(xi; t = 0) → P(xi; t = tf) (18.1)

where the xi are the variables of the substantial changes (i= 1, 2, … , n); in the

case of a food, the variables x can be physical, chemical or microbiological char-

acteristics; characteristics related to consistency and so on; t=0 is the initial value

of t, and t= tf is the final value of t when the process is stopped.

To define the various types of stability, let us consider two circles of radii r and

R (r<R), with a common centre. The initial point of the trajectory P(xi; t= 0) is

located inside a circle of radius r. On the basis of the behaviour of this trajectory,

the following types of stability can be distinguished.

18.2.2.1 Asymptotic stability• The trajectory remains inside the circle of radius R.

• Its end is inside the circle of radius r.

A special case is exponential stability, in which the trajectory reaches the equi-

librium state fastest, out of all the various asymptotic trajectories. In many cases

the system can be described by a linear model (discussed later), the elements of

which determine the stable or unstable behaviour. If all these elements are neg-

ative, the system is exponentially stable. Because nonlinear models are mostly

very complicated, a linear approximation is used if possible. (This approximation

is used for modelling the Maillard reaction that takes place in batch conching (see

Section 16.5.2).) Therefore, exponential stability is a highlighted topic of stability

theory.

18.2.2.2 Marginal (or Lyapunov) stability• The trajectory remains inside the circle of radius R.

• It does not return into the circle of radius r.

The term Lyapunov stability is applied in all problems that are not connected to

cyclic motion, and this type of stability is deduced in all cases where the trajec-

tory does not leave the circle of radius R. Essentially, asymptotic stability can be

regarded as a subconcept of marginal (or Lyapunov) stability.

18.2.2.3 Instability• The trajectory leaves the circle of radius R.

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606 Confectionery and chocolate engineering: principles and applications

18.2.2.4 Blowing upThis is a special type of instability that refers to the case in which the trajectory

very quickly diverges to infinity. In linear systems, instability is equivalent to

blowing up because unstable poles always lead to exponential growth of the

system states. However, for nonlinear systems, blowing up is only one form of

instability.

18.2.3 Local and global stabilityIf asymptotic (or exponential) stability holds for any initial state, the equilibrium

point is said to be globally asymptotically (or exponentially) stable. Marginal sta-

bility is a type of local stability that refers to a given time interval only.

The distinction between global and local stability needs tools for the analysis of

trajectory function, which is a function of many variables in general. For further

details, see Slotine and Li (1991).

It is important to point out the fact that in many engineering applications,

marginal (Lyapunov) stability is not enough; for example, in mechanical systems,

asymptotic stability may be an essential requirement. However, in food science,

marginal stability seems to be essential, as a type of local stability.

18.3 Shelf life as a case of marginal stability

The concept of shelf life can be defined (Mohos, 1990) by a time value tsh as

follows.

There are vectors Pmin and Pmax prescribed by the product specification so that

for every xi = xi(t) (where i=1, 2, … , n),

Pmin ≤ P(x; t) ≤ Pmax (18.2)

in the time interval t= 0→ t= tsh. Let us consider how this definition relates to

the different types of stability.

The concepts of stability expressed earlier and the definition in Eqn (18.2) can

be related as follows:

P(x; r)min ≤ P(x; t) ≤ P(x; R)max (18.3)

in the time interval t= 0→ t= tsh, where P(x; r)min symbolizes the circle of radius

r and P(x; R)max symbolizes the circle of radius R. The evolution of x(t) can be

imagined as an advance in a tube, the cross-section of which is of radius R and

the length of which is defined by the coordinate t (Fig. 18.1).

The shelf life is the time interval in which x(t) does not leave the region

{P(x; r)min; P(x; R)max}, taking account of every variable. This definition is

characteristic of marginal (Lyapunov) stability.

It should be mentioned that asymptotic stability is not suitable for defining

food stability; for example, dried jelly is asymptotically stable but defective.

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Stability of food systems 607

Marginally stable

Ra

diu

s o

f circle

Asymptoticallystable

Unstable

Shelf life00

r

x(t)

R

Time t

Figure 18.1 Shelf life defined as a kind of marginal (Lyapunov) stability.

18.4 Stability matrix of a food system

18.4.1 Linear modelsIn the simplest case, the evolution of a system can be described by one variable

in a linear form, that is dx/dt= kx, where k is constant and P(x; t) is an integral

of this differential equation. If k is negative, we have asymptotic stability; if k is

positive, we have instability. The form of linear systems is similar:

ddt(x) = Kx (18.4)

where x is a column vector of variables with n rows and K is an (n× n) matrix of

constants (the stability matrix). The investigation of the stability of linear systems

can be done with the help of the K matrix.

The case of nonlinear systems is much more difficult. For further details, see

Borbély (1961) and Slotine and Li (1991).

18.4.2 Nonlinear modelsThe stability matrix of a linear model is a practical formulation of the fact that

• There are n linear differential equations.

• The system characterized by these equations as uniform whole can be handled

by mathematical tools from the point of view of stability. In this case, every

equation has a solution of the same form, and the only difference is manifested

in the positive or negative value of the elements of the stability matrix.

If the differential equations describing the system’s kinetics are not linear, such

a general form of solution cannot be given: every case has to be studied one

by one.

A stability matrix can be also constructed for nonlinear models. However, it

consists of qualitative relations only: if A and B are model variables, the related

element of the stability matrix rA,B expresses merely the fact that the model con-

tains also the differential equation dA/dt= F(B). Notwithstanding, the stability

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608 Confectionery and chocolate engineering: principles and applications

matrix expresses a requirement for considering the system as a uniform whole with

respect to stability, although the mathematical possibilities do not provide a uni-

form solution.

In this narrow sense, the stability matrix of a food system refers to parameters

(variables) of the following types:

• Physical (P)

• Chemical (C)

• Sensory (S)

• Microbiological (M)

Here, P, C, S and M are sets of individual parameters, for example:

• P: viscosity (p1), elasticity (p2), interfacial tension (p3) and so on

• C: water content (c1), pH (c2), reducing sugar content (c3) and so on

• S: odour (s1), colour (s2), stickiness (s3), fracture properties (s4) and so on

• M: numbers of cells of various bacteria (m1), total number of cells (m2) and

so on.

Such methods for the investigation of food stability are not in widespread use.

An attempt has been made using the example of conching (see Section 16.5.2).

Further reading

Hirsch, M.W., Smale, S. and Devaney, R.L. (2004) Differential equations, dynamical systems, and an

introduction to chaos, Academic Press is an imprint of Elsevier (USA).

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CHAPTER 19

Artisan chocolateand confectioneries

19.1 Actuality of artisanship in the confectionerypractice

Nowadays various demands have stimulated the prosperity of artisanship in the

confectionery practice:

– Unemployment: The intensive production of confectioneries has made almost

unnecessary the physical work, contributing to the increase of unemploy-

ment in the developed countries, and the unemployed are looking for work.

Although the large-scale industry will never be driven back in favour of man-

ufacture, some displacement of balance seems probable.

– Consumers’ peculiar needs: The big factories of high productivity prefer relatively

narrow assortment, therefore, to fulfil the special needs for small-volume

products (fortified by herbs of a given region, prepared for special nutritional

requirements, prepared due to certain traditions, etc.) does not meet the

interest of them. However, the artisanship is capable for fulfilling such con-

sumers’ needs thanks for its flexibility.

– Special market: Although the artisan products often are more expensive than

the products sold in malls, warehouses because of their peculiarity and of low

productivity of manufacture, this is not a handicap in their proper segment of

market: in the confectionery shops, coffee-houses and so on.

19.2 The characteristics of the artisan products

These are as follows:

– Uniqueness: This means, on the one hand, that the product in question is exclu-

sively made by a given company or a few companies but its manufacture is

of small size. On the other hand, such a product has peculiar properties that

sharply distinguish it from the other products on the market. Thus the char-

acteristics of uniqueness are the exclusivity of the producer, peculiar product

properties and small size of manufacture.

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610 Confectionery and chocolate engineering: principles and applications

Uniqueness concerns also manufacturing products meeting special nutritional

requirements, for example, changing from wheat-based foods to rye-, oat-, corn-

and rice-based foods.

It is well known that some illnesses are in close connection with nutrition,

for example, diabetes I/II types, gluten sensitivity, any type of food allergy and

so on. However, also endometriosis, a less known but very frequent gynae-

cological illness, may be – among others – a consequence of the not proper

nutrition (see Mills and Vernon, 1999, p. 278, 319).

The fortified foods offer countless possibilities for artisan producers to innova-

tive solutions.

Last but not least, the traditional cookery is an abundant treasure; the refreshed

recipes of old times are always big success.

A usual question in connection with such products is how to declare the

special property since the claims of health are strictly regulated. Even the reg-

ulation supplies the answer. But the principle is simple: to label exactly the

facts. For example, if the use of sugar cannot be entirely eliminated in the

workplace, the claim labelled is with reduced sugar content or the product may

contain traces of sucrose and not sugar free.

– Handmade: The handwork plays an essential role in making artisan products.

This makes possible for expressing the typical features of the artisan product,

but the portion of handwork may not be strictly prescribed. Evidently, some

semi-finished goods (cocoa paste, cocoa butter, chocolate, fondant, etc.) made

by factories have to be purchased, similarly as the smith himself does not pro-

cess the iron ore to iron or steel but buys the steel plate bar as semi-finished

goods to prepare knife, ironwork and so on. In this sense, our modern world

differs from the antiquity; however, handicraft cannot be devoided in the fields

where the large-scale industry cannot meet the needs.

– Shelf life: The artisan confectioneries have to meet the requirements of shelf life

being valid for the products made by the large-scale industry. This practically

means a shelf life of more months at least.

19.3 Raw materials and machinery

– Semi-finished products: Rich sortiment of semi-finished products are at disposal

for artisan technologies (chocolates, nut pastes, fruit preparations, milk prepa-

rations, cereal derivatives, materials of decoration, etheric oils, herb extracts,

fortifying ingredients, etc.).

– Special machinery for small-scale production: There are machinery companies spe-

cialized for supplying the necessary small-scaled equipment.

– Own production of semi-finished products and/or machinery: The peculiar artisan

products may need peculiar raw materials or machinery as well, which cannot

be purchased in conventional way. These have to be developed by the artisan

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Artisan chocolate and confectioneries 611

workshop itself. The own production of special raw material or machinery for

special purposes ensures against the copying of the product by the concurrents.

19.4 The characteristics of the artisan confectionerytechnologies

The output of an artisan workshop is typically small, some hundred kilograms per

shift at most, which consists of batches of about 20–100 kg. (The continuous

production is not typical because of the handwork.)

The law of scaling up plays an essential role in planning an artisan workshop.

The technical–technological conditions of a batch less than 100 kg entirely dif-

fer from that of more than 100 kg although this is not always obvious at first

sight. (The same relates to the financial conditions as well.) Leaving out of con-

sideration the law of scaling up may cause very troublesome surprises. A typical

mistake is to think: If I can well prepare meals in my household, then I can well

manage a restaurant as well. To manage a restaurant, a workshop and so on is an

entirely other task than to prepare meals in the kitchen although there is some

bewildering resemblance.

The following scales [kg production/day] have to be distinguished: <100;

100–1000; >1000; >10 000.

For avoiding such mistakes, the theoretical knowledge and the practical expertise

have to be acquired and permanently improved. It is expedient, on the other

hand, to search partly the traditional recipes, partly the references of the up-to-

date market trends as well.

A typical mistake may be to concentrate exclusively on the productive oper-

ations and to neglect the connecting operations as ripening (see Section 16.4), pack-

aging and storage. These are organic part of technology and need properly large,

air-conditioned places. Moreover, their time demands have to be reckoned with.

If these requirements are not met, the product quality suffer a loss, and finally

the product will disappear from the market.

19.5 Managing an artisan workshop

The head of an artisan workshop is obliged to display the activity of various

directions albeit has to participate as worker casually even also manually in pro-

duction. Mostly the head himself is the founder of such small enterprise who is

the single person having an entire review of all the matters of the firm as tech-

nology, machinery, product planning/development and marketing. On the one

hand, this fact may be an advantage as well. However, this double engagement of

the head (boss and worker) often causes a loss in the result (by accident a failure)

of the enterprise. To prevent such troubles, two rules are advisable to be taken

into consideration:

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612 Confectionery and chocolate engineering: principles and applications

– The order: market>product>financial conditions> technology etc.

– A primary task of the boss is to manage the venture and to employ expert(s).

Finally, the continuous learning is essential. There are excellent handbooks,

which provide both theoretical and practical help, for example, Gisslen (2012),

Li (2009), Pyler and Gorton (2008a,b, 2009a,b), Washburn and Butt (2003) and

Wenniger (2005).

19.6 An easy and effective shaping technologyfor producing praline bars

The artisan technologies can fetch very much from the technique of confection-

ers, mainly from the different ways of handwork shaping. The sharp dividing

line between the artisan products and the confectioners’ products is the shelf life

which has to be more months relating to the artisan products while it is some

days in case of confectioneries’ products only.

One of the most liked products is praline which can be made in very varied

forms and flavours; however, the machinery of praline manufacture is rather

expensive. The shaping technology presented by Figures 19.1 and 19.2 derives

from the technique of confectioners but it is effective, relatively cheap and makes

possible for shaping various pralines.

Figure 19.1 shows that the product has a filling of 6 mm width, covered up and

down by chocolate of 1 mm width. For shaping three frames are used, the height

Sketchof product

1 mm

1 mm

6 mm

6 mm

Frame 1

Figure 19.1 Handwork shaping of praline by frames of various size.

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Artisan chocolate and confectioneries 613

Filling

Frame 1

Plastic sheets

Turn over

Cutting wire

Frame 3

Frame 2Couverture 1

Couverture 2

Figure 19.2 The steps of the handwork shaping.

of which are 6 mm (Frame 1), 7 mm (Frame 2) and 8 mm (Frame 3). The frames

are different in height only. The steps of shaping are shown by Figure 19.2:

Step 1: Frame 1 is placed on a plastic (or metal) Sheet 1, and then the inside of

Frame 1 is filled by filling. The surface of filling is smoothed down by

sword, removing away the surplus of filling. Finally, the filling is cut

around by knife – Frame 1 will be used to the next sheet – and the

semi-finished product on the Sheet 1 has to be relaxed for some hours.

Step 2: Frame 2 of 7 mm height is placed around on the relaxed filling, and the

empty upper layer of 1 mm is filled by tempered chocolate. This is Cou-

verture 1. The filled Sheet 1 has to be cooled.

Step 3: Frame 2 has to be placed back on the cooled, covered filling around on

plastic Sheet 1, and then the filling has to be separated from the Sheet

1 by a cutting wire (Frame 2 ensures here that the filling will be not

broken). Then the filling covered by Sheet 2 (together with Sheet 1 and

Frame 2) has to be turned over; Frame 3 of 8 mm height has to be placed

around on the filling being on Frame 2. Finally the empty upper layer

of 1 mm is filled by tempered chocolate. This is Couverture 2. The filled

Sheet 2 has to be cooled.

Step 4: The filling covered up and down by chocolate is separated from Frame 3

by knife.

The cutting to final shape of pralines can be made by a cutting machine which

parallely cuts in two directions (perpendicularly or in some angle) or by hand. For

relaxation, the sheets with the semi-finished products are placed on the shelves

of movable stands which can be rolled into air-conditioned room for some hours

and back for the next step.

The filling can be some kinds of praline paste made from roasted nuts, sugar,

vegetable fats and so on or some kinds of sugar masses (based on flavoured

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614 Confectionery and chocolate engineering: principles and applications

fondant, caramel or their variations with jellies or foams for softening the fill-

ing). If the packaging per piece provides a hermetic closing, the filling of sugar

mass will not be dried through the uncovered sides of the praline (the fat-mass

fillings do not apt to be dried).

A short calculation of efficiency is presented as follows:

Let us suppose that the inner sizes of the sheets are 245×245 mm, the height

is 8 mm and, after shaping, the netto sizes are 240×240× 8 mm, and the broken

fringe has a width of 5 mm. Moreover, the filling contains chocolate as well, thus

the broken fringe can be recycled without any loss. The supposed density of the

product is about 1 g/cm3.

The netto amount of the finished product on a sheet is 460.8 g.

If the plant works with 100 sheets, the mass demand (filling+ chocolate) is

about 50 kg/day. This means about 1 t finished product per month.

Sizes of a piece (mm) Pieces per sheet Amount of a piece (g)

2×2 12×12= 144 3.2

2×6 12×4= 48 9.6

3×8 8× 3=24 19.2

The capacity is determined by the number of filled sheets. Only three frames

of different size are needed and a sword and a knife. Cutting and packaging are

optimal by machinery.

Further reading

ADM Cocoa (2009) De Zaan Cocoa Manual, ADM Cocoa International, Switzerland.

Belton, P. and Taylor, J. (2002) Pseudocereals and Less Common Cereals, Springer-Verlag, New York.

Case, S. (2006) Gluten-Free Diet: A Comprehensive Resource Guide, Case Nutritional Consulting, Regina,

Canada.

Coles, R., Dowell, D.M. and Kirwan, M.J. (2003) Food Packaging Technology, Blackwell Publishing

Ltd.

Fenster, C. (2007) Gluten-Free Quick and Easy, Penguin, East Rutherford, NJ.

Gisslen, W. (2005) Professional Baking, 4th edn, John Wiley & Sons, Inc.

Hagman, B. (2000) The Gluten-Free Gourmet Bakes Bread, Holt & Co., New York.

Pyler, E.J. and Gorton, L.A. (2008) Baking-Science and Technology, Vol. I–II, 4th edn, Sosland Pub-

lishing Company.

Steele, R. (2004) Understanding and Measuring the Self-Life of Food, Woodhead Publishing Limited.

US Food and Drug Administration. Gluten-Free Labeling, http://www.cfsan.fda.gov/~dms/

gluttobi.html

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PART IV

Appendices

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APPENDIX 1

Data on engineering properties ofmaterials used and made by theconfectionery industry

A1.1 Carbohydrates

See Table A1.1.

For further details, see Desent and Bouscher (1961).

See Tables A1.2 and A1.3.

Mean specific heat capacity of sucrose (in the range 0–100 ∘C) is

cp = 0.2712+0.00103t (kcal/kg ∘C); (1 cal= 4.1868 J).

For further details, see Maczelka (1962, p. 27).

See Tables A1.4–A1.8.

For further details, see Tonn (1961).

See Table A1.9.

Specific heat capacity of aqueous sugar solutions (Sokolovsky, 1958, p. 32) is

cP = 1 − (0.6 − 0.0018t)S

where cP is the specific heat capacity of the aqueous sugar solution (kcal/kg=4.1868 kJ/kg), t is the temperature (∘C) and S is the sugar concentration (m/m).

Thermal conductivity of aqueous sugar solutions (Sokolovsky, 1958, p. 32) is

𝜆 = 𝜆W(1 − 10−5 × KS)

where 𝜆 is the thermal conductivity of the aqueous sugar solution at 20 ∘C(kcal/m h K= 1.163 W/m K); 𝜆W is the thermal conductivity of water at 20 ∘C;

K is a constant, with a value of 556 at 20 ∘C; and S is the sugar concentration

(m/m).

The thermal conductivity of an aqueous sugar solution of concentration

80 m/m% (at 20 ∘C) is 0.28 kcal/m h K=0.32564 W/m K.

Thermal diffusivity of crystalline sugar (Sokolovsky, 1958, p. 32) is

a = 4.93 × 10−4 m2∕h = 4.93 × 10−4 × 2.778 × 10−4 m2∕s = 1.3696 × 10−7 m2∕s

See Table A1.10.

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Table A1.1 Thermophysical data for sugar.

Type T (∘C) 𝝆 (kg/m3)𝝀 (W/mdegree)

c (W s/kgdegree)

a×106

(m2/s)

Cube −5 — 0.157 1340 0.1347

15 1600 0.153 1361 0.1280

35 — 0.145 1390 0.1194

Castora — 900 0.139 712 0.2390

Icingb — 660 0.139 879 0.2360

Invert 15 1198 0.336 3207 0.0875

35 1188 0.334 3199 0.0833

60 1160 0.353 3408 0.0894

Dextrosec 1538.4 (Sokolovsky, 1959)

Dextrose hydrate 1571.4 (Sokolovsky, 1959)

Maltose 1500 (Sokolovsky, 1959)

a0.1% water content.b0.3% water content.cWater-free.

Source: Antokolskaja (1964).

Table A1.2 Thermal conductivity of crystalline sugars.

Type 𝝀 (W/m degree)

Powder 0.069

Raffinated 0.081

Light pressed 0.093

Castor 0.58

Raw 0.17

Source: Antokolskaja (1964).

Table A1.3 Specific and molar heat capacity of crystalline sugars.

T (∘C)c (W s/kgdegree)

C (W s/moldegree)

0 1 088.57 385 604

20 1 214.17 415 749

30 1 256.04 435 427

40 1 323.03 452 174

50 1 356.52 464 734

60 1 419.32 485 668

70 1 469.57 502 416

80 1 532.37 523 350

90 1 578.42 540 097

Source: Antokolskaja (1964).

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Data on Engineering Properties 619

Table A1.4 Melting point of sugars.

Sugar Melting point (∘C)

Dextrose 146

Maltose 108

Sucrose 170–188

Raw sugar 170–188

Powdered sugar 170–188

Fructose 104

Source: Data from Antokolskaja (1964).

Table A1.5 Density of saturated sugar solutions as a function

of temperature.

T (∘C)Sugar content

(g/100 cm3 water)Density(kg/m3)

0 179.2 1314.0

5 184.7 1319.2

10 190.5 1323.5

15 197.0 1328.0

20 203.9 1331.9

25 211.4 1342.7

30 219.9 1342.7

35 228.4 1348.0

40 238.1 1353.5

45 248.7 1359.2

50 260.4 1365.1

55 273.1 1371.2

60 287.3 1377.5

65 302.9 1384.0

70 320.5 1390.8

75 339.9 1397.7

80 362.1 1404.9

85 386.8 1412.2

90 415.7 1419.9

95 448.6 1427.7

100 487.2 1435.9

Source: Data from Antokolskaja (1964).

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Table A1.6 Concentration of saturated sugar/water solutions as a function of temperature.

t (∘C) % t (∘C) % t (∘C) %

0 64.18 34 69.38 68 75.8

1 64.31 35 69.55 69 76.01

2 64.45 36 69.72 70 76.22

3 64.59 37 69.89 71 76.43

4 64.73 38 70.06 72 76.54

5 64.87 39 70.24 73 76.85

6 65.01 40 70.42 74 77.06

7 65.15 41 70.6 75 77.27

8 65.29 42 70.78 76 77.48

9 65.48 43 70.96 77 77.7

10 65.58 44 71.14 78 77.92

11 65.73 45 71.32 79 78.14

12 65.88 46 71.5 80 78.36

13 66.03 47 71.68 81 78.58

14 66.18 48 71.87 82 78.8

15 66.33 49 72.06 83 79.02

16 66.48 50 72.25 84 79.24

17 66.63 51 72.44 85 79.46

18 66.78 52 72.63 86 79.69

19 66.93 53 72.82 87 79.92

20 67.09 54 73.01 88 80.15

21 67.25 55 73.2 89 80.38

22 67.41 56 73.39 90 80.61

23 67.57 57 73.58 91 80.84

24 67.73 58 73.78 92 81

25 67.89 59 73.98 93 81.3

26 68.05 60 74.18 94 81.53

27 68.21 61 74.38 95 81.77

28 68.37 62 74.58 96 82.01

29 68.53 63 74.78 97 82.25

30 68.7 64 74.98 98 82.49

31 68.87 65 75.18 99 82.73

32 69.04 66 75.38 100 82.97

33 69.21 67 75.59

Source: Data from Sokolovsky (1958).

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Data on Engineering Properties 621

Table A1.7 Thermophysical data for sucrose solutions with various boiling points.

Concentration(m/m%) T (∘C)

𝝀 (W/mdegree)

c (W s/kgdegree) 𝜼 (N s/m2)×106

0 100.0 0.682 4187 282.4

10 100.2 0.645 4120 366.7

20 100.4 0.642 3864 452.1

30 100.7 0.570 3626 619.7

40 101.2 0.531 3358 960.1

50 102.0 0.493 3256 1765.2

60 103.5 0.456 2939 3341.1

Source: Data from Antokolskaja (1964).

Table A1.8 Thermophysical characteristics of sucrose–water solutions.

Concentration(m/m%) T (∘C)

𝝀 (W/mdegree)

c (W s/kgdegree) 𝝂 ×106 (m2/s) a (Prandtl)

20 50 0.5700 3760 0.9065 6.38

60 0.5809 3775 0.7605 5.26

70 0.5893 3790 0.6420 4.37

80 0.5965 3805 0.5610 3.76

30 50 0.5368 3546 1.282 9.71

60 0.5956 3568 1.082 7.84

70 0.5536 3591 0.9063 6.49

80 0.5604 3614 0.7750 5.48

40 50 0.502 3333 2.140 16.52

60 0.510 3363 1.701 12.97

70 0.518 3393 1.389 10.48

80 0.524 3423 1.153 8.62

50 50 0.468 3119 4.173 33.82

60 0.475 3157 3.148 25.30

70 0.482 3195 2.442 19.47

80 0.488 3232 1.956 15.50

60 50 0.433 2906 11.02 93.90

60 0.440 2951 7.63 64.75

70 0.447 2996 5.54 46.82

80 0.452 3041 4.15 34.98

80a 15 0.326 1361 0.1280

aTonn (1961).

Comment: Since the Prandtl number Pr is equal to 𝜈/a, a= 𝜈/Pr. For example (in the first row),

a= (0.9065×10−6/6.38) (m2/s)=0.1421× 10−6 m2/s.

Source: Data from Sokolovsky (1959).

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Table A1.9 Thermal conductivity (W/m K) of sucrose–water solutions.

Temperature (∘C)Concentration(m/m%) 0 20 30 40

0 0.583 0.599 0.614 0.628

10 0.551 0.566 0.581 0.594

20 0.520 0.535 0.548 0.560

30 0.488 0.501 0.514 0.526

40 0.457 0.470 0.480 0.492

50 0.391 0.437 0.449 0.458

60 0.384 0.405 0.415 0.419

50 60 70 80

0 0.641 0.652 0.663 0.672

10 0.607 0.617 0.628 0.636

20 0.572 0.538 0.592 0.600

30 0.536 0.547 0.555 0.563

40 0.502 0.512 0.519 0.526

50 0.481 0.477 0.484 0.491

60 0.434 0.441 0.449 0.455

Source: Data from Antokolskaja (1964).

Table A1.10 Boiling point of sucrose–water solutions.

Concentration(m/m%)

Boilingpoint (∘C)

10 100.1

20 100.3

30 100.6

40 101.0

50 101.8

60 103.0

70 105.5

80 109.4

90 119.6

Source: Data from Antokolskaja (1964).

An approximate formula for the boiling point of sugar–water solutions is

(Sokolovsky, 1958, p. 19)

T (∘C) = 100 ∘C + 2.33(S∕W )

where T is the boiling point, S is the concentration of sugar (m/m%) in

the solution and W is the concentration of water (m/m%) in the solution. For

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Data on Engineering Properties 623

Table A1.11 Elevation of boiling point (∘C) of sugar solutions as a function of concentration at

various pressures.

Pressure (mm Hg=133.2 Pa)

92.51 149.38 233.7 355.1 525.76 760

Sugar (%) 50 ∘C 60 ∘C 70 ∘C 80 ∘C 90 ∘C 100∘C

5 0.05 0.05 0.05 0.06 0.06 0.06

10 0.10 0.10 0.11 0.11 0.12 0.12

15 0.17 0.18 0.18 0.19 0.19 0.20

20 0.26 0.27 0.28 0.28 0.29 0.30

25 0.39 0.40 0.42 0.43 0.41 0.45

30 0.52 0.54 0.55 0.57 0.58 0.60

35 0.69 0.71 0.73 0.76 0.78 0.80

40 0.80 0.85 0.90 0.95 1.00 1.05

45 1.02 1.10 1.18 1.25 1.32 1.40

50 1.32 1.40 1.52 1.61 1.72 1.80

55 1.70 1.82 1.94 2.06 2.18 2.30

60 2.30 2.15 2.60 2.75 2.90 3.05

65 2.80 3.00 3.20 3.40 3.60 3.80

70 3.65 3.90 4.18 4.46 4.75 5.05

75 5.05 5.40 5.80 6.20 6.60 7.00

80 (6.80) 7.30 7.85 8.35 8.90 9.40

85 (10.00) 10.75 11.50 12.25 13.00

90 (16.00) 17.20 18.40 19.60

Source: Data from Sokolovsky (1958).

example, if S=20% and W= 80%, then T(∘C)= 100+2.33(20/80)= 100.5825 ∘C(in Table A1.10, 100.3 ∘C). If S=90% and W=10%, then T(∘C)=100+ 2.33

(90/10)= 120.97 ∘C (in Table A1.10, 119.6 ∘C).

For example, if the pressure is 92.51 mmHg (=92.51 mmHg×133.2 Pa/mmHg=12 322.332 Pa), then the boiling point of water is 50 ∘C, and an aqueous sugar

solution of 70 m/m% concentration has a boiling point t= (50+ 3.65) ∘C.

See Tables A1.11–A1.20.

According to Sokolovsky (1958, p. 103), the specific heat capacity of starch

(c ′P) can be calculated from

c′P = [acP + f (100% − a)]∕100%

where cP =0.2697 cal/g∘C (and f= 1) or cP =1.1284 kJ/kg ∘C (and f= 4.1839) is

the specific heat capacity of the dry content of starch and a (%) is the water

content of the starch. [This relation is based on the fact that the specific heat

capacity of water is about 1 cal/(grade g)= 4.1839 kJ/(grade kg) and the values

of the specific heat capacity are additive according to the ratio of ingredients.]

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Table A1.12 Solubility of sugar in water in the presence of glucose syrup.

A B C D E

20 ∘C 67.09 0 203 0 203

57.51 10.56 180.2 33.1 213.3

51.23 17.74 165.09 57.17 222.26

4.51 21.76 163.16 73.19 236.35

43.26 28.8 154.82 103.07 257.89

50 ∘C 72.25 0 260.36 0 260.36

62.97 10.05 233.39 37.25 270.64

55.05 18.26 208.16 69.01 277.17

51.03 24 204.37 96.12 300.49

46.81 28.86 193.19 119.52 312.71

44.47 32.02 189.15 136.2 325.35

37.96 40.54 176.56 188.56 365.12

70 ∘C 76.22 0 322.83 0 322.83

67.43 9.92 207.7 43.7 341.49

60.6 17.55 277.35 80.32 357.67

55.14 24.95 276.95 125.31 402.26

52.7 28.1 274.48 146.35 420.83

49.69 32.16 273.77 177.19 450.96

A= concentration of sugar (m/m%) in 100 g of solution.

B= concentration of glucose syrup (m/m%) in 100 g of solution.

C= sugar (g) per 100 g of water.

D=glucose syrup dry content (g) per 100 g of water.

E=C+D.

Source: Data from Sokolovsky (1958).

The values of the specific heat capacity of commercial starch products are as

follow:

Temperature (∘C) c′P (cal/g)

0–20 0.2765

21–42 0.2978

43–62 0.3061

See Table A1.21.

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Table A1.13 Solubility of sugar in water in the presence of invert sugar.

A B C D E

23.1 ∘C 67.59 0 208.55 0 208.5557.84 11.9 191.14 39.32 230.4647.31 25.39 173.3 93 266.328.66 36.9 158.18 150.98 309.16

30 ∘C 68.11 — 213.58 — 213.5856.32 14.94 195.96 51.98 247.9450.97 21.86 187.6 80.46 268.0649.91 23.21 185.68 86.34 272.0248.95 24.46 184.09 91.99 276.0846.36 28.01 180.88 109.29 290.1739.23 37.48 168.43 160.93 329.3632.06 47.02 153.25 224.76 378.0131.85 47.62 155.13 231.95 387.0826.03 56.37 147.9 320.28 468.1821.18 63.68 139.89 420.61 560.520.59 64.47 137.82 431.52 569.34

50 ∘C 72.22 — 260.36 — 260.3662.81 11.42 243.73 44.31 288.0453.8 22.65 228.45 96.17 324.6246.2 32.32 215.08 150.46 365.5435.75 46.05 196.43 253.2 449.45

A= concentration of sugar (m/m%) in 100 g of solution.

B= concentration of glucose syrup (m/m%) in 100 g of solution.

C= sugar (g) per 100 g of water.

D=glucose syrup dry content (g) per 100 g of water.

E=C+D.

Source: Data from Sokolovsky (1958).

Table A1.14 Boiling point of aqueous glucose syrup

solutions at atmospheric pressure.

G (%) Boiling point (∘C)

20 100.5525 100.730 100.8535 101.0540 101.4545 10250 102.7555 103.7560 105.0565 106.670 108.475 110.4580 11385 117.7590 127

G (%)=glucose syrup dry content (m/m%).

Source: Data from Sokolovsky (1958).

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Table A1.15 Elevation of boiling point of glucose solutions as a function of concentration at

various pressures.

Pressure (mm Hg)

92.51 149.8 233.7 355.1 525.76 760

Glucose (%) 50 ∘C 60 ∘C 70 ∘C 80 ∘C 90 ∘C 100 ∘C

5 0.08 0.03 0.09 0.1 0.11 0.11

10 0.16 0.17 0.18 0.19 0.21 0.22

15 0.25 0.26 0.28 0.30 0.32 0.35

20 0.39 0.41 0.41 0.48 0.51 0.55

25 0.51 0.55 0.59 0.63 0.67 0.7

30 0.62 0.66 0.70 0.75 0.80 0.85

35 0.78 0.84 0.9 0.96 1.02 1.05

40 1.04 1.11 1.2 1.28 1.36 1.45

45 1.15 1.55 1.66 1.78 1.9 2

50 1.98 2.12 2.28 2.42 2.59 2.75

55 2.7 2.9 3.1 3.3 3.59 3.75

60 3.63 3.9 1.17 4.45 4.75 5.05

65 4.73 5.07 5.43 5.89 6.19 6.6

70 6.04 6.47 6.93 7.4 7.9 8.l0

75 7.47 8.02 8.58 9.17 9.79 10.45

80 9.29 9.98 10.69 11.42 12.17 13

85 12.01 13.6 14.69 15.59 16.65 17.75

90 19.14 20.5 21.08 23.62 25.27 27

1 mmHg=133.2 Pa.

Source: Data from Sokolovsky (1958).

A1.2 Oils and fats

See Table A1.22.

An approximation for the thermal diffusivity (a) for cream margarine in the

temperature range 20–32 ∘C is

a × 108 = 2.7778[2.65 − 0.02(T − 20)] (m2∕s)

where T is in degrees Celsius.

See Table A1.23.

A1.3 Raw materials, semi-finished products andfinished products

See Table A1.24.

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Table A1.16 Dynamic viscosity (N s/m2 =Pa s) of sucrose–water solutions.

Temperature (∘C)Concentration(m/m%) 20 30 40 50 60 70 80 90

60 0.0572 0.0331 0.0206 0.0137 0.0095 0.0069 0.0053

61 0.0678 0.0386 0.0238 0.0156 0.0107 0.0077 0.0058

62 0.0809 0.0454 0.0275 0.0178 0.0121 0.0086 0.0064

63 0.0970 0.0634 0.0320 0.0204 0.0137 0.0098 0.0071

64 0.1171 0.0636 0.0374 0.0235 0.0156 0.0108 0.0079

65 0.1428 0.0760 0.0441 0.0272 0.0172 0.0122 0.0088

66 0.1759 0.0916 0.0522 0.0317 0.0206 0.0139 0.0099

67 0.2190 0.1113 0.0622 0.0372 0.0239 0.0159 0.0112

68 0.2780 0.1388 0.0747 0.0440 0.0279 0.0183 0.0127

69 0.3540 0.1697 0.0906 0.0524 0.0328 0.0212 0.0145

70 0.4600 0.2141 0.1111 0.0631 0.0388 0.0248 0.0167

71 0.6737 0.2739 0.1381 0.0768 0.0463 0.0292 0.0194

72 0.3561 0.1737 0.0945 0.0559 0.0348 0.0227

73 0.4695 0.2220 0.1178 0.0682 0.0418 0.0268

74 0.6310 0.2885 0.1487 0.0841 0.0507 0.0319

75 0.8640 0.3805 0.1900 0.1050 0.0620 0.0384

76 1.2140 0.5130 0.2463 0.1330 0.0768 0.0466

77 0.7010 0.3234 0.1707 0.0951 0.0572

78 0.9800 0.4330 0.2216 0.1215 0.0711

79 1.430 0.5930 0.2927 0.1562 0.0896

80 2.160 0.8320 0.3939 0.2044 0.1152 0.0830

81 1.2000 0.5460 0.2722 0.1505 0.0940

82 1.8000 0.7700 0.3727 0.2000 0.1110

83 1.2500 0.5190 0.2800 0.1420

84 1.7000 0.7400 0.3760 0.1860

Source: Data from Antokolskaja (1964).

Table A1.17 Dynamic viscosity of saturated dextrose–water solutions.

T (∘C)Concentration ofdextrose (m/m%)

Dextrose dissolvedin 100 g water

Viscosity(N s/m2)

20 47.72 91.60 0.0183

30 54.64 120.46 0.0187

40 61.83 162.14 0.0224

50 70.91 243.80 0.0509

60 74.73 295.00 0.0662

70 78.23 359.94 0.0784

80 81.83 436.31 0.1040

90 84.63 552.77

Source: Data from Sokolovsky (1958).

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Table A1.18 Interfacial tension of sugar solutions at 20 ∘C.

Concentration(g/100 g) 𝝈 (N/m)

Concentration(g/100 g) 𝝈 (N/m)

0 0.0727 29.8 0.0760

6.8 0.0731 31.0 0.0762

10.0 0.07335 40.7 0.0771

13.1 0.0736 47.5 0.0780

20.5 0.0745 51.2 0.0787

22.2 0.0749 62.7 0.0796

Source: Data from Antokolskaja (1964).

Table A1.19 Dynamic viscosity (N s/m2) of honey as a function of temperature (∘C) and water

content (m/m%).

Temperature (∘C)Watercontent (%) 10 20 30 40 50 60 70 80

14 — 59.2 14.4 4.6 1.5 1.0 0.70 0.25

16 — 22.8 5.9 2.1 0.9 0.6 0.30 0.15

19 28.0 6.5 2.7 1.0 0.5 0.3 0.20 0.10

24 4.52 1.3 0.5 0.4 0.2 0.1 0.05 0.03

Source: Data from Antokolskaja (1964).

Table A1.20 Thermophysical characteristics of starch syrup used for caramel production.

Dry content(m/m%) t (∘C) 𝝆 (kg/m3) 𝝀 (W/m K) cP (W s/kg K)

a×106

(m2/s)

80 20 1420 0.326 1967.8 0.1167

40 1395 0.314 2009.7 0.1139

60 1370 0.314 2051.6 0.1111

80 1340 0.302 2093.4 0.1055

85 20 1450 0.314 1884.1 0.1167

40 1425 0.302 1925.9 0.1111

60 1400 0.302 1967.8 0.1083

80 1370 0.291 2008.7 0.1055

88 20 1480 0.314 1842.2 0.1167

40 1455 0.302 1884.1 0.1111

60 1430 0.302 1925.9 0.1083

80 1400 0.291 1967.8 0.1055

92 20 1520 0.314 1758.5 0.1167

40 1490 0.302 1800.3 0.1111

60 1460 0.291 1884.1 0.1055

80 1430 0.279 1925.9 0.1028

Source: Schriftsammlung der Arbeiten des WKNU (1950).

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Table A1.21 Dynamic viscosity of aqueous solutions of invert sugar

as a function of temperature.

Total drycontent(m/m%)

Invert sugarcontent(m/m%) t (∘C) 𝜼 (Pa s) t (∘C) 𝜼 (Pa s)

74.00 73.65 30.0 0.663 50.0 0.140

78.84 79.35 10.1 5.344 45.1 0.431

81.75 78.97 20.3 23.714 45.0 1.648

74.00 73.65 40.2 0.304 70.5 0.060

79.84 79.35 30.7 2.076 60.0 0.145

81.75 78.97 30.2 7.752 70.0 0.157

Source: Data from Sokolovsky (1959).

Table A1.22 Temperature dependence of the thermal parameters of

margarine.

TFor household use,𝝀 (W/m degree)

Cream margarine,a×106 (m2/s)

20 — 0.0736

22 0.165 0.0717

24 — 0.0714

26 0.172 —

27 — 0.0711

29 0.173 0.0678

32 0.179 0.0667

Source: Data from Derneko and Schafchid (1959).

For cocoa mass,

𝜆 = 1.163(0.325 − 0.005t) W∕mK

a × 108 = 2.7778(4.65 − 0.005t) m2∕s

For chocolate mass (Rapoport and Tarchova, 1939) and for the temperature

range 30–70 ∘C,

𝜌 = (1320 − 0.5t) kg∕m3

𝜆 = 1.163(0.2 + 0.0007t) W∕m K

cP = 1674.7 W s∕kgK

a × 108 = 2.7778(4 + 0.017t) m2∕s

See Table A1.25.

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Table A1.23 Thermal properties of vegetable oils and fats at 20 ∘C.

Thermal conductivity 𝜆 (106 ×W/m K)

Sunflower oil 0.1675

Soy oil 0.1763

Sunflower oil (hydrogenated) 0.1675

Thermal diffusivity a (10×m2/s)

Sunflower oil 0.944

Soy oil 1.056

Specific heat capacity cP (kJ/(kg ∘C))

Sunflower oil (raffinated) 1.7752

Soy oil 1.8149

Sunflower oil (hydrogenated) 2.1311

Specific heat capacity cP (kJ/(kg ∘C)) of hydrogenated vegetable oils

cP = cP.20[1+ 𝛼(t−20)]

where cP.20 =2.147 kJ/kg ∘C and 𝛼 × 103 =1.380 K−1

Density 𝜌 (kg/m3)

Arachis oil 913.7

Sunflower oil 918.9

Soy oil 919.4

Dielectric constant (permittivity) 𝜀t (F/m) as a function of temperature (t=0–100 ∘C)

Arachis oil 𝜀t =3.051− 0.00313(t−20)

Sunflower oil 𝜀t =3.11−0.0034(t− 20)

Source: Data from Kiss (1988).

Table A1.24 Thermophysical properties of cocoa butter, cocoa mass and

chocolate.

t (∘C) 𝝆 (kg/m3) 𝝀 (W/m K) cP (W s/kg K) a (106 m2/s)

Cocoa butter

10 927 0.291 2512 0.1250

30 910 0.325 2512 0.1444

50 895 0.372 2512 0.1867

70 880 0.430 2512 0.1944

Chocolate

0 1235 0.214 1482.1 0.1172

10 — 0.223 1854.7 0.0975

20 — 0.233 2122.7 0.0889

35 — 0.246 1603.5 0.1244

Cocoa mass

10 1110 0.372 2837.7 0.1279

30 1100 0.360 2637.7 0.1250

50 1090 0.349 2637.7 0.1194

70 1080 0.337 2837.7 0.1197

Source: Data from Antokolskaja (1964).

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Table A1.25 Chemical properties of cocoa butter.

Property Value

Acid degree 1.6–6.0 (exceptionally up to 8)

Acid value 0.9–3.4 (exceptionally up to 4.5)

Saponification value 192–197

Iodine value 32–42 (exceptionally up to 45)

Peroxide value (mEqO2/kg) <2

Table A1.26 Physical properties of cocoa butter.

Property Value

Melting point (complete fusion) of modifications

𝛾 form 16–18 ∘C𝛼 form 21–24 ∘C𝛽 (IV) form 27–29 ∘C𝛽 (V) form 33–35 ∘C𝛽 (VI) form 36–37 ∘CHeat of melting, mean value [𝛽 (IV) form] 150.68 kJ/kg

Specific heat capacity, solid and liquid 2.093 kJ/kg

Density in liquid state at 30 ∘C 901 kg/m3

Table A1.27 Dynamic viscosity (Pa s) of cocoa butter as a function

of temperature (∘C).

t (∘C) 𝜼 (Pa s) t (∘C) 𝜼 (Pa s) t (∘C) 𝜼 (Pa s)

35 0.0520 50 0.0278 65 0.0192

40 0.0383 55 0.0249 70 0.0158

45 0.0349 60 0.0206 75 0.0154

Source: Data from Sokolovsky (1959).

For further details, see Fincke (1965).

See Table A1.26.

For further details, see Fincke (1965).

See Tables A1.27–A1.29.

According to Danilova (1961), the data for honey can be calculated in the tem-

perature interval 5–35 ∘C as follows:

𝜌 = 1442 − 0.4t (kg∕m3)

𝜆 = 1.163(0.29 + 0.00075t) (W∕m K)

cP = 4186.8(0.54 + 0.0035t) (W s∕kgK)

a × 108 = 2.7778(4.3 − 0.033t) (m2∕s)

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Table A1.28 Variation of the dynamic viscosity (Pa s) of chocolate as a function of the conching

time.

Conching time (h)

0 0.5 1 2 3 4 5 24 48 72 96

Chocolate,

t=50–60 ∘C80 — 45 37.5 35 33.5 23 — — —

Sport, t=32 ∘C 35 — 15 12 12 12 — — 11 11 —

Prima, t=32 ∘C 25.5 — 15.5 14.5 — 14 — 12 11 — —

Extra, t=32 ∘C 30.5 27 25 21 — 18.5 15 11.4 11 — 11

Chocolate,

t=32 ∘C7.6 — — — — — — 5.00 4.65 5.3 —

(Water content %) 1.19 — — — — — — 0.96 — 0.91 —

Source: Data from Antokolskaja (1964).

Table A1.29 Thermophysical characteristics of some raw materials used in the confectionery

industry.

Material t (∘C) 𝝆 (kg/m3) 𝝀 (W/(m K)) cP (W s/kg K) a×106 (m2/s)

Cocoa beans 20 560 0.105 2260.9 0.0819

50 0.099 2260.9 0.0777

70 0.093 2260.9 0.0763

110 0.093 2260.9 0.0750

Citric acid 15 1542 0.179 1394.2 0.1436

30 — 0.177 1381.6 0.1430

50 0.174 1873.3 0.1411

Melange −10 952 0.209 4438 0.3249

5 — 0.456 3810 0.1167

15 1015 0.463 3747.2 0.1222

25 1010 0.467 3642.5 0.1277

Honey −5 1010 0.654 1821.3 0.1250

15 1435 0.349 2306.9 0.1055

20 1345 — 2428.3 0.1055

35 1345 0.370 2993.6 0.0867

Source: Data from Danilova (1961).

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Table A1.30 Thermophysical properties of sweets and chocolate.

Product 𝝆 (kg/m3) 𝝀 (W/m K) c (W s/kg K) a×106 (m2/s)

Pralines with

fruit juicea

0.1−7.4× 10−4(t−40)

Wafer — 1.163(0.046+0.0015t) 4186.8(0.35+0.00033t) 2.7778(7.7−0.28t)

Zwieback — — 4186.8(0.572−0.0007t) 2.7778(3.35+0.0047t)

Sport cake — 1.163(0.098+0.0001t) 4186.8(0.575−0.0022t) 2.7778(2.8+0.121t)

Chocolate 1315 1.163(0.2+0.0007t) 1591−1675 2.7778(4+0.017t)

t= temperature in ∘C.

Latent heat of melting: 124.604 kW s/kg (Danilova, 1961).aAntokolskaja (1964).

Table A1.31 Hardness of various chocolate brands.

Brand Hardness (N/m2)

Prima 5981

Goldetikett 5680

Sport 3130

Vanillin 3230

Extra 3430

Cream 1860

Soy 1270

Source: Data from Sokolovsky (1959).

For further details, see Kältetechnik (1960).

See Table A1.30.

For chocolate mass, the following relationships were given by Rapoport and

Tarchova (1939) for the temperature range 30–70 ∘C:

𝜌 (kg∕m3) = 1320 − 0.5t

𝜆 (W∕m K) = 1.163(0.2 + 0.0007t)

c (W s∕kgK) = 1674.7(= 0.4kcal∕kg ∘C)

a × 108 (m2∕s) = 2.7778(4 + 0.017t)

where t (∘C) is the temperature.

For the viscosity of chocolate, see Section 4.9.1 and Appendix 3.

See Tables A1.31–A1.35.

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Table A1.32 Thermophysical properties of sweets.

Product t (∘C) 𝝆 (kg/m3) 𝝀 (W/m K) c (W s/kg K) a×106 (m2/s)

Wafer 30 — 0.106 — 0.1900

Zwieback 15 — 0.123 2365.5 0.0944

25 — 0.123 2302.7 0.0967

30 — 0.124 2302.7 0.0972

Filled drops 5 1370 0.436 2080.8 0.1528

30 — 0.436 2281.8 0.1394

45 — 0.436 2453.5 0.1297

Romaschka (drops) 1224 0.283 1704 0.1353

Jelly (marmalade) 25 1411 0.384 2951.9 0.0922

50 — 0.372 2834.5 0.0944

85 — 0.360 2784.2 0.0950

Marzipan 14 1360 0.372 1808.7 0.1514

25 — 0.366 1800.3 0.1500

35 — 0.359 1779.4 0.1486

Pralines — 1204 0.250 1410.9 0.1475

Pralines with fruit juice filling 25 940 0.212 2101.8 0.1075

50 — 0.215 2491.2 0.0919

85 — 0.222 3328.5 0.0708

Lakton — 519 0.099 1724.9 0.0867

Cream 25 642 0.116 2181.3 0.0830

45 — 0.120 1997.1 —

65 — 0.122 1687.3 —

85 — 0.124 1624.5 —

Cake 25 705 0.128 2177.1 0.0833

Unsere Marke 45 — 0.128 1967.8 0.0917

Sport 25 — 0.116 2177.1 0.0830

45 — 0.120 1997.1 0.0933

65 — 0.122 1687.3 0.1128

85 — 0.124 1624.5 0.1219

Cocoa powder 0 — 0.062 1226.7 0.1067

10 — 0.063 1377.5 0.0967

15 1475 0.064 1557.5 0.0864

20 — 0.064 1988.7 0.0680

27 — 0.065 1821.3 0.0753

35 — 0.066 1423.5 0.0983

40 — 0.066 1285.3 0.1094

Honey cake 15 538 0.080 1791.9 0.0833

22 — 0.081 1771.0 0.0855

30 — 0.085 1825.4 0.0864

Honey cake Minze 520 0.099 1984.5 0.0928

Sachsen — 648 0.087 1930.1 0.0808

Halawa 0 950 0.196 1976.2 0.1047

26 — 0.206 2265.1 0.0958

40 — 0.200 2265.1 0.0930

60 — 0.213 2499.5 0.0894

(continued overleaf )

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Data on Engineering Properties 635

Table A1.32 (continued)

Product t (∘C) 𝝆 (kg/m3) 𝝀 (W/m K) c (W s/kg K) a×106 (m2/s)

Chocolate gold 10 1270 0.244 1674.7 0.1139

anchor 30 1260 0.256 1674.7 0.1122

50 1250 0.267 1674.7 0.1278

70 1240 0.267 1591.0 0.1361

Soy beans 18 1150 0.219 2344.6 0.0980

35 — 0.209 1992.9 0.0911

Sport 15 — — 1381.6 —

Extra (milk) 15 — — 1967.8 —

For cocoa powder, 𝜌=857–1475 (kg/m3).

Source: Data from Danilova (1961).

Table A1.33 Density of sugar confectionery products.

Product Density (kg/m3)

Bon-Bon drops with chocolate–hazelnut filling (35%) 1350–1355

Drops with berry filling 1430–1435

Drops 1220–1225

Fruit jelly bonbon 1359

Source: Data from Antokolskaja (1964).

For hard-boiled sugar mass, in the temperature range 15–85 ∘C,

𝜆 = 1.163(0.265 + 0.0005t) (W∕mK)

cP = 4186.8(0.43 + 0.0025t) (W s∕kgK)

a × 108 = 2.778(4.55 − 0.02lt) (m2∕s)

On the basis of the figures published by Antokolskaja (1964), the following

approximate formulae can be used in the temperature range 0–80 ∘C.

For fondant mass,

𝜆 = 0.43 + (t − 10)8.3 × 10−4 (W∕mK)

cP = 1778 + 15.7(t − 10) (W s∕kgK)

For fondant filling,

a × 106 = 0.16 − 0.001(t − 20) (m2∕s)

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Table A1.34 Dynamic viscosity (Pa s) of various fondant masses as a function of

temperature (∘C).

Temperature (∘C) Viscosity (Pa s)

Fondant mass for Riviera (water content 10.5%; invert sugar 6.3%)

70 5.2

68 5.4

67 6.0

66 8.0

65 8.6

62 10.4

60 11.6

Fondant mass for Happy Childhood (water content 10.5%; invert sugar 5.8%)

79 16.0

77 20.0

75 23.0

74 36.0

72 44.0

Fondant mass for Shio-Shio-San (water content 9.0%; invert sugar 6.0%)

80 8.0–9.0

79 13.0

77 18.4

76 21.6

75 25.2

74 32.0

70 50.0

Toffee mass for Kis-Kis (water content 17%)

60 2.48

70 1.15

80 0.67

90 0.36

100 0.26

Toffee mass for Kis-Kis (water content 9%)

60 559.3

80 116.6

85 64.4

90 43.0

100 33.7

Toffee mass for Kis-Kis (water content 8%)

70 487.8

85 122.8

90 43.0

Toffee mass for Gold Key (water content 19%)

60 3.91

70 2.18

80 1.13

90 0.62

100 0.38

Source: Data from Antokolskaja (1964).

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Data on Engineering Properties 637

Table A1.35 Thermophysical properties of semi-products used for cakes.

t (∘C) 𝝆 (kg/m3) 𝝀 (W/m K) c (W s/kg K) a×106 (m2/s)

Toffee

25 1400 0.291 2239.9 0.0928

40 — 0.291 2260.9 0.0919

60 — 0.291 2281.8 0.0911

85 — 0.291 2311.1 0.0900

Hard-boiled sugar mass

Water content 2%

20 1600 0.314 1381.6 0.1444

40 1570 0.291 1465.4 0.1278

60 1540 0.267 1832.8 0.1055

80 1500 0.256 1718.6 0.1000

Water content 3–5%

20 1550 0.314 1716.8 0.1187

40 1520 0.302 1758.5 0.1111

60 1490 0.291 1842.2 0.1055

80 1460 0.279 1884.1 0.1000

Fondant

20–60 1392 0.373 1737.5 0.1542

With nuts 1005 0.173 1490.5 0.1058

20 1397 0.352 1632.8 0.1480

With cream 1397 0.327 1511.4 0.1564

Source: Data from Antokolskaja (1964).

For hard-boiled sugar mass,

cP = 1100 + 6.67(t − 10) (Ws∕kgK)

a × 106 = 0.1 − 6.67 × 10−4(t − 50) (m2∕s)

See Tables A1.36–A1.38.

For Zwieback dough,

𝜆 = 1.163(0.275 + 0.005t) (W∕mK)

cP = 4186.8(0.62 + 0.0012t) (W s∕kgK)

According to Danilova (1961), for short dough (sheeted),

𝜆 = 1.163(0.28 + 0.00014t) (W∕mK)

cP = 4186.8(0.58 − 0.0013t) (W s∕kgK)

a × 108 = 2.778(3.65 + 0.0143t) (m2∕s)

See Tables A1.39–A1.46.

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Table A1.36 Dynamic viscosity (Pa s) of hard-boiled sugar masses with different molasses

contents as a function of temperature (∘C).

Water (%) Temperature (∘C) Dynamic viscosity (Pa s) Molasses (%)

1.91 135 18.4 15

125 31.0

115 79.7

105 240

95 950

90 2 020

85 4 680

80 11 800

75 31 700

1.84 135 — 25

125 37.2

115 95.8

105 325

95 1 400

90 3 030

85 7 320

80 17 400

2.48 135 — 25

125 —

115 55.0

105 154.7

95 690.0

90 1 562.3

85 4 470

80 12 100

75 39 900

2.3 135 — 35

125 —

115 100.3

105 382

95 2 000

90 4 820

85 11 500

80 30 060

75 95 600

2.7 135 — 50

125 —

115 110

105 390

95 2 400

90 5 000

85 11 700

80 35 000

Source: Nachschlagewerk des Konditors (1958) and Sokolovsky (1958).

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Data on Engineering Properties 639

Table A1.37 Density and dynamic viscosity of biscuit dough

as a function of temperature.

t (∘C) 𝝆 (kg/m3) 𝜼 (Pa s)

Kneading under pressure (water content 38%)

18 880 11.5

19 880 9.5

20 880 7.9

Kneading at atmospheric pressure (water content 37%)

20 1034 7.4

21 1034 6.5

22 1032 5.9

23 1032 5.5

24 1027 4.9

25 1027 4.3

26 1024 4.0

Source: Data from Antokolskaja (1964).

Table A1.38 Density and thermophysical properties of wafer batter and of biscuit and cracker

doughs.

t (∘C) 𝝆 (kg/m3) 𝝀 (W/m K) cP (W s/kg K) a×106 (m2/s)

Wafer batter

15 — 0.477 3621.6 0.1205

25 — 0.477 3600.6 0.1250

40 — 0.483 3600.6 0.1267

60 1100 0.483 3558.8 0.1244

85 — 0.488 3600.6 —

Zwieback dough

15 1165 0.331 2625.1 0.1083

22 — 0.338 2713.1 0.1069

40 — 0.348 2847.0 0.1047

Semi-sweet biscuit dough

20 — 0.401 2909.8 0.1036

26 1222–1330 0.409 29515.9 0.1039

36 — 0.420 2997.7 0.1050

Cracker dough (laminated)

15 1295 0.326 2352.9 0.1069

22 — 0.328 2323.7 0.1092

30 — 0.329 2260.9 0.1125

40 — 0.335 2219.0 0.1167

Sweet biscuit dough

15 1280 0.338 2491.1 0.1061

22 — 0.340 2512.1 0.1056

30 — 0.338 2533.0 0.1044

Hard-sweet biscuit dough

15 1330 0.385 2658.8 0.1083

24 — 0.407 2888.9 0.1055

30 — 0.430 3181.9 0.1014

Source: Data from Antokolskaja (1964).

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Table A1.39 Dynamic viscosity of sweet biscuit dough

as a function of time of kneading.

Time ofkneading (min) 𝜼 (MPa s)

10 0.38

20 0.36

30 0.26

40 0.17

60 0.60

80 0.69

90 1.1

Source: Data from Antokolskaja (1964).

Table A1.40 Viscosity (MPa s) of the cracker dough for Krokett and the sweet biscuit dough for

Sachar as a function of the amount of gluten of different qualities.

Viscosity (MPa s)

Elasticity ofgluten

Amount ofgluten (%)

Cracker dough(39 ∘C) (water

content 24–25%)

Sweet biscuit dough(25–26 ∘C) (watercontent 17–19%)

Weak 17 0.86 1.00

20 0.95 2.0

33 1.00 2.60

Medium 19 0.36 0.10

22 0.70 0.80

32 0.96 0.85

Strong 19 0.30 0.80

22 0.25 0.70

24 0.25 0.65

34 0.25 0.60

Source: Data from Antokolskaja (1964).

Table A1.41 Dynamic viscosity of honey-cake dough

(water content 20%) as a function of time of

kneading at 30 ∘C.

Time of kneading (min) Viscosity (MPa s)

15 0.25

30 0.26

45 0.30

60 0.29

Source: Data from Antokolskaja (1964).

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Data on Engineering Properties 641

Table A1.42 Dynamic viscosity of honey-cake dough as a

function of temperature.

Temperature (∘C) Viscosity (MPa s)

20 0.55–0.93

30 0.27

40 0.26

Source: Data from Antokolskaja (1964).

Table A1.43 Dynamic viscosity of honey-cake dough as a

function of water content.

Brand name Water content (%) Viscosity (MPa s)

Moskauer Batoni 20.0 0.40

20.8 0.25

21.0 0.18

22.6 0.16

23.0 0.14

Honey 21.0 0.30

23.0 0.20

Source: Data from Antokolskaja (1964).

Table A1.44 Density and dynamic viscosity of wafer batter as a function of

water content at 20 ∘C (two types, with different elasticity values of gluten).

Water content (%) Density (kg/m3) Viscosity (Pa s)

Gluten content of flour 27%

60.0 1136–1140 4.2–4.6

62.0 1154 1.1–1.2

64.0 1142–1144 1.15–1.20

65.0 1133–1137 0.83–0.84

Gluten content of flour 32%

60.6 — 12.4

62.0 — 9.5

64.0 — 3.3

65.0 — 2.3

66.0 — 1.1

Source: Data from Antokolskaja (1964).

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642 Confectionery and chocolate engineering: principles and applications

Table A1.45 Dynamic viscosity of wafer batter (water

content 62.3–62.6%) as a function of temperature.

Temperature (∘C) Viscosity (Pa s)

15 1.80

20 1.51

25 1.40

30 1.08

Source: Data from Antokolskaja (1964).

Table A1.46 Thermal conductivity of raw materials.

Raw material Water content (m/m%) 𝝀 (cal/g ∘C)

Wheat flour Dry content 0.340

13.0 0.426

13.5 0.429

14.0 0.432

14.5 0.436

15.0 0.439

15.5 0.442

Crystalline sugar 0.1–0.2 0.301

Sugar powder 0.5 0.308

Maize starch 13.0 0.423

Cow’s milk 87.5 0.940

Condensed milk 30.0 0.630

Sodium carbonate 1.0 0.539

Salt 2.0 0.220

Ammonium carbonate — 0.610

Butter 14.2 0.688

13.6 0.574

13.5 0.557

Butter, fried margarine 0.1 0.521

15.0 0.500

Honey 18.0 0.450

Starch syrup 20.0 0.700

Invert syrup 33.5 0.600

Egg 74.0 0.760

Crystalline vanillin 0.5–1.0 0.310

Flavourings — 0.540

Source: Data from Nachschlagewerk des Konditors (1958).

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APPENDIX 2

Comparison of Brix and Bauméconcentrations of aqueous sucrosesolutions at 20 ∘C (68 ∘F)

Degrees Brix Degrees Baumé

5 2.8

10 5.6

15 8.3

20 11.1

25 13.8

30 16.6

35 19.3

40 22

45 24.6

50 27.5

55 30.2

60 32.5

65 35

70 37.6

75 40.3

80 42.5

85 44.9

90 47.4

95 49.5

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644 Confectionery and chocolate engineering: principles and applications

Comment: Linear interpolation provides fair results:

Degrees Brix Degrees Baumé Interpolated values

10 5.57

15 8.34

12.5 6.96 6.955

60 32.49

65 35.04

62.5 33.77 33.765

80 42.47

85 44.86

82.5 43.67 43.665

For a detailed scale (per 0.5 ∘Bx), see Meiners et al. (1984, Vol. 1/I, p. 11).

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APPENDIX 3

Survey of fluid models: some trendsin rheology

A3.1 Decomposition method for calculation of flowrate of rheological models

A3.1.1 The principle of the decomposition methodReher et al. (1969) gave the formulae of the volume velocity of various rheolog-ical fluids which are studied here later. The expressions of flow rate are mainly

rather complicate; thus it is difficult to recognize the essential physical relations

and to use those. The principle of the method is that the expressing of flow rate

Q is decomposed into two factors, namely, K and M:

Q (m3∕s) = K × M (A3.1)

where K (m3/s)=R4𝜋Δp/(8L𝜂¤) is the flow rate of an ideal Newton fluid of

viscosity 𝜂¤ that contains Δp proportionally and M is a dimensionless number that

contains Δp but not proportionally, R is the radius of the cylindrical tube, L is

the length of the tube, 𝜂¤ is the apparent dynamic viscosity of the fluid and

Δp is the pressure difference (PD) between two ends of the tube. M (0≤M≤1)

can be regarded as the degree of efficiency relative to the flow rate of an ideal

Newtonian fluid:

M = Qnon-Newtonian∕Qideal Newtonian (A3.2)

In the case of fluids of plastic nature, there is a yield stress 𝜏0 which is the value

of the shear stress corresponding to D=0 (where the shear stress is 𝜏 =RΔp/2L).

Therefore, the flow of plastic fluids may be characterized by a dimensionless

number, now designated by Bu as Buckingham number: Bu= 𝜏0/𝜏. For plastic

fluids, M is a function of Bu. Taking into account that 𝜏 =RΔp/2L, Eqn (A3.1) is

modified in this case to

Q = R3𝜋𝜏0∕(4𝜂¤)(1∕Bu) × M = R3𝜋𝜏0∕(4𝜂¤) × F (A3.3)

where F= (1/Bu)×M (Bu> 0).

Both M and F can be tabulated in function of Bu= 𝜏0/𝜏 = 2L𝜏0/(RΔp) enabling

one to solve the following problems (where 𝜏0 is known in both cases):

(a) Δp is known and Q is to be calculated; M is used.

(b) Q is fixed and Δp is to be calculated; F is used.

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646 Confectionery and chocolate engineering: principles and applications

Since in the case of non-Newtonian fluids Q and Δp are not proportional, the

decomposition method decomposes Q into a factor K containing Δp proportion-

ally and a factor M(Bu) containing Δp not proportionally and tabulates the values

of M (and F) as a function of Bu. As a result, by calculating the value of Bu, all the

usual calculations can be done; the other parameters (R, L, 𝜂¤) are proportional

to Q.

In certain fluid models, the role of Bu in M is replaced by similar parameters,

which are always dimensionless.

A3.1.2 Bingham modelThe decomposition method can be presented by the simplest example related to

the Bingham fluids described by the equation

𝜏 = 𝜂PlD + 𝜏0𝜏 = 𝜂PlD + 𝜏0 (A3.4)

where 𝜏 is the shear stress, 𝜂Pl is the plastic viscosity, D is the shear rate and 𝜏0

is the yield stress (for further details on yield stress, see Section 4.4.2.4). In the

case of the generalized Bingham model, the plastic viscosity 𝜂Pl is dependent on

the shear rate D or the shear stress 𝜏.

From the Buckingham–Reiner equation (where Bu≡ 𝜏0/𝜏R is the Bucking-

ham number), the following equation can be obtained with some algebraic

manipulation:

Q = [R4𝜋Δp∕(8L𝜂Pl)](1 − (4∕3)Bu + (1∕3)Bu4) (A3.5)

Consequently, we can write

Q = K × M

where

K = R4𝜋Δp∕(8L𝜂Pl) (the Newtonian part) (A3.6)

and

M(Bu) = 1 − (4∕3)Bu + (1∕3)Bu4 (A3.7)

which is a dimensionless number.

M and F=M/Bu can be tabulated as functions of Bu (Table A3.1).

If Bu= 1 (i.e. no flow), then M(Bu)= 0, which shows that M functions as a

degree of efficiency. As mentioned in Section 12.3, Lapitov and Filatov (1963)

performed such a decomposition of the Buckingham–Reiner equation in practice.

(In the following calculations, SI units are used exclusively.)

Example A3.1Suppose 𝜏0 =0.5 Pa, 𝜂Pl = 3 Pa s, R= 2×10−2 m, L= 10 m and Δp=2× 105 Pa.

Then 𝜏R =RΔp/(2L)= 2×102 Pa and Bu= 𝜏0/𝜏R = 0.0025.

From Table A3.1: M(Bingham)= 0.996667.

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Survey of fluid models: some trends in rheology 647

Table A3.1 The M and F factors of Bingham model.

Bu M (Bingham) F (Bingham)

0.1 0.8667 8.667

0.2 0.733867 3.669333

0.3 0.6027 2.009

0.4 0.4752 1.188

0.5 0.354167 0.708333

0.6 0.2432 0.405333

0.7 0.1467 0.209571

0.8 0.069867 0.087333

0.9 0.0187 0.020778

0.0025 0.996667 398.6667

0.003 0.996 332

0.0035 0.995333 284.381

0.004 0.994667 248.6667

0.002 0.997333 498.6667

0.0021 0.9972 474.8571

On the basis of the data in Table A3.1: K≈ 0.4186×10−3 m3/s and

Q ≈ 0.996667 × 0.4186 × 10−3 m3∕s ≈ 0.427 × 10−3 m3∕s

Example A3.2Also the inverse task can be solved by using this method.

We want to raise the flow rate up to Q=0.5× 10−3 m3/s while all the

other parameters remaining unchanged. The increased value of Δp is to be

calculated:

Q = 0.5 × 10−3 = [R3𝜋𝜏0∕(4𝜂Pl)] × F(Bingham)

= (3.14∕2) × (2 × 10−6) × F(Bingham)

From this equation, F(Bingham)≈ 477.7.The correspondent Bu number (see

Table A3.1) is cc. Bu= 0.0021= 0.5/𝜏R, and 𝜏R =238 Pa=RΔp/(2L)=2× 10−2

Δp/20 and Δp=2.38×105 Pa.

A3.1.3 Casson modelsA3.1.3.1 Casson model (n= 1/2)The usual form of flow curve is

√𝜏 =

√𝜏0,CA +

√𝜂CA

√(𝜕w∕𝜕r) (A3.8)

where 𝜏 is the shear stress (Pa=N/m2), 𝜏0,CA is the Casson yield stress (Pa), 𝜂CA

is the Casson (dynamic) viscosity (Pa s) and 𝜕w/𝜕r is the shear rate (s−1).

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648 Confectionery and chocolate engineering: principles and applications

The (decomposed) flow rate is

Q = (Δp𝜋R4∕8L𝜂CA)(1–16∕7 Ca + 4∕3 Ca2–1∕21 Ca8) (A3.9)

where Ca=√𝜏0,CA/

√𝜏R =

√r0/

√R (=

√Bu) is the Casson number,(The Casson

number Ca is not to be confused with the Cauchy number, also denoted by Ca.)

M(Ca) = (1 – 16∕7 Ca + 4∕3 Ca2– 1∕21 Ca8) . (A3.10)

A3.1.3.2 Generalized Casson model (0<n<1)Taking into account that the flow curve of Casson typed fluids is

𝜏n = K0 + K1Dn. (A3.11)

The flow rate Q=Q(Δp) can be calculated from the integral (Rabinowitsch–

Mooney equation):

Q = 𝜋R3∕𝜏3R∫

𝜏R

𝜏0

D𝜏2 d𝜏 (A3.12)

where 𝜏 = rΔp/2L, R is the radius of the tube (r is used as a variant), L is the length

of the tube, 𝜏0 = r0Δp/2L is the yield stress, Δp is the pressure difference between

the two ends of the tube, K0 = (𝜏0)1/n is a constant, K1 = (𝜂n)1/n is a constant and

𝜂n is the dynamic viscosity of a generalized Casson fluid with exponent n.

From the flow curve (A3.11), we obtain

D = (1∕𝜂)(𝜏n − 𝜏0n)1∕n (A3.13a)

However, this expression does not make possible a direct integration of the

Rabinowitsch–Mooney equation (A3.12). If the expression for D is changed into

the form

D = (1∕𝜂)𝜏[1 − (𝜏0∕𝜏)n]1∕n, (A3.13b)

then Newton’s generalized binomial theorem can be applied (Taylor and Zafi-

ratos, 1991, p. 524; Filep, 1997) which results in an infinite power series:

(1 − xn)1∕n = 1 +k∑

1

(1∕k!)(1∕n − 1)(1∕n − 2) · · · (1∕n − [k − 1])(−x)n (A3.14)

where 0≤ x≤ 1. If 1/n= 1, in finite power series resulted (i.e. in the case of Bing-

ham fluid). Moreover, if 1/n is not an integer, the power series is infinite but

convergent also in these cases.

Neglecting the details, the result of integration for any value of n is

Q = 𝜋ΔpR4∕(8𝜂nL) × M (A3.15)

where K1 = (𝜂n)1/n is a constant and 𝜂n is the dynamic viscosity of a generalized

Casson fluid with exponent n. For specific values of n, we have the following

results:

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Survey of fluid models: some trends in rheology 649

Table A3.2 The values of M in case of four types of generalized Casson model (n=1; 4/5; 2/3;

1/2) in function of Buckingham numbers.

Bu Bingham n=4/5 n=2/3(Heinz) n=1/2 (Casson)

0.01 0.986667 0.9609 0.91778779 0.784761904

0.02 0.973333 0.932112 0.87059359 0.703417845

0.03 0.96 0.906331 0.83164581 0.644102634

0.04 0.946668 0.882359 0.79737306 0.596190354

0.05 0.933335 0.859668 0.76628203 0.555565117

0.06 0.920004 0.837962 0.73756517 0.520116013

0.07 0.906675 0.817052 0.71072242 0.488589033

0.08 0.893347 0.796808 0.68541649 0.460167088

0.09 0.880022 0.777136 0.6614061 0.43428259

0.1 0.8667 0.757963 0.63851092 0.410522249

0.2 0.733867 0.585081 0.45008597 0.244387972

0.3 0.6027 0.433738 0.30600754 0.147677011

0.4 0.4752 0.296128 0.18956824 0.086501641

0.5 0.354167 0.169214 0.09534568 0.047446405

0.6 0.2432 0.051818 0.02236004 0.023321899

0.7 0.1467 −0.05622 −0.0278088 0.009534225

0.8 0.069867 −0.15439 −0.0517485 0.002756897

0.9 0.0187 −0.24165 −0.0445527 0.000338176

M(Bu) M(4/5) M(2/3) M(Ca)

Bingham model, n= 1 (for the sake of completeness; see Eqn A3.5):

M = 1 − (4∕3)Bu + (1∕3)Bu4 (A3.16a)

Casson model, n= 1/2:

M = (1–16∕7Ca + 4∕3 Ca2–1∕21 Ca8); Ca2 = Bu (A3.16b)

Casson-type (or Heinz) model, n= 2/3:

M = [1 –(9∕5)Bu2∕3 + (9∕16)Bu4∕3–(1∕4)Bu3 + (9∕128)Bu8∕3

+ (267∕640)Bu4 + · · ·] (A3.16c)

Casson-type model, n= 4/5:

M = [1–(25∕16)Bu4∕5 + (25∕105)Bu8∕5–(25∕256)Bu12∕5

+ (11345∕107520)Bu4 + · · ·] (A3.16d)

Table A3.2 shows the values of M belonged to different models.

It can be observed that if Bu>0.5, the power series for n=4/5 and 2/3 is not

useful in practice as an approximation, because the convergence will be very

slow. Additional terms would be required for a more exact approximation.

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650 Confectionery and chocolate engineering: principles and applications

It can be observed, moreover, that higher values of n are associated with higher

values of Q and that the effectiveness of Casson fluids (n= 1/2) is very poor! Con-

sequently, the increase in the exponent n may be of great practical importance.

It can be proved that (see the 1st edition of this book) the higher the exponent

n in the flow curve of a generalized Casson fluid, the higher its flow rate. The

numerical example presented in Table A3.2, l demonstrates this result.

The rheological properties of human blood can be modelled as Casson fluid,

with n=1/2 (see, e.g. Charm and Kurland, 1965 or Lee et al., 2007). We ask

whether any method (e.g. consumption of lecithin) exists to increase the expo-

nent n=1/2 in order to improve the flow of blood, that is, to increase the flow

rate of blood in the arteries.

The search for an analytical method for determination of the exponent n has not

been successful; therefore an iteration method can be recommended. The cru-

cial question is the value of n, because if it is known, then K0 and K1 can be

determined by linearization.

In order to choose the appropriate value of n for iteration, the following has to

be taken into consideration: if the flow curve 𝜏 = 𝜏(D) is concave, then the rela-

tion n< 1 holds; however, if the flow curve is convex, then n> 1. The reasonable

process of iteration is (𝜏1 vs D1), (𝜏0.5 vs D0.5), (𝜏0.75 vs D0.75), (𝜏0.875 vs D0.875)

and so on. The basis of decision is to minimize the value of standard deviation

(SD) related to the linear model.

A3.1.3.3 Theoretical background of the Casson and the Bingham modelsCasson (1959) developed a theoretical model that is based on the supposition that

in suspensions, the particles form rod-like agglomerates. These rods are cylindri-

cal, their half-length is L and the cross-sectional radius is r, and the value of

J= L/r is a function of shear rate. Starting from this theoretical model, Casson

derived a linear relationship between J and y= (𝜂0D)−1/2 if J≫ 1:

J = 𝛼 + 𝛽y = 𝛼 + 𝛽(𝜂0D)−1∕2 (A3.17)

where 𝜂0 is the dynamic viscosity of the dispersion media, D is the shear rate

and 𝛼 and 𝛽 are constants. Moreover, if a is a constant relating to the spatial

orientation of the rods and c is the concentration of the dispersed particles, using

the notations A= (a𝛼 − 1) and B= (1/D)1/2a𝛽, the Casson model has the form

𝜏1∕2 = [𝜂0(1–c)−A]1∕2D1∕2 + (B∕A)[(1–c)−A∕2 − 1] (A3.18)

which is the usual form of the Casson equation:

𝜏1∕2 = K1D1∕2 + K0 (A3.8)

where K1 = 𝜂2CA (𝜂CA is the so-called Casson viscosity) and K0 = 𝜏2

0.CA (𝜏0,CA is

the so-called Casson yield stress) are constants.

According to the studies of Mohos (1966a), a general equation

𝜏n = K1Dn + K0 (A3.11)

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Survey of fluid models: some trends in rheology 651

can be applied to describe the rheological properties of milk chocolate, where

1/2≤ n≤1. However in some cases where the milk proteins have been strongly

denatured owing to the effect of increased temperature (>60 ∘C) during conching

or transportation, n>1.

Mohos (1967b) demonstrated that Eqn (A3.11) can be derived from the

assumption

J = 𝛼 + 𝛽y = 𝛼 + 𝛽(𝜂0D)−n. (A3.19)

The generalization of the Casson model by Equation (A3.19) gives a theoretical

foundation for the Bingham model as well if n= 1, that is, the Bingham model can

be regarded as a special case of the Casson model, the plastic viscosity of which

is given by the equation

𝜂Pl = 𝜂0(1–c)−A (A3.20)

where A= (a𝛼 − 1)> 1 (see earlier text).

The expression shows that the plastic viscosity in this form is independent of

the shear rate, but it is dependent on the concentration c of the dispersed particles

and proportional to the viscosity 𝜂0 of the disperse medium. The similarity of Eqn

(A3.20) and Eqn (4.193) of Habbard is rather evident.

A3.1.4 Herschel–Bulkley–Porst–Markowitsch–Houwink (HBPMH)(or generalized Ostwald–de Waele) model

The Herschel–Bulkley–Porst–Markowitsch–Houwink (HBPMH) model is a power

law which takes into account a yield stress 𝜏0:

𝜏 = 𝜏0 + kDn. (A3.21)

For determination of the constants 𝜏0, k and n, a simple algebraic manipulation

is needed:

𝜏2 − 𝜏1 = k(D2)n − k(D1)n = k(D1)n[(D2∕D1)n − 1]

𝜏3 − 𝜏2 = k(D3)n − k(D2)n = k(D2)n[(D3∕D2)n − 1]

where the values of D are chosen in the way that it holds

D2/D1 =D3/D2 (e.g. 2; 3; 4.5 [s−1]).

Then

(𝜏3 − 𝜏2)∕(𝜏2 − 𝜏1) = (D2∕D1)n (A3.22a)

and n can be calculated. If n is known already, then

k = (𝜏i+1 − 𝜏i)∕[(Dn)i+1–(Dn)i] (A3.22b)

𝜏0 = (𝜏–kDn) (A3.22c)

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652 Confectionery and chocolate engineering: principles and applications

Table A3.3 Calculation for applying the HBPMH model.

D 𝝉 D0.63 4.93 * D0.63 𝝉0

10 26.85037 4.265795 21.03037028 5.82

15 32.97091 5.507284 4.93 27.1509114 5.82

20 38.36586 6.601595 32.54586484

25 43.27839 7.598051 37.45839153

30 47.8378 8.52288 42.01780002

35 52.12307 9.392103 46.30307006

40 56.18684 10.2164 4.93 50.36684111

45 60.06639 11.00332 54.24638513

50 63.7893 11.75848 4.93 57.96929544 5.82

Example A3.3Since HBPMH model is often applied in the food industry, an example is given

here to demonstrate the evaluation described earlier. In Table A3.3 the values

in column 2 were calculated according to the formula 𝜏 = 5.82+4.93D0.63. The

values of D (column 1) and 𝜏 (column 2) are known, and the unknown values

(n= 0.63; k= 4.93; 𝜏0 = 5.82) are to be searched.

By using Eqn (A3.41a) for D1 = 20, D2 = 30 and D3 = 45 [s−1], we obtain

(𝜏3 − 𝜏2)∕(𝜏2 − 𝜏1) = (60.06639 − 47.8378)∕(47.8378 − 38.36586) ≈ 1.29

= (30∕20)n = 1.5n

Thus n = ln 1.29∕ ln 1.5 = 0.6296 ≈ 0.63.

Column 3 shows the values of D0.63. The values in column 4 are obtained

from the relation (𝜏 i +1 − 𝜏 i)/[(D0.63)i+1 − (D0.63)i = one of the two unknowns

(k= 4.93). For example,

(32.97091 − 26.85037)∕(5.507284 − 4.265795) = 4.93

The column 5 contains the values 4.93 * D0.63, and column 6 contains the differ-

ence (column 2− column 5)= 𝜏0 =5.82.

Calculation of Flow Rate and Decomposition

Reher et al. (1969) do not discuss this generalized case; therefore, the calcula-

tion of flow rate Q=Q(Δp) is briefly presented here due to the following integral

(Rabinowitsch–Mooney equation):

Q = 𝜋R3∕𝜏3R∫

𝜏R

𝜏0

D𝜏2 d𝜏 (A3.12)

where 𝜏 = rΔp/2L. From the flow curve Eqn (A3.21), we obtain

d𝜏 = knD(n–1) dD

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Survey of fluid models: some trends in rheology 653

and the boundaries of integration are 𝜏0 ↔D= 0 and 𝜏R ↔D. For simplicity we

write 𝜏R = 𝜏, and thus the integral that is to be done is

Q = 𝜋R3∕𝜏3R∫

𝜏R

𝜏0

D𝜏2 d𝜏 = 𝜋R3∕𝜏3

D

0D(𝜏0 + kDn)2knD(n – 1) dD (A3.23)

Using the notation: Bu= 𝜏0/𝜏 (Buckingham number), after some algebraic trans-

formation, we obtain

Q = n𝜋R3(RΔp∕2Lk)1∕n(1–Bu)[Bu2∕(n + 1) + 2Bu(1–Bu)∕(2n + 1)

+ (1–Bu)2∕(3n + 1)]. (A3.24)

The expression

M(Bu) = (1–Bu)[Bu2∕(n + 1) + 2Bu(1–Bu)∕(2n + 1) + (1–Bu)2∕(3n + 1)] (A3.25)

is a dimensionless number that may be tabulated. The decomposed flow rate is

Q = n𝜋R3(RΔp∕2Lk)1∕n × M(Bu). (A3.24a)

Obviously, if Bu=1→Q= 0, the flow does not start (see Eqn A3.25).

A3.1.5 Ostwald–de Waele model (The power law)If 𝜏0 =0 in Eqn (A3.23), the Ostwald–de Waele model is obtained for which the

flow rate can be calculated:

Q = n𝜋R3(RΔp∕2L)1∕n∕(3n + 1). (A3.26)

Equation (3.28) is a derivative of Eqn (3.26) with Bu= 0, that is, 𝜏0 = 0.

Evidently, the number n/(3n+ 1) does not need to be tabulated.

If n=1, that is, k= 𝜂, then from Eqn (A3.26),

Q = 𝜋R4RΔp∕8𝜂L

which is just the Hagen–Poiseuille equation.

The flow curve of the Oswald–de Waele model can be easily linearized by plot-

ting 𝜏 = kDn in the form ln 𝜏 = ln k+ n ln D from which the intercept= ln k and the

slope= n can be obtained.

A3.2 Calculation of the friction coefficient (𝝃) ofnon-newtonian fluids in the laminar region

The decomposition method gives the flow rate in the form

Q = K × M = [R4𝜋Δp∕(8L𝜂¤)] × M. (A3.27)

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654 Confectionery and chocolate engineering: principles and applications

In the laminar region, a modified dynamic viscosity can be defined as

𝜂M = 𝜂¤∕M (A3.28)

Using this, the friction coefficient can be expressed as

𝜉 = 64∕Re (A3.29)

where

Re = Dv𝜌∕𝜂M = Dv𝜌M∕𝜂¤ (A3.30)

where 0<M<1. Thus

𝜉 = 64𝜂¤∕(Dv𝜌M). (A3.31)

In the laminar region, which is essential in the case of non-Newtonian fluids, the

friction coefficient 𝜉 can be derived from the Hagen–Poiseuille equation for the

flow rate.

The friction coefficient is defined by the equation

Δp = 𝜉(L∕D)𝜌v2∕2 (A3.32a)

or

Δp∕L = (𝜉∕D)𝜌v2∕2 (A3.32b)

where Δp is the PD inducing the flow, 𝜉 is the friction coefficient defined by Eqn

(A3.31), L is the length of the circular tube, D is the diameter of the tube, 𝜌 is the

density of the fluid and v is the linear velocity of the fluid.

A3.3 Tensorial representation of constitutiveequations: The fading memory of viscoelasticfluids

A3.3.1 Objective derivatives and tensorial representationof constitutive equations

The tensorial representation makes possible for studying the development of flow in

space (3D) and time.

When studying the linear one-dimensional (1D) Maxwell model, we obtained an

equation in the form

(d𝛾∕dt) = (1∕G)(d𝜏∕dt) + 𝜏∕𝜇 (A3.33)

where 𝛾 is the deformation, t is the time, G is the elastic modulus and 𝜇 denotes

viscosity. We would like to transform this empirical equation into a 3D tensorial

expression (𝛾 →d; 𝜏→𝜎; the tensors are written in bold letters in the following),

and we write

2𝜇d = (𝜇∕G)(d𝛔∕dt) + 𝛔 (A3.34)

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Survey of fluid models: some trends in rheology 655

but this expression does not satisfy the objectivity principle. According to this

principle, the stress tensor does not depend on the frame in which we use it (or

its components) or, in other words, it must be invariant under any rotation.

Namely, let us consider the stress tensor when the frame of reference is rotated.

After rotation we have

𝛔′ = R 𝛔 RT (A3.35)

the image of 𝛔, where R is an orthogonal tensor. Taking the time derivative

leads to

(d𝛔′∕dt) = (dR∕dt)𝛔RT + R(d𝛔∕dt)RT + R𝛔(dRT∕dt), (A3.36)

that is, (d𝛔′/dt)≠ (d𝛔/dt) which shows that (d𝛔/dt) is not objective, not indepen-

dent of the frame of reference.

For the first time such considerations were used by Jaumann (1905) in the

fluid mechanics. Similarly Oldroyd (1950) introduced the Oldroyd (or upper

convective contravariant) derivative as follows:

M ≡ (d��∕dt) = (𝛔∕dt) − L𝛔 − LT (A3.37)

where L is the velocity gradient tensor. In this way, it is possible to provide a

proper tensorial formulation of the constitutive equation, as well as to make

an empirical law being primarily valid for small deformations consistent with large

deformations.

The invariant derivative of an a vector can be similarly given – the invariant

differentiation is carried out in the body-fixed frame:

(da∕dt) = a + La. (A3.38)

Using the upper convected derivative, Oldroyd gave the upper convected

Maxwell (UCM) model:

𝜆�� + 𝛕 = 2𝜂D (A3.39)

where 𝛕 is the extra stress if

𝛔(x, t) = 𝜎T(x, t) = −pI + 𝛕 (A3.40)

is a symmetrix vector field, u(x, t) is a solenoidal vector field satisfying

div u = 0, (A3.41)

and D[u] stands for the symmetrix part of L(x, t)≡ grad u: velocity gradient field.

Also other invariant derivatives similar to Eq (A3.37) can be defined, and with

the help of them, different forms of Maxwell model can be given: lower con-

vected (LCM), corotational (COM) or interpolated Maxwell model. For more

details, see Lodge (1964), Joseph (1990) and Ancey (2005).

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656 Confectionery and chocolate engineering: principles and applications

A3.3.2 Boltzmann’s equation for the stress in viscoelasticsolids: The fading memory of viscoelastic fluids

Boltzmann’s equation is an 1D expression in which the 𝜀(x, t) permanent elastic

response proportional to 𝛽 is not suppressed:

𝜏(x, t) = 𝛽𝜀(x, t) +∫

t

−∞m(t − 𝜏)[𝜀(x, t) − 𝜀(x, 𝜏)]d𝜏. (A3.42)

The idea of fading memory was expressed by Boltzmann as the requirement

that m is a positive monotone-decreasing function. Boltzmann’s theory is better

than Maxwell’s since Maxwell’s model allows only a single time constant, the

relaxation time in the exponential. However, it is impossible to fit the relaxation

data for stress relaxation to an exponential curve with a single constant in the

most cases. The supposition that different stressed structures in a fluid relax at

different rates leads to the concept of relaxation spectrum. For details, see Joseph

(1990, p. 567).

For the case when the deformation is a small perturbation of states of rest, a

simplified constitutive equation can be used:

𝛕 = 2𝜇D[u] + 2∫

0G(s)D[u(x, t-s)]ds (A3.43)

where u(x, t) is the velocity and D[u] is the symmetric part of the velocity gradi-

ent. These deformations depend on a Newtonian viscosity 𝜇 and a smooth relax-

ation function G(s), where G(s)> 0, G′(s)< 0, G′′(s)> 0, for 0≤ s= t− 𝜏 <∝, and 𝜏 is

the past time.

With the help of Eqn (A3.48) the static (or zero shear rate) viscosity can

be characterized. Suppose the case when shearing with one component of

velocity of u(x) is dependent on one variable x. In addition, the shear stress

𝛕(k)= 𝛕12 depends on the shear rate D= k(x)=D12; then (A3.48) reduces to

𝜏12 = (𝜇+ 𝜂)D12, where

𝜇∗ = (𝜇 + 𝜂) (A3.44a)

is the zero shear viscosity and

𝜂 =∫

0G(s)ds (A3.44b)

is the elastic viscosity.

For each steady flow of Newtonian fluids, it holds

τ = 2𝜇∗D[u]. (A3.45)

For Newtonian fluids, 𝜇* =𝜇 (Newtonian viscosity) and 𝜂 = 0. For elastic fluids,

𝜇* ≥ 𝜂. It is easy to measure the zero shear viscosity 𝜇*, but the measurement

leaves 𝜇 and 𝜂 undetermined. From the relaxation function G(t), we could find

𝜇=𝜇* − 𝜂. For details, see Joseph (1990, p. 543).

Fractional derivatives for describing the fading memory of viscoelastic fluids

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Survey of fluid models: some trends in rheology 657

Up to the beginning of the 1980s, the concept of fractional derivatives in conjunc-

tion with viscoelasticity had to be seen as a sort of curve-fitting method. Then,

Bagley and Torvik (1983) gave a physical justification for this concept.

The constitutive equations of Hooke and Newton elements may be generalized

using fractional derivatives. The resulting fractional constitutive equation

𝜎 = p(dn∕dtn)𝜀 (A3.46)

(where 𝜎 is the shear stress, 𝜀 is the shear strain, t is time and (dn/dtn) is an

n-ordered differential operator) includes p as a proportionality factor and n as

the order of derivative which is commonly taken to range between 0 and 1. If n

is 0, Eqn (A3.46) describes the behaviour of a spring where p specifies the springs’

stiffness. For n=1, Eqn (A3.46) defines the constitutive equation of a dashpot, in

which p defines the viscosity. Thus, the fractional constitutive equation (A3.46)

interpolates between the material behaviour of a spring and that of a dashpot.

The rheological element which refers to Eq (A3.46) was therefore introduced

by Koeller (1984) as a spring pot. Fractional derivatives provide the property of

the fading memory as it is known from viscoelastic media (see Schmidt and Gaul,

2002; Di Paola et al., 2012).

Mainardi and Spada (2011) discuss the creep, relaxation and viscosity prop-

erties of viscoelastic substances by using Mittag–Leffler function. For t≥ 0, the

Mittag–Leffler function decays for short times like a stretched exponential and for

large times with a negative power law. Furthermore, it turns out to be completely

monotonic in 0< t<∞ (i.e. its derivatives of successive order exhibit alternating

signs like e−t), so it can be expressed in terms of a continuous distribution of

elementary relaxation processes.

Presentation of the results of Mainardi and Spada (2011) has greatly benefited

from a recently published Fortran code for computing the Mittag–Leffler function

of complex argument (Verotta, 2010a,b) coupled with an open-source program

for manipulating and visualizing data sets (Wessel and Smith, 1998).

A3.3.3 Constitutive equations of viscoelastic fluidsOn the basis of the generalized Newtonian model and the UCM model, many

constitutive equations have been proposed during the last decades, but none of

them has been proven to be superior to others (see Larson, 1987, 1988, 1994;

Armstrong et al., 1992). A comprehensive survey is given by Peters et al. (1999)

on the constitutive equations of viscoelastic fluids/melts.

One of the mostly used models is the Giesekus model (for a detailed discussion,

see Joseph, 1990; Olsson, 1995; Kedar Mukund Deshpande, 2004). Moreover,

the following models have to be mentioned: Phan-Thien–Tanner (PTT) model,

the Marucci models, the Giesekus model, the Leonov models and the Larson

model (see Peters et al., 1999).

Khan and Larson (1987) compare the simple tensorial constitutive equations

(Giesekus, Phan-Thien and Tanner, Johnson and Segalman, White and Metzner,

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658 Confectionery and chocolate engineering: principles and applications

Larson and Acierno et al.) for polymer melts in shear and biaxial and uniaxial

extensions.

Saramito (2007) gives a historical summary of the different constitutive

equations of the elastoviscoplastic fluids and proposes an equation which

assures – contrary to the Oldroyd and the Shwedoff models – a continuous

change from a solid to a fluid behaviour of the material.

Omowunmi (2011) deals with the numerical method for modelling

time-dependent viscoelastic fluid flow and supplies a detailed discussion

on the linear elastic dumbbell kinetic theory, the FENE-dumbbell model, the

Johnson–Segalman model and the PTT model.

For modelling and simulation of dilute solution of linear flexible polymers, some

simple models are applied:

• The FENE-dumbbell model which is the most simple kinetic theory model for

a dilute solution of linear flexible polymers, consists of a Hookean dumbbell,

that is, two beads connected by a Hookean spring, suspended in an incom-

pressible Newtonian fluid. The beads represent molecular segments of sev-

eral monomers, and the spring describes the entropic effects to which the

end-to-end vector of the polymer is subject. The linear (Hookean) spring force

is realistic only for small deformations from the equilibrium (Gaussian distri-

bution) and puts no limit to the extent to which the dumbbell can be stretched

(see Herrchen and Ottinger, 1997). Advanced variations are the FENE-C and

FENE-CR models (see Chilcott and Rallison, 1988).

• Boger fluids (Boger, 1977/1978) help test linear viscoelastic theories of fluids

with a constant viscosity and a quadratic first normal-stress difference in the

limit of small shear rates. The most interesting and well-known flow phenom-

ena of Boger fluids were the huge vortex development in entry flows through

abrupt contractions (Boger, 1987) and the enhanced extrudate swell in exit

flows through circular capillary dies (Boger, 1984; Mitsoulis, 1986). Rao (2014)

supports a comprehensive survey on the rheological models of fluid foods.

For the methods of rheometry, see Schramm (1998).

A3.3.4 Application of the constitutive equations to doughrheology

Hosseinalipour et al. (2012) give a review of dough rheological models used in

numerical applications. Some further studies on the application of the constitu-

tive equations are as follows:

Bagley et al. (1988) discuss the behaviour of a hard wheat flour dough

which has been measured in lubricated uniaxial compression experiments

at different compressional rates (crosshead speeds). The scientific interest in

elongational flows is of long standing. In 1906 Trouton used uniaxial stretching

experiments to determine an elongational viscosity, which can be shown for a

Newtonian fluid to be equal to three times the viscosity measured in shear. In

examining various constitutive relations (Rasper, 1975; Petrie, 1977, 1979a, b)

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Survey of fluid models: some trends in rheology 659

and instrumental solutions (Brabender Extensograph, Chopin Alveograph and

Texture Profile Analysis studies), Bagley et al. (1988) found that the UCM model

seemed particularly convenient for an initial analysis of a constant crosshead

speed experiment on doughs. The governing differential equation assumes a

relatively simple form which is readily solved numerically and demonstrates the

relevance of this simple model to the interpretation of the results of extensional

deformation of viscoelastic doughs.

Letang et al. (1999) studied the rheological properties of doughs prepared from

an industrial soft wheat flour mixed with water using the traditional Braben-

der farinograph. These doughs are characterized using dynamic rheometrical

measurements. In parallel, an innovative microscopy study, the environmental

scanning electron microscope (ESEM), is investigated and found to be very well

suited for the observation of such doughs. A change in the slope of the curve

giving the maximum of consistency is observed at a typical water content, due

to the presence of excess free water. The main rheometrical characteristics |g*|

and tan 𝛿 are exhibited for this kind of dough. Their adequacy to differentiate

between various doughs is emphasized. Parameters such as mixing time, water

content and rest time are shown to influence both the rheometrical properties

and the microscopic structure of doughs. Changes generated by mixing are inter-

preted at the molecular level. It is shown that the study of the microstructure is

essential to compare the evolution of different doughs.

Figueros et al. (2013) studied stress relaxation and creep recovery performed

on wheat kernels versus doughs, taking into account the influence of glutenins

on rheological and quality properties. The Hernández-Estrada model built up

from linear generalized Maxwell and generalized Kelvin–Voigt models is used

for data evaluation. Stress relaxation, creep and compliance equations are given,

and the parts of the plotted curves which correspond to each additive of these

equations are presented at the same time.

Carrillo-Navas et al. (2014) studied the viscoelastic relaxation spectra of some

native starch gels with oscillatory mechanical tests for characterizing the rheo-

logical properties of starch gels. Simple phenomenological models (e.g. Maxwell

and Kelvin–Voigt) were used for describing the viscoelastic dynamics of starch

gels in the face of shear stress applications.

A3.3.5 Rheological properties at the cellular and macroscopicscale

A review is given by Verdier (2003) on the role of the rheological properties

at the cellular and macroscopic scale. At the cellular scale, the different com-

ponents of the cell are described, and comparisons with other similar systems

are made in order to state what kind of rheological properties and what consti-

tutive equations can be expected. This is based on the expertise collected over

many years, dealing with components such as polymers, suspensions, colloids

and gels. Various references are considered. The various methods available in

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660 Confectionery and chocolate engineering: principles and applications

the literature are presented, which can allow one to go from the microscopic to

the macroscopic properties of an ensemble of cells, in other words a tissue. Con-

stitutive laws are also proposed and criticized. The most difficult part of modelling

is taking into account the active part of cells, which are not just plain materials,

but are living objects.

A3.4 Computer simulations in food rheology andscience

Computational fluid dynamics (CFD) provides a qualitative (and sometimes even

quantitative) prediction of fluid flows by means of mathematical modelling (par-

tial differential equations), numerical methods (discretization and solution tech-

niques) and software tools (solvers, pre- and post-processing utilities). As a rule,

CFD does not replace the measurements completely, but the amount of exper-

imentation and the overall cost can be significantly reduced. The experiments

are expensive, slow, sequential and single purpose; however, simulations are

cheaper, faster, parallel and multipurpose. A detail discussion of CFD exceeds

the volume of this book; therefore, only some references are given later in order

to facilitate the studying CFD.

For details on the computational rheological studies of bread and dough, see

Bagley et al. (1988), Shen Kuan Ng (2007) and Hosseinalipour et al. (2012). In a

comprehensive study, Pink et al. (2013) describe computer simulation techniques

that have been, or can be, used in food science and engineering.

For showing the efficiency of CFD, Guo-Tao Liu et al. (2004) studied that the

numerical simulations of pulsating blood flow through models of stenotic and

tapered arteries have been performed to investigate the distributions of the wall

shear stress.

Commercially available CFD softwares are ANSYS CFX (http://www.ansys

.com), FLUENT (http://www.fluent.com), STAR-CD (http://www.cd-adapco

.com), FEMLAB (http://www.comsol.com) and FEATFLOW (open source) (http:

//www.featflow.de).

A3.5 Ultrasonic and photoacoustic testing

A3.5.1 Ultrasonic testingToday fat and fat crystallization are studied by methods that are time consuming,

expensive and not optimized for in-line measurements. Therefore, new methods

are being developed by Bragd et al. (2007) at SIK (Gothenburg, Sweden). Previ-

ously, a method for in-line rheometry combining the Doppler-based ultrasound

velocity profiling (UVP) technique with PD measurements, commonly known

as UVP-PD, has been developed. This in-line UVP-PD method was successfully

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Survey of fluid models: some trends in rheology 661

applied to highly concentrated and opaque fat blends. The UVP-PD method could

rheologically characterize and differentiate between different fat blends. In addi-

tion, new ultrasound-based methods have been developed for acoustic charac-

terization, for monitoring crystallization kinetics under dynamic conditions and

for determination of the solid fat content (SFC). Experimental results showed, for

example, that the SFC can be determined in-line using ultrasonics in good agree-

ment with pNMR. Ultrasound-based methods can thus be regarded as rapid and

powerful research tools as well as a feasible in-line tool for process monitoring

and quality control.

Wassell et al. (2010) measured the in-line viscosity and the solid fat profile of

fat blends by using ultrasound Doppler method.

Tittmann (2011) presents an empirical method for measuring the viscosity of

mineral oil. In a built-in pipeline application, conventional ultrasonic methods

using shear reflectance or rheological and acoustical phenomena may fail due

to attenuated shear wave propagation and an unpredictable spreading loss by

protective housings and comparable main flows. This method predicted the vis-

cosities of two types of the mineral oil with a maximum statistical uncertainty

of 8.8% and a maximum systematic error of 12.5% compared to directly mea-

sured viscosity using a glass-type viscometer. The validity of this method was

examined by comparison with the results from theoretical far-field spreading. A

similar solution can be available for measuring chocolate viscosity in pipeline.

For details on ultrasonic testing, see Berke (2002), Wu (2011) and Rienstra

and Hirschberg (2013).

A3.5.2 Photoacoustic testingLou and Xinga (2010) report on the use of photoacoustic (PA) method to mea-

sure the viscosity of viscous liquids. The theoretical and experimental study was

performed on the influence of viscosity effects on PA generation. We provide evi-

dence that the frequency spectrum of PA signal is precisely related to the viscosity.

Measurements are validated on different water–glycerol mixtures. They have

predicted and verified that the amplitude and frequency spectrum of the PA wave

is quite sensitive to liquid viscosity. The technique allows rapid, non-invasive and

in situ measurement of viscous liquids, which could be used for the viscosity mea-

surement of human blood. It is also a potential alternative method for the routine

determination of materials viscosity in chemical and food industry.

Further reading

Garrity, T.A. (2002) All the Mathematics You Missed but Need to Know for Graduate School, Cambridge

University Press.

Itskov, M. (2007) Tensor Algebra and Tensor Analysis for Engineers, Springer-Verlag, Berlin, Heidel-

berg.

Powers, J.M. (2013) Lectures on Intermediate Fluid Mechanics, University of Notre Dame, Indiana,

USA.

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662 Confectionery and chocolate engineering: principles and applications

Rohsenow, W.M., Hartnett, J.P. and Cho, Y.I. (eds) (1998) Handbook of Heat Transfer, 3rd edn,

McGraw-Hill, New York.

Shapirov, R.A. (2004) Quick Introduction to Tensor Analysis, Bashkir State University, Ufa, Russia.

Kay, D.C. (1988) Schaum’s Outline of Theory and Problems of Tensor Calculus, McGraw-Hill, New

York.

Steffe, J.F. (1996) Rheological Methods in Food Process Engineering, 2nd edn, Freeman Press, East

Lansing, MI.

Tscheuschner, H.-D. (1993) Schokolade, Süsswaren, in Rheologie der Lebensmittel (eds D. Weipert,

H.D. Tscheuschner and E. Windhab), Behr’s Verlag, Hamburg.

Tscheuschner, H.-D. (1993) Rheologische Eigenschaften von Lebensmittelsystemen, in Rheologie

der Lebensmittel (eds D. Weipert, H.D. Tscheuschner and E. Windhab), Behr’s Verlag, Hamburg.

VDI-GVC (2006) VDI-Wärmeatlas, Springer, Berlin.

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APPENDIX 4

Fractals

A4.1 Irregular forms: fractal geometry

It is well known that Mandelbrot studied the length of the coast of Britain

using maps of various scales and with compasses set to span various distances:

smaller scales gave longer results. If the compass setting was 500 km, then

the length obtained was 2600 km; if the compass setting was 17 km, then

the length obtained was 8640 km. A Portuguese encyclopaedia gave a larger

value for the length of the Portuguese/Spanish border than a Spanish one did,

since Portugal is a smaller country than Spain and the map used in Portugal

for the measurement had more detail. The study of such irregular shapes led

Mandelbrot to establish a new geometry called fractal geometry (the word fractal

refers to the Latin word fractus, meaning broken) (Mandelbrot, 1977, 1983;

Peitgen and Richter, 1986; Peitgen and Jürgens, 1990; Peitgen et al., 1991;

Schröder, 1991).

Fractals have fine structure at arbitrarily small scales and are too irregular

to be easily described in traditional Euclidean geometric language. Many such

objects can be found in nature: crystals, electrochemically deposited zinc metal

leaves (with a dendritic growth pattern), the arteries and veins of a kidney, land-

scapes, etc.

At the turn of the nineteenth and twentieth centuries, mathematicians came

up with some 10 different notions of dimensions, which are all related and are all

special forms of Mandelbrot’s fractal dimensions. Of these notions of dimensions,

the box-counting dimension has the most application in science.

Bushella et al. (2002) deal with the theoretical basis for the application of fractal

geometry to characterization of flocs and aggregates, as well as survey on the

strengths and limitations of the techniques. Among the experimental techniques

that have been commonly used are scattering (light, X-ray or neutron), settling

and imaging, and these are in detail discussed by the authors. Of the scattering

techniques available, light scattering provides the greatest potential for use as

a tool for structure characterization even though interpretation of the scattered

intensity pattern is complicated by the strong interaction of light and matter.

Light scattering potentially provides a useful tool for checking settling results.

Pabst and Gregorová (2007, pp. 44–46) deal with several experimental

methods to determine the fractal dimension, for example, small-angle X-ray

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664 Confectionery and chocolate engineering: principles and applications

scattering (SAXS), small-angle neutron scattering (SANS), adsorption tech-

niques (Pfeifer–Avnir approach, Frenkel–Halsey–Hill equation or FHH approach,

Neimark–Kiselev approach) and mercury porosimetry (based on Washburn

equation). The basis of adsorption technique is that real solids have surface

areas which are proportional to rD, where D is the fractal dimension ranging

from 2 (for perfectly flat surfaces) to 3 (for extremely rough surfaces) and r is

the particle size.

Tang and Marangoni (2006) review the study of the morphology and physi-

cal properties of fat crystal networks which are essential from the point of view

of confectionery industry. Various microscopical and rheological methods can

be used to quantify the microstructure of fats, with the ultimate aim of relating

structure to mechanical response. Even though a variety of physical models have

been proposed to explain the relationship between the mechanical properties of

fats and their microstructure, the fractal scaling model most closely describes

the experimentally observed behaviour. Methods used to determine the frac-

tal dimension of a fat crystal network such as box counting, particle counting,

Fourier transform, light scattering and oil migration are in detail explained.

However, different methods of fractal-dimension determination may provide

contrasted results as the following reference shows. Narine and Marangoni

(1999a) studied the difference between cocoa butter and Salatrim. Rheological

measurements on both fat networks yielded fractal dimensions of 2.37 for

cocoa butter and 2.90 for Salatrim®. Image analysis of the microstructure of

cocoa butter yielded a fractal dimension of 2.31; however, the microstructure

of Salatrim® does not lend itself to fractal analysis via image analysis. It was

observed that the microstructure of Salatrim® is random instead of fractal.

In the next sections some methods are briefly presented which are interesting

from the point of view of confectionery industry.

A4.2 Box-counting dimension

The structure to be studied is put onto a grid with a mesh size C, and the number

of grid boxes that contain some of the structure is counted. This gives a number,

say, N, which is dependent on C, of course. Then we plot the logarithms, and find

log N ∼ log (1∕C)D(b) (A4.1)

where D(b) is the box-counting dimension, ≤2 for a plane.

(Comment: In a plane, the box-counting dimension can never exceed 2; at the

same time, however, the self-similarity dimension can do so. The reason for

this discrepancy is that in the case of curves that have overlapping parts, the

box-counting dimension does not take these overlapping parts into account.)

Figure A4.1 shows two shapes on a grid, and Table A4.1 presents the evalua-

tion of them.

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Fractals 665

(a) (b)

Figure A4.1 (a) and (b) show two shapes on a grid for evaluation of the box-counting

dimension.

Table A4.1 Evaluation of the two shapes shown in Figure A4.1 according to Eqn

(A4.1).

N 1/C ln N ln(1/C) Slope=D(b)

Shape (a)

4 2 1.386294 0.693147 1.715562

15 4 2.70805 1.386294

50 8 3.912023 2.079442

141 16 4.94876 2.772589

Shape (b)

4 2 1.386294 0.693147 1.766623

16 4 2.772589 1.386294

54 8 3.988984 2.079442

158 16 5.062595 2.772589

A4.3 Particle-counting method

The particle-counting method was applied to determine the fractal dimension of

a structure consisting of fat crystal networks by Narine and Marangoni (1999a).

The images of fat networks that are acquired from polarized light microscopy are

not suitable for analysis by the traditional methods of fractal-dimension deter-

mination. The reason is that such images are subsets of two-dimensional (2D)

space but represent a subset of a three-dimensional (3D) network. Therefore,

the number of particles present in a 3D portion of the sample is counted by first

representing all the particles present in that portion of the sample in the plane of

the image. Those particles which do not appear in the picture owing to geomet-

rical shadowing are missed, but the number of these can be rendered negligible

by making the thickness of the sample very small.

In order to calculate the value of D (with d= 3, i.e. in space), the number of

microstructural elements N(R) projected onto a square area of side length R is

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666 Confectionery and chocolate engineering: principles and applications

counted, the square being drawn in the focal plane of the image:

N = R∕𝜎, N ≫ 1

and

N = cRD (A4.2)

where N(R) is the number of microstructural elements in the image, R is the

linear size of the fractal, 𝜎 is the linear size of one particle (microstructural ele-

ment), d is the usual topological dimension (in the following, always equal to

1 for a line, 2 for a plane and 3 for space), D is the fractal dimension and c is a

constant.

A4.4 Fractal backbone dimension

According to Narine and Marangoni (1999b), the fractal backbone dimension

x of a network may be thought of as an indicator of the spatial distribution of

microstructural elements in chains, and the elements in the chains constitute a

microstructure. These chains are arbitrary in terms of the fact that a microstruc-

tural element may belong to any chain. In a 2D system such as the screen of a

microscope, the following formula holds:

N ∼ (R∕𝜎)x (A4.3)

where R is the length of an area enveloping the fractal chain and x is the fractal

backbone dimension (the chemical length exponent or tortuosity).

For details of the microscopic method of determination, see Narine and

Marangoni (1999b).

Further reading

Coniglio, A., De Arcangelis, L. and Herrmann, H.J. (1989) Fractals and multifractals: applications

in physics. Physics A, 157, 21–30.

Falconer, K. (1990) Fractal Geometry – Mathematical Foundation and Applications, John Wiley &

Sons, West Sussex, England.

MacLennan, M., Fotheringham, A.S. and Batty, M. (1991) Fractal Geometry and Spatial Phenom-

ena – A Bibliography, State University at Buffalo, NY.

Ould Eleya, M.M., Ko, S. and Gunasekaran, S. (2004) Scaling and fractal analysis of viscoelastic

properties of heat-induced protein gels. Food Hydrocolloids, 18, 315–323.

Pabst, W. and Gregorová, E. (2007) Characterization of Particles and Particle Systems, ICT Prague,

Czech Republic.

Rothschild, W.G. (1998) Fractals in Chemistry, Wiley-Interscience, New York.

Shamsgovara, A. (2012) Analytic and Numerical Calculations of Fractal Dimensions, Department of

Mathematics Royal Institute of Technology, KTH.

Stauffer, D. and Stanley, H.E. (1996) From Newton to Mandelbrot: A Primer in Theoretical Physics

with Fractals for the Personal Computer, 2nd edn, Springer, Berlin.

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Fractals 667

Tarasov, V.E. (2005) Continuous medium model for fractal media. Physics Letters A, 336, 167–174.

Wang, Y., Lin, X.Q., Wang, L.-J. and Li, D. (2011) Rheological study and fractal analysis of

flaxseed gum-whey protein isolate gels. Journal of Medical and Bioengineering, 2 (3), 201–206.

Z. Jie, Z. Ruirui, Buyuan H., B. Sufang (2007): Fractal Image Processing and Analysis by Pro-

gramming in MATLAB, Proceedings of the 8th WSEAS International Conference on Mathe-

matics and Computers in Biology and Chemistry, Vancouver, Canada, June 19–21.

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APPENDIX 5

Introduction to structure theory

The system theory of chemical engineering was developed by Seitz and Blickle

(1974), Blickle and Seitz (1974), Seitz et al. (1975, 1976) and Blickle (1978), and

it was adapted to food engineering by Mohos (1978a,b,c,d, 1982).

A5.1 The principles of the structure theory of blickleand seitz

A5.1.1 Attributes and their relations: structureStructure theory deals with the attributes of a system and their relations. The attributes

have qualitative and quantitative characteristics. The structure theory has been

used by Blickle, Seitz et al. originally for chemical engineering. Mohos (1982)

adapted it for food engineering; however, the structure theory as one of the sys-

tem theories can be applied in many fields of science and engineering.

In chemical engineering the attributes may be reasonably distinguished as

follows:

– S: Substantial attributes (e.g. atoms, ions and other chemical properties or phys-

ical properties, such as density and energy)

– M: Attributes of machinery (e.g. type of tank, tube, distiller, etc.)

– C: Attributes of the technological changes (e.g. dissociation, double decomposition,

substitution, distillation, etc.).

An attribute can be regarded as a set of attribute elements, and the structure of

this attribute is modelled by an internal product of its elements, that is, the relations

between these elements. The relations between different attributes are modelled

by an external product of attributes. This method of system theory entirely follows

the algebra of relations.

The structure theory defines the chemical changes as a mapping h (H ∋ hi

where i= 1, 2, … , n, and H is the set of changes), the kernel of which is the struc-

ture of the input materials and the picture is the structure of the output materials.

Between the changes two algebraic operations can be defined: series coupling

(⊕) and parallel coupling (⊗). It can be presented (Blickle and Seitz, 1975) that

the set H and these two algebraic operations establish an algebraic structure (H;

⊕; ⊗) which is a non-distributive lattice (see Birkhoff, 1948). By means of this

algebraic structure, the chemical changes (operations) can be modelled.

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Introduction to structure theory 669

SSubstances

CChanges

MMachinery

Figure A5.1 Technological triangle.

For simplicity the sets of the substantial attributes, the attributes of machinery

and the attributes of the technological changes can be regarded as vertices of a

technological triangle (Mohos, 1982) (see Figure A5.1).

A typical example for the technological triangle is as follows: if you want to

choose the machinery for a technological task, catalogues are to be studied which

contain some way of description on the attributes (parameters) of the machinery

offered, on the properties of substances (substantial attributes) which may be

produced by it and on the technological changes (attributes of operation) which

may be implemented by it.

This procedure may be electronically executed too – at this time the offers of

suppliers can be found in this way in the Internet. In the 1970s Blickle and Seitz

built up a tailor-made computer in Muszaki Kémiai Kutató Intézet (Research

Institute of Industrial Chemistry, Veszprém, Hungary) for solving such tasks.

The machinery offers published in the Internet can be built up according to the

method of system theory as well.

Obviously, the technological triangle has some similarity to the geometric

property of a triangle which justifies the nomination triangle: if you know two

sets of attribute and have the data set of technological triangle, then you can

determine also the third attribute set. The data set of technological triangle has

to be constructed by the machinery producers for offering their products.

In chemical engineering these attributes and relations are more or less discov-

ered, and the systematization is done by system theory.

A5.1.2 Structure of attributes: a qualitative descriptionThe ai elements of the A attribute set characterize a part of W of a four-dimensional

space (x; y; z; t) where A∋ ai and W∋ [xi; yi; zi; ti] which the latter is a point of W;

moreover, x, y, z are space coordinates and t is time. Γ(k; i) is a function of values

1 or 0 which refers to the A set where k refers to the part of W: [xk; yk; zk; tk] and

i refers to the element of the A set: ai.

If there exists the attribute combination {ai; aj} between two attributes in the

point k, then

Γ(k; i) = Γ(k; j) = 1 = Γ(k; i ∧ j). (A5.1)

Otherwise, Γ(k; i ∧ j) = 0 (if this combination does not exist) (where ∧ is the

logical disjunction).

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670 Confectionery and chocolate engineering: principles and applications

Example A5.1 (Blickle and Seitz, 1975, p. 35)The types of phase systems may be characterized by combinations

bi = fj ∧ fj ∧ gk (A5.2)

where

i = 1,2,3,4,5

f: phases; solid (j= 1), liquid (j= 2) and gaseous (j= 3)

g: homogeneous (k= 1) or heterogeneous (k= 2) relation

In detail,

b1 = f1 ∧ f1 ∧ (g1 ∨ g2): homogeneous solid phase or a mixture of powders

b2 = f2 ∧ f2 ∧ g1: homogeneous liquid phase

b3 = f2 ∧ (f1 ∨ f2 ∨ f3) ∧ g2: solid or liquid or gaseous substance dispersed in liquid

b4 = f3 ∧ f3 ∧ g1: homogeneous gaseous phase

b5 = f3 ∧ (f1 ∨ f2) ∧ g2: solid or liquid substance dispersed in gas

A5.1.3 Hierarchic structuresAmong the types of structures, the hierarchic structures are especially remark-

able since they can be characterized by the so-called arranging relation signed by

→; : for example, a→ b means that a is contained by b. For example, an atom (a)

is contained by a molecule (b) which is contained by a phase (c): the atom, the

molecule and the phase are elements of different hierarchic levels.

The properties of the arranging relation are:

– Reflexive: a → a.

– Non-commutative: If a→ b, then b a (i.e. b is not contained by a).

– Transitive: If a→ b and b→ c, then a→ c (heredity).

A5.1.4 Structure of measure: a quantitative descriptionThe attribute combinations which are possible (Γ= 1) may be characterized by

measures as well: for example, combinations of atoms (compounds) have molar

mass, molar volume, melting point and so on. The ratio of measures of the

same type referring to different attribute classes is called homogeneous measure,

for example, mass/mass [kg/kg], or on the contrary case the heterogeneous measure

can be defined, for example, volume/mass [l/kg].

A5.1.5 Conservative elements: conservative substantialfragments

In chemistry the atoms and certain atomic groups (ions, radicals, etc.) can be

regarded as conservative elements, that is, these elements do not change (do

not get split) in the chemical reactions. This fact is the base of the stoichiometric

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Introduction to structure theory 671

equations, and this supposition is used in chemical engineering as well. In the

world of chemicals, the most complex substantial organization is the phase (the

peak of hierarchy), and this fact leads to Gibbs’ phase rule.

Concerning the cellular substances the situation is entirely different, and also

foods consist of cellular substances. Structure theory intends to surmount these

difficulties by definition of the conservative substantial fragment (CSF) (Mohos,

1982): The CSF can be regarded as conservative in the technological changes

of a given food technology. Evidently, CSF is bound by this definition to

individual cases of a given food technology, and their conservative property is

not valid in general. The concept of conservative substantial fragment is defined

as follows:

I The set of the CSF of the system studied (C) is a union of the A and B sets:

C = A ∪ B.

II The elements of the A set are such CSF which are brought about by physi-

cal operations exclusively and which have different properties compared to

each other. It is supposed that the chemical changes taking place in these

fragments can be neglected from the point of view of study.

III The elements of the B set are chemical atoms or atomic groups, and practi-

cally only these fragments participate in the chemical operations performed

in the technological system.

IV The fragments defined in this way behave as conservative substantial parts,

that is, their quality remains unchanged during the proper operations. Con-

sequently, they can be regarded as quasi-chemical components for which the

following conservative equation is valid (Damköhler II equation for the flux

of component; see Chapter 1):

div[civ] − div[D grad ci] + 𝜔𝛽Δci + 𝜈ir = −𝜕ci∕𝜕t (1.4)

where ci is the concentration of i component ([mol/m3] for the elements of

the B set; [kg/m3] for the elements of the A set), D is the diffusion coeffi-

cient [m2/s], 𝛽 is the component transfer coefficient [m/s], 𝜈i is the degree

of reaction for i component and r is the velocity of reaction [mol/m3 s].

The source additive (𝜈i r) in the Damköhler II is worthy of distinguished atten-

tion: if the elements of the A set are the matter, then 𝜈i is the degree and r

is the velocity of physical transform, respectively, for example, the decompo-

sition of cells by breaking up. In this case the unit of r may be, for example,

[kg cocoa mass/m3 s].

A simple example is as follows: If alcohol is distilled from mash, this technological

change can be regarded similar to the case of evaporating an aqueous alcohol

solution. In the first case, the non-alcoholic part of mash and, in the second one,

the water can be regarded as unchanged, and in both cases only the change of

alcohol content is the changing variable. That is, the mash is separated into two

parts that are independent of each other. This is an approximation which works

in certain interval of temperature only.

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672 Confectionery and chocolate engineering: principles and applications

A5.1.6 New way of lookingA5.1.6.1 Permutations of operationsAn interesting goal of system theory is that with permutations of the same or sim-

ilar operations, it reveals new technological paths. An everyday example for such

way of thinking is to replace comminution of sugar with its dissolution in water

if possible. Evidently, if we prepare an aqueous sugar solution, crystalline sugar

has to be used; however, the best case is when the aqueous sugar solution is

obtained directly from the sugar factory. Regarding this example from an alge-

braic point of view, to crystallize sucrose and then to dissolve it again are inverse

operations which have to be avoided if possible.

Another example from the household practice is as follows:

– First to Boil the eggs, then to break them→ boiled eggs.

– First to Break the eggs, then to fry them in hot oil→ham and eggs.

– First to Break the eggs, then to pour them into boiling soup→ special boiled

eggs.

In these cases the breaking and the various types of thermal effects are per-

muted.

System theory and its adaptation to food engineering offer a lot of new appli-

cations, but first of all a new way of looking.

A5.1.6.2 Combinations of raw materialsThe combinations of raw materials can lead to different compositions. Let us denote

four different raw materials as 1, 2, 3 and 4. Their possible combinations are 1,

12, 13, 14, 2, 23, 24, 3, 34, 4, 123, 134, 234 and 1234. However, by changing the

proportion (x, y, z) of the ingredients, a combination, for example, 234 means a

lot of different compositions: (x× 2+ y× 3+ z×4).

On the other hand, if the sign + denotes some kind of operation, new products

may be developed by permutations such as (12+ 3), (23+ 1) and (31+ 2).

A5.1.6.3 Combinations of the elements of the set of machineryattributes (M)

The example is the planning of a mixing equipment. The groups of elements of

set M are as follows:

ai: shape of the equipment; i=1, 2, 3, …, for example, a2 = cylinder

bj: open or closed, j= 1, 2, …, for example, b1 = open

ck: types of mixing element, k= 1, 2, 3, …, for example, c4 = Z-kneader

dl: types of heating/cooling, l=1, 2, 3, …, for example, d3 =heating with water

(10–50 ∘C, tempered jacket)

em: capacity, m= 1, 2, 3, …, for example, e6 =100 kg (volume)

fn: batch/continuous, n=1, 2, for example, f1 = batch

As a result, the combination (a2 ∧ b1 ∧ c4 ∧ d3 ∧ e6 ∧ f1) means an equipment

which is of cylinder shape, an open Z-kneader, has a tempered jacket with cir-

culated warm water, and its volume is 100 kg, suitable for batch mixing.

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Introduction to structure theory 673

A5.2 Modelling a part of fudge processing plant bystructure theory

The modelled part of fudge processing plant consists of units: machine of dis-

solution, machine of evaporation and machine of caramelization. This example

shows how to choose the appropriate machine of dissolution. (Legend – 1:

yes; 0: no)

Characteristics Statesof materials

Liquid Solid GaseousDense Thin Water soluble Non-WS

Water 0 1 1 0 0

Sugar, crystalline 0 0 1 0 0

Corn syrup 1 0 1 0 0

Condensed milk 1 0 1 0 0

Lecithin 1 0 0 1 0

Salt 0 0 1 0 0

Characteristics of operations:

Parameters of intensityNumber of Type of

revolution (min−1) impeller Temperature (∘C)<30 <120 >120 Baffled Turbine <100 >100

Mixing, dissolution 0 1 0 1 0 1 0

Emulsification 0 0 1 0 1 1 0

Warming 0 0 0 0 0 1 1

The coupling of the operations (see Figure A5.2).

Mixingdissolution

X min

Warming + tempering(X – t)min at T(1), then (Y + t)min at T(2) temperature

EmulsificationY min

Figure A5.2 The coupling of operations in the model.

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674 Confectionery and chocolate engineering: principles and applications

We want to choose a machine that is capable of achieving mixing, dissolution

and emulsification in single unit.

Characteristics of machinery:

Open Closed Impeller Warming Tempering Dosing/outlet

Multiple Turbine <100 ∘C >100 ∘C (min)stage

0 1 1 1 1 0 1 6/2

Suppose that there is a database which contains the characteristics of materials,

operations and machinery of many food machines. This database is actually a

technological triangle. The characteristics of two vertices will be fed into this

database, and the appropriate software provides the characteristics of the third

vertex. For example, if the characteristics of materials and operations are fed,

then the characteristics of machine(s) being capable for achieving the prescribed

task will be provided.

Such databases are owned and issued by each machine factory albeit usually

not in computerized form but in technical brochures or on websites.

Further reading

von Bertalanffy, L. (1968) General System Theory: Foundations, Developments, Applications, Braziller,

New York.

Zadeh, L. (1969):Biological Application of the Theory of Fuzzy Sets and Systems, The Proceedings

of an International Symposium on Biocybernetics of the Central Nervous System Boston: Little Brown.

pp. 199–206.

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APPENDIX 6

Technological layouts

See Figures 6.1–6.27.

Fibre, stone,

metal, etc.

Too small/large

beansShell, germ

Winnowing

separation

Roasting,

cooling

Raw-bean

cleaning,

sorting

Storage of

cocoa beans

Storage of

cocoa liquor,

homogenization

Fine

grinding

Pre-grinding of

cocoa nibs

Figure A6.1 Production of cocoa liquor (traditional method).

Fibre, stone,

metal, etc.Too small/large

beans

Shell,

germ

Winnowing

separation

Thermal

shock,

cooling

Roasting of

cocoa nibs

Raw-bean

cleaning,

sorting

Storage of

cocoa beans

Storage of

cocoa liquor,

homogenizationFine

grinding

Pre-grinding of

cocoa nib

Figure A6.2 Production of cocoa liquor (method of nib roasting).

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676 Confectionery and chocolate engineering: principles and applications

Fibre, stone,

metal, etc.

Too small/large

beans Shell,

germ

Winnowing,

separation

Raw-bean

cleaning,

sorting

Storage of

cocoa beans

Storage of

cocoa liquor,

homogenization Fine grinding

Roasting of

cocoa liquor

Pre-grinding of

cocoa nibs

Pasteurization

+

thermal

shock,

cooling

Figure A6.3 Production of cocoa liquor (method of roasting cocoa liquor).

Storage of

chocolate mass,

homogenization

Sugar

powderCocoa

liquorCocoa

butter

Cocoa

butter

Wet

conchingDry conching

Refining

(five-roll

refiners)Homogenization

of ingredients

Cocoa

butterMilk

powderHazelnut

paste Lecithin Emulsification

Vapour, acids

Figure A6.4 Production of milk chocolate mass (traditional method).

Tempering 3

(=30–32°C)Tempering 2

(=27°C)

Tempering 1

(=32°C)

Storage of

chocolate

mass (=50°C)

Cooling 3

(chocolate

=12°C)

Cooling 2

(chocolate

=9°C)

Cooling 1

(chocolate

=16°C)

Warming the moulds

(=30°C)Demoulding

Vibration

Warm side Cool side

Moulding

(dosing)

Packaging

of bars

Figure A6.5 Production of chocolate bar.

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Technological layouts 677

Vapour Aqueous

alkali

solution

Cocoa

butter

For chocolate

For moulding

Vapour + odours

Deodorization

by film

evaporation

Pressing

(separation)Cooling

the cake

Kibbling

the cake

Cool airPulverization

Tempered air

TemperingPackaging of

cocoa powder

Air Air

Acidic

solution

for

neutralization

Storage of

cocoa liquor

‘Preparation’

(chemical

reaction

+evaporation)

Figure A6.6 Production of cocoa powder and cocoa butter (alkalization of cocoa liquor).

Vapour

Shell,

germPre-roasting

the beans

Pre-grinding of

cocoa nibsWinnowing,

separation

Fine grinding

‘Nib

alkalization’

(roasting,

chemical

reaction

+

evaporation)

Raw-bean

cleaning,

sorting

Aqueous

alkali

solution

Cocoa

butterCocoa cake

Pressing

(separation)

Acidic

solution

for

neutralization Storage of

cocoa

beans

Figure A6.7 Production of cocoa powder and cocoa butter (Dutch process).

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678 Confectionery and chocolate engineering: principles and applications

Tempering

chocolate

for shellWarm side

Turning

back,

coolingPre-

cooling,

scraping

SpinningVibrating,

flipping

Vibrating Dosing,

filling

Nut

+

fat

cream

or

cherry

+

fondant

cream

Depositing

Cooling the

filling

Cool

side

Rim heating

Final cooling Demoulding Sorting

Packaging of

pralinesTempering

the moulds Moulds

Bottoming

Tempering

chocolate

for bottoming

Figure A6.8 Praline production.

Sugar

siloGlucose

syrupAtmospheric

evaporation

Vacuum

evaporation

DissolvingPre-

dissolving

Water

tank

Sugar

solution

or wax

Warm

air

CoolingCutting

the ropeSurface

treatmentPackaging

the drops

Warm

tempering

(decoration)

Cool

tempering

(colouring,

flavouring)

Filling

Shaping

the rope

+

dosing

of

filling

Figure A6.9 Drops manufacture.

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Technological layouts 679

Sugar siloCream of

tartar

Atmospheric

evaporation

Vacuum

evaporation

Cool tempering

(colouring, flavouring)

Warm tempering

(decoration)

Rope shaping

+

filling

Pulling

Cutting

the ropeCooling

Warm

vapour

GlycerineWater

tank

Dissolving

Surface

wetting

in warm

room

Packaging

the sweetsFilling

Figure A6.10 Production of grained sweets with cremor tartari. By addition of glucose syrup

instead of cremor tartari, a simpler technology can be installed which results in a similar

quality of product.

Sugar siloAtmospheric

evaporationCrystallization

Solidification

of fondant centresMogul

system

Conditioning

the starch Demoulding

Couverture chocolate,

tempered

Air

Bottoming

Arranging the

centres on the

covering machine

Packaging

the covered

fondant product Covering

machine

Covering

with chocolate

curtain

Dosing into starch

(colouring, flavouring)

Cooling

Water

tank

Dissolving

Glucose

syrup

Shaping

the starch

moulds

Figure A6.11 Production of fondant centres by Mogul and covering by chocolate.

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680 Confectionery and chocolate engineering: principles and applications

Sugar silo

Crystallization

on the surface

of centers

Packaging

the centers

Draining

the candy pots

Drying

the centres

Loading

the candy pots

Storage

of centres

Flooding

the candy pots

Puffer

storageCooling

(=28–32°C)Evaporation

(=105–107°C)

Circle

of

candy

pots

Circle of

candy

solution

Water

tank

Dissolving

Figure A6.12 Covering the fondant centres by candy layer (candis layer, traditional).

Sugar

siloMilk

(e.g. milk

powder

etc.)

Molten butter

Emulsification

Evaporation

Caramelization

(evaporation)

Emulsifier

Cooling

Shaping

e.g. by Mogul

Homogenization

(colouring

flavouring)

Fondant

mass

Glucose

syrup

WaterDissolving

Figure A6.13 Manufacture of toffee and fudge (by adding fondant mass).

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Technological layouts 681

Sugar

silo

Gelling

agent

DissolvingPuffer

(pectin gel)

Water

Shaping,

e.g. by Mogul

Colouring,

flavouring

(sol → gel

transition of

pectin gel)

Cooling

(sol → gel

transition

Glucose

syrup

Evaporation

(=106 °C)

Homogenization

+

boiling

Figure A6.14 Jelly manufacture (general scheme). For further details, see Chapter 11.

Sugar

siloWater Air

FoamingDissolvingFoaming

agent

Glucose

syrupEvaporation Shaping,

e.g. by Mogul

or extruder

Other

ingredients

Figure A6.15 Manufacture of sweet foams.

Sugar

Water

Glucose

syrupHoney,

brown sugar,

molasses, etc.Emulsifier

Butter

or fat

FlavoursDissolvingDissolving

Dissolving

Evaporation

Fondant gun

Foaming

(continuous)

Shaping

by cutting

Covering

with chocolate

and/or packaging

ButterPasteurization,

homogenization

Pasteurization,

homogenization

Extruder

(homogenization)

Figure A6.16 Montelimar manufacture (continuous).

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682 Confectionery and chocolate engineering: principles and applications

Sugar

Sugar

melting

(=200–210°C)

Nuts

HoneyGlucose

syrup

Rolling

CuttingCovering with

chocolate

or packaging

Homogenization

Figure A6.17 Croquante manufacture.

Blanching

(=80°C,

10–20 min)

Sorting

almonds Shelling

ShellsWarm

water

Grinding

by rolling

Shaping

by cutting or

extruder

Cooking

(=30–40 min)

Impurities

Sugar

(crystalline)

Homogenization

Bitter

almonds

(=5%)Cooling

Sorting

almonds

Figure A6.18 Marzipan manufacture (traditional).

Dragee

centresWetting Drying

Drying

Packaging

Glazing

Colouring,

flavouring

Drying

Drying

Sugar

solution

Wetting

Repeated

Air

(cold/warm)

Air

Air

Air

Sugar

solution

Castor/icing

sugar

Castor/icing

sugar

Figure A6.19 Dragee manufacture (cold/warm method).

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Technological layouts 683

Dragee

centres, e.g.

hazelnuts

‘Wetting’ Hardening Air

PackagingRepeatedTempered

chocolate

Figure A6.20 Manufacture of chocolate dragee.

Icing

sugar

Binding agent,

e.g.

gelatin

solution

Homogenization Rolling

Colouring,

flavouring

Packaging Drying

Cutting

or

punching

out

Figure A6.21 Manufacture of lozenges.

Icing

sugar/

glucose

Homogenization

and granulation

Homogenization

Homogenization

Drying

Lubricant

Lubricant PackagingTabletting

Indirect

methodDirect

method

Colouring,

flavouringBinding agent,

e.g.

gelatin

solution

Figure A6.22 Manufacture of tablets.

Chicle

gumZ-kneading Extrusion

Rolling

PackagingPackaging

CuttingShaping,

e.g. into

balls

Glucose

syrup

Icing

sugar

Surface

treatment

Colouring

flavouring

(special)

Pre-warming

(ca. 60°C)

Figure A6.23 Manufacture of chewing and bubble gums.

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684 Confectionery and chocolate engineering: principles and applications

Packaging

Special

operations

Icing

sugar

Flour Relaxation Sheeting

Sheeting

and

gauging

LaminationScrap return

Cutting

Baking

powder

Baking

(ca. 160°C)

Baking

(ca. 200°C)Baking

(ca. 180°C)

Water

Cooling

Oil spraying

Surface

treatment

Cracker

production

Vegetable

fat

Z-kneading

(ca. 35°C)

Figure A6.24 Manufacture of semi-sweet biscuits and crackers.

Packaging

Icing

sugar

Flour

Baking

powder

Shaping by

extrusion +

cutting

or

moulding

Baking

(ca. 175°C)Baking

(ca. 175°C)Baking

(ca. 150°C)

Cooling Surface

treatment

Vegetable

fat

Z-kneading

(ca. 20°C)

Figure A6.25 Manufacture of short-dough biscuits.

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Technological layouts 685

Packaging

Wheat

flour

Rye

flour

WaterSpices

Honey

Scrap

Cooling

Baking

powder

Baking

(ca. 160°C)Baking

(ca. 200°C)

Baking

(ca. 180°C)

Surface

treatment

(covering by

chocolate

or

candy crust)

Z-kneading

(ca. 60°C)

Relaxation

(ca. 2 weeks)Re-kneading

Sheeting

and

gaugingShaping by

rotary moulding

or punching out

Figure A6.26 Manufacture of Lebkuchen (honey cakes).

Sugar

solution

Oil/fat

SaltEgg/egg

derivatives

Emulsification Suspending Flour

Filtering

Buffer storage

Dosing/baking

PackagingCutting

Cooling

Cooling

Scrap

return

Cream

preparation Spreading/

layering

Lecithin

Milk/milk

derivatives

Figure A6.27 Wafer manufacture.

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686 Confectionery and chocolate engineering: principles and applications

Further reading

Alikonis, J.J. (1979) Candy Technology, AVI, Westport, CT.

Almond, N., Wade, P., Gordon, M.H. and Reardon, P. (1991) Biscuit, Cookies and Crackers, Elsevier

Applied Science, London.

Beckett, S.T. (ed.) (1988) Industrial Chocolate Manufacture and Use, Van Nostrand Reinhold, New

York.

Biscuit and Cracker Manufacturers Association (1970) The Biscuit and Cracker Handbook, Biscuit

and Cracker Manufacturers Association, Chicago.

Cakebread, S.H. (1975) Sugar and Chocolate Confectionery, Oxford University Press, Oxford.

Ellis, P.E. (ed.) (1990) Cookie and Cracker Manufacturing, Biscuit and Cracker Manufacturers Asso-

ciation, Washington, DC.

Fabry, Y. and Bryselbout, P.H. (1985) Guide Technologique de la Confiserie Industrielle, SEPAIC, Paris.

Faridi, F. (ed.) (1994) The Science of Cookie and Cracker Production, Chapman and Hall, New York.

Gutterson, M. and Noyes Development Corporation (1969) Baked Goods Production Processes,

NDC, LondonFood Processing Review 9.

Haseleu, A. (2003): Materialwissenschaftliche Untersuchung des Dragierverhaltens von Zuck-

eralkoholen, PhD, Technischen Universität Berlin (D 83)

Kempf, N.W. (1964) The Technology of Chocolate, The Manufacturing Confectioner Publishing Co.,

Glen Rock, NJ.

Kulp, K. (ed.) (1994) Cookie Chemistry and Technology, American Institute of Baking, Kansas.

Lees, R. (1980) A Basic Course in Confectionery, Specialized Publications Ltd, Surbiton, UK.

Manley, D. (1998) Biscuit, Cookie and Cracker Manufacturing Manual(Vol 1: Ingredients, Vol 2:

Biscuit doughs, Vol 3: Biscuit dough piece forming, Vol 4: Baking and cooling of biscuits,

Vol 5: Secondary processing in biscuit manufacturing, Vol 6: Biscuit packaging and storage.),

Woodhead Publishing, Cambridge, UK.

Meiners, A. and Joike, H. (1969) Handbook for the Sugar Confectionery Industry, Silesia Essenzen-

fabrik, Gerhard Hanke K.G. Norf, West Germany.

Meursing, E.H. (1983) Cocoa Powders for Industrial Processing, 3rd edn, Cacaofabriek de Zaan, Koog

aan de Zaan, The Netherlands.

Pratt, C.D., de Vadetzsky, E., Landwill, K.E. et al. (1970) Twenty Years of Confectionery and Chocolate

Progress, AVI, Westport, CT.

Schwartz, M.E. (1974) Confections and candy technology, Noyes, Park Ridge, NJ.

Smith, W.H. (1972) Biscuit, Crackers and Cookies, Applied Science, London.

Sullivan, E.T. and Sullivan, M.C. (1983) The Complete Wilton Book of Candy, Wilton Enterprises,

Woodridge, IL.

Wade, P. (1988) Biscuit, Cookies and Crackers, Elsevier Applied Science, London.

Whiteley, P.R. (1971) Biscuit Manufacture, Applied Science, London.

Wieland, H. (1972) Cocoa and Chocolate Processing, Noyes Data Corp., Park Ridge, NJ.

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References

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Acker, L. and Diemair, W. (1956) Zeitschrift für die Süsswarenwirtschaft, 9, 1187.

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Afoakwa, E.O., Paterson, A., Fowler, M. and Vieira, J. (2008) Effects of tempering and fat

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Aguilar, C.A., Dimick, P.S., Hollender, R. and Ziegler, G.R. (1995) Flavor modification of milk

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Index

Aability of sucrose to crystallize, 40absorption of light, 198accidental admixtures, 405acetylated starches, 446acid-hydrolysed starches, 446acidic conversion of starch, 41acrylamide (acrylic amide, IUPAC name:

prop-2-enamide), 538, 539acrylamid formation, 539activation energy of diffusion, 136, 137addition of glucose solution to promote the

Maillard reaction, 571adsorption, 211, 212, 216, 270, 580, 587, 664adsorption/desorption of water, 580

on the surface of foods, 587adsorption isotherm, 212adsorption on free surface of liquids, 216adsorption techniques

for determining fractal dimension, 664for particie size distribution

determination, 270aerated chocolate mass/fillings, 408, 556aerated fillings, 408aeration of the chocolate mass, 556afterburner, 577after-crystallization during storage, 395agar, 46, 424–426

flakes, 425gel properties, 426jelly recipe, 46setting, 425

ageing, 376, 604of foods, 604

agglomerationby baking, 513in the confectionery industry, 512under the effect of gelling/foaming agents, 513from liquid phase, 513phenomena during conching, 177of powders tabletting (or dry granulation), 513

aggregatesgels and sediments, 238

aggregation, 501, 512degree, 344and flocculation models, Berg and Brimberg, 366in a fluidized bed, 516

aggregation/de-aggregation of chocolate particles,546

agitated ball mill, 557air-conditioned places, 611

Confectionery and Chocolate Engineering: Principles and Applications, Second Edition. Ferenc Á. Mohos.© 2017 John Wiley & Sons Ltd. Published 2017 by John Wiley & Sons Ltd.

air flow in tube, 471air pollution in connection with roasting, 577algebraic operations, 668algebra of relations, 668alginates, 429alkalization, 398

of cocoa material preparation, 398, 535, 540of cocoa nibs or mass, 535

a, b′ and b main crystal forms, 381, 384alternative sweeteners, 315alveograph, 190Amadori compounds, 534, 535Amadori rearrangement, 534, 535amount of loss, 52amphipathic (capillary active) substances, 210, 217amphipatic compounds, 210amphoteric properties of gelation, 450, 451amylograph, 141amylopectin, 444, 445amylose, 444, 445analogy between the rheological models and the

electrical networks, 154analogy to reaction kinetics, 230analysis of dilatometry data using the Avrami

equation, 363Andreasen’s pipette method of particle size analysis

by sedimentation, 238angel kiss, 458angle of friction in a melangeur, 282angle of pulling, 277, 281angle of repose, 101Antoine rule, 325apparent gel strength of agar gel, 426, 428apparent secondary nucleation, 344apparent viscosity, 128, 302apple pectins, 441application of cocoa butter equivalents (CBEs)

in chocolate, 399, 401improvers (CBIs) in chocolate, 399, 401

application of cocoa butter improvers (CBIs) inchocolate, 399, 401

aqueous alkali, 541aqueous solutions

of carbohydrates, 306–308invers sugar, 311–312of sucrose and glucose syrup, 309–311

aqueous sucrose solutions containing invert sugar,311

Ardichvili’s equation for velocity of a plane inroller extrusion, 499

arranging relation, 670

737

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Arrhenius equation/model, 82, 183, 530Arrhenius law on temperature dependence of

acidic inversion, 530Arrhenius model used for caramel, 183arterial and venous casts of a kidney, 663artificial (intensive) sweeteners, 57artisan confectionery technologies, 611artisan products, 609asparaginase pre-treatment of raw potatoes and

dough, 540asymptotic stability, 605atomic force microscopic methods, 159attenuation factor, 87attractive forces, 201

affecting in granulation, 510attractive potential, 221attractive, repulsive, resultant forces/potential,

201, 221, 510attribute combinations, 670attributes of a system and their

relations/combinations, 668, 670attributes of machinery, 668attributes of the technological changes, 668autoimmune disease, 58average chain-terminal distance, 203Avrami equation/exponents/parameters, 360–363,

387axial diffusion remixing in continuous conching,

553

Bbackbone fractal dimension, 168background of the Casson and the Bingham

models, 650Bagley-Machikhin-Birfeld method, 470Bagley plot, 484, 486, 488baked products, 233baking, 535, 562, 566baking, baked products/powders, 233, 465, 535,

562, 566baking powders, 465Balshin’s equation for the change of density under

the effect of compression, 523Bancroft’s rule, 230barometric formula, 212, 238bar-style agar, 425batch conching, 547batch conching /crystallization/roasters, 374, 547,

572batch crystallization, 374batch roasters, 572Batel’s equation for capillary attractive forces, 504beater blade mill, 557Becker-Döring equation of rate of true secondary

nucleation, 345beer fermentation (by yeast), 245Benbow-Bridgwater

analysis of capillary extrusion, 498equation for plug flow, 498

Bennett’s formula on Rosin-Rammler (RR)distribution, 273

benzaldehyde as volatile marker of chocolateflavour, 556

BET isotherm, 588, 589BFMIRA process, 558biaxial extension, 141, 142, 184

of dough, 184bimodal morphologis of emulsion, 244binding mechanisms, 502Bingham fluids, 126, 132, 134, 171, 178, 468, 488,

646, 647Bingham model, 171, 468, 646, 647Bingham plastic

materials, 132viscosity, 171

biscuit/cake/doughs/production (by yeast orbaking powder), 192, 245

biscuits and wafers produced for special nutritionalpurposes, 59

black box process by Veerle De Graef, 413blancmange-type puddings, 435blending, 512blending animal fats by Soós, 413bloom grade, 449bloom inhibition, 396bloom strength, 449Boger fluids, 658boiling end-point of agar solution, 428

with cooking, 428boiling points

of aqueous glucose syrup solutions atatmospheric pressure, 625

of aqueous sugar solutions, 318, 319, 334, 335,622, 625

of bulk sweeteners, 318, 319, 334, 335, 622, 625of sucrose/water solutions, 318, 319, 334, 622

Boltzmann distribution, 212, 238Boltzmann’s equation for the stress in viscoelastic

solids, 656bonding/cold welding, 518, 519boundary layer, 210, 349bowl roasters (Sirocco type), 572box counting, 664box-counting dimension, 663, 664Brabender extensograph, 189, 659Brabender farinograph, 189, 659Brabender torque rheometer, 141branching theories on gelation, 258bread dough, 185, 245breadmaking, 245breaking (cracking) load of agar gel, 426bridging theory

of La Mer and Healy, 234briquetting of the chocolate particles

during conching, 545during the refining process, 545

Brownian flocculation, 235Brownian movement, 237, 501, 604browning phenomena, 604Brucheigenschaft, 393bubble collapse by disproportionation, 251bubble growth, 139, 140, 248

size distribution, 248bubbling-inhibitor, 219bubbly foam, 245Buckingham number (Bu), 468, 645, 646

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Buckingham-Reiner equation, 646Buckingham’s II-theorem, 13, 17bulk compressibility, 117bulk density, 63bulk modulus, 117bulk sweeteners, 56, 315, 317bulk viscosity, 254bundles/micelles/crystallites, 204buoyancy (or Archimedes) force, 464Burgers model, 152Buscall’s equation of hindered settling, 237butterscotch, 535 see also caramel

CCakebread’s equation

non-sucrose ingredients, 593, 594caking, 101calcium conversion in an alginate gel, 430calcium tartrate, 531calculating the boiling points

of carbohydrates/water solutions at decreasedpressures, 319

at decreased pressures, 319calculation of efficiency, 614calendering, 139–141, 496

in the dough industry, 496candying with ‘candis layer’, 564capacitive dielectric (capacitance) heating, 85capacity of a screw mixer, 495capillary attractive forces in the case of no liquid

bridges, 504capillary depression, 215capillary effect, 586capillary forces, 206, 215, 253, 502, 504, 510, 586

in freely moving fluid surfaces, 502capillary pressure of the meniscus, 253capillary rheometer, 184capillary rise, 206, 215caramel, 182, 527, 534–536, 552caramelization, 182, 527, 534–536, 552

in milk chocolate, 552caramelized milk powders made by a roll dryer,

536caramel odour, 535, 536caramel taste, 535, 536carboxymethyl starch, 445carcinogenity of acrylamide, 539Carle & Montanari system, 558carrageenan, 459carrageenans, 432, 459Carreau model, 174Cartesian product of phases, 31cascade theory on gelation, 258casein micelles, 216Casimir-Polder–Lifschitz formula, 506Casson body, 132Casson equation, 132Casson generalized, 172Casson models, 172, 468, 647Casson number, 648Casson viscosity, 173, 468Casson (dynamic) viscosity, 647Casson yield stress, 173, 647

casting into starch moulds, 564catalytic ability of various acids in inversion,

according to Ostwald, 528Cauchy’s equation of motion, 121

strain, 111, 121Cauchy strain, 111CBE/CBR/CBS:cocoa butter

equivalent/replacer/susbstitute veg. fats,365–407

CBE:cocoa butter equivalent vegetable fats, 392CBR:cocoa butter replacer vegetable fats, 392CBS:cocoa butter substitute vegetable fats, 392cellular structure, 3, 23cellular substances, 12, 671centrifugal coffee roaster, 576chair shape of triacylgylcerols (TAGs), 382changes during baking, 567, 568characteristic length for impeller/tank/particle in

dissolution, 313, 314characteristics of the artisan products, 609characteristics of ventillator, 477chemical activities, 72, 339, 340chemical changes in flavonoids, 541chemical composition/physical properties of cocoa

butter due to its origin, 387chemical length exponent (or tortuosity), 666chemical potential, 65, 339chemical properties of cocoa butter, 631chemo-gels (pectin gels), 443cherries preserving in ethanol, 543chewing parameters, 194Chilton-Colburn analogy, 351, 353chips, 562choco crumb, 535chocolate, 171, 408, 563

mass, 171spreads, 408

Chopin Alveograph, 659cis-trans isomers/ rotation, 383citrus pectins, 441classical theory of nucleation, 342classification of food powders, 96classification of gels regarding the nature of the

structural elements, 169classification of rheological behavior, 124, 125classification of the confectionery products

according to their characteristic phaseconditions, 30

classification of the confectionery products vs. theircharacteristic phase conditions, 30

classification scheme of phase transitionsby Ehrenfest, 73by Fisher, 73

Clausius-Clapeyron equation, 583closing inventory, 54–55clusters of particles, 342coalescence, 234, 241coating fats with high trans-fat portion, 411cocoa butter, average composition, 382cocoa butter equivalents (CBEs), 365cocoa butter replacers (CBRs), 365cocoa butter replacers (non-lauric) (CBR), 403cocoa butter substitutes (CBSs), 365, 406, 407

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