Laboratory of Rheology and Food Laboratory of Rheology and Food EngineeringEngineering

Applicazioni della reologia a processi Applicazioni della reologia a processi industrialiindustriali

LaRIALaRIALaboratory of Rheology and Food Laboratory of Rheology and Food

EngineeringEngineering

Domenico GabrieleDomenico Gabriele

CONTRIBUTO DELLA REOLOGIA ALLE PROBLEMATICHE

INDUSTRIALIMATERIALI• Caratterizzazione delle materie prime in funzione del loro utilizzo;• Caratterizzazione dei prodotti in funzione delle proprietà attese.

PROCESSI• Progettazione di nuovi impianti in relazione delle proprietà delle materie prime e dei prodotti;• Controllo e miglioramento degli impianti esistenti in relazione alle proprietà di materie prime e prodotti.

Laboratory of Rheology and Food Laboratory of Rheology and Food EngineeringEngineering

A rheological approach to soft ice A rheological approach to soft ice cream productioncream production

LaRIALaRIALaboratory of Rheology and Food Laboratory of Rheology and Food

EngineeringEngineering

FoamsFoams

Multiphase systemA viscoleastic medium entrapping gas bubble

Ice cream (frozen state)Instant Whipped cream (unfrozen state)

Some applications in dairy industry

Shaving foamsFire-fighting foamsFood foams (texture determined by gas cells)

Laboratory of Rheologyand Food Engineering

“Ready-to eat” ice creamSeller point or home production“Soft” structureReduction or absence of ice crystalsLow pressure aeration

……. Possible solutionAeration and storage at low-moderate pressure (4-8 atm), cooling, extrusion, bubble expansionHigh overrun, smooth texture, stabilisation through emulsion film properties

Ice CreamFrozen state

Whipped creamNon Frozen state

Aerated dairy emulsionsAerated dairy emulsionsThe situation…….

…. The new trend…

““INSTANT” ICE INSTANT” ICE CREAMCREAMAerated

emulsions

Under-Under-pressure pressure EmulsionEmulsion Soft Ice-CreamSoft Ice-Cream

Gas Loss

Structure Structure collapsingcollapsing

Extrusion

““Instant” Ice Creams Instant” Ice Creams

……. Emulsion rheological properties….. Emulsion rheological properties….• Low freezing point (no ice)• Low viscosity (flow at low temperature)• High elasticity (gas retention, proper texture)

Product characteristics …..Product characteristics …..• Stability• Ice cream texture• Low ice content• Flow through a nozzle at low temperature (T<0°C)• Low driving force (4-8 atm)• High overrun• Good gas retention

… … Process conditionsProcess conditionsOperating conditions (T, P)Geometry (nozzle dimensions)

New product developmentNew product development

Optimal Optimal formulation……formulation……• FFatsats• WaterWater• SugarsSugars• EmulsifiersEmulsifiers• Proteins Proteins • Stabilizers Stabilizers

RHEOLOGICAL RHEOLOGICAL CHARACTERISATIOCHARACTERISATIO

NN

… and …

…………Nozzle designNozzle designOperating conditionsOperating conditionsFlow through the nozzle Flow through the nozzle

BALANCEBALANCEEQUATIONSEQUATIONS

Material characterisation – 1 Material characterisation – 1

ID Base

OUT IN Homogeniser

E2 E1 50% (w/w) of dextrose

Sucrose Ultrasound bath

E3 E2 22% (w/w) of milk Milk cream Ultrasound bath E4 E1 E/S 3:1 E/S 1:1 Ultrasound bath E5 E3 4.5% (w/w) of milk Glycerol Pressure

homogeniser E6 E5 Milk Fructose,

SucrosePressure homogeniser

E7 E3 Fatty acids mono and dyglicerides (lipophilic)

tartaric acid esters of mono- and diglycerides of fatty acids (hydrophilic)

Pilot plant

Sample characteristics

Base emulsion (E1)

Milk (whole and powder skim milk)Vegetable fatsGlucose syrupDextroseEmulsifiers1/stabilizers2 3:1

1fatty acids mono and diglycerides2carrageenan and guar gum

Mixing, Homogenisation in ultrasound bath

Other emulsions (E2-E7)

ARES-RFS TA InstrumentsParallel plates (50 mm)

Freezing pointTime cure (1 Hz; -1°C/min; T= 4 °C freezing point);Time sweep (1 Hz)

Elastic componentFrequency sweep test (0.1 – 10 Hz; T= -5°, 0°, 4°C);

Low temperature viscosityFlow Curve (0.1 – 100 s-1; T= -5°, 0°, 4°C);

Material characterisation – 2 Material characterisation – 2

Freezing point Freezing point

Sample E1 – Time cure….. Sample E1 – Time cure…..

0.01

0.1

1

10

100

-15 -10 -5 0 5T [°C]

G', G

" [k

Pa]

0

0.1

0.2

0.3

0.4

0.5

tg

[-]G'

G"tan_delta

0.01

0.1

1

10

100

-15 -10 -5 0 5T [°C]

G', G

" [kP

a]

0

0.1

0.2

0.3

0.4

0.5

tg

[-]G'

G"tan_delta

…… …… Sample E1 – Time sweepSample E1 – Time sweep

0.01

0.1

1

10

100

0 100 200 300 400 500time [s]

G', G

" [kP

a]T=-8°CT= -9°C

FP - 9°C

FP FP - - 10°C10°C

Frequency sweepFrequency sweep

Sample E1Sample E1

10

100

0.1 1 10Frequency [Hz]

G* [P

a]

-5°C 0°C 4°C

10

100

0.1 1 10Frequency [Hz]

G* [P

a]

-5°C 0°C 4°C

0.1

1

10

100

0.1 1 10 100Shear rate [s-1]

Visc

osity

[Pa.

s]

-5°C 0°C4°C

Flow curveFlow curve

Experimental results - 1 Experimental results - 1

Weak gel model (three-dimensional network)1

z1

ωAω*G 21 ωωω

A, network strengthz, network extension

Dynamic testsDynamic tests

Flow curveFlow curvePower law model

nγkγτ k, consistency indexn, flow index

1Gabriele et al., Rheol. Acta. 40 (2001)

ID Note FP [°C] A [Pa∙s1/z] z [-] k [Pa∙sn] n [-]

E1 - -9 44.0 5.05 6.70 0.37

E2 sucrose -6 56.1 5.11 10.6 0.29

E3 Fat -10 82.3 5.30 12.40 0.37

E4 E S -9 180.8 7.92 27.66 0.25

E5 glycerol -12 25.8 4.49 3.68 0.47

E6 - -10 24.7 4.30 2.98 0.34

E7 Emulsifier -14 12.8 3.39 4.33 0.44

Emulsion choice

All data at -5°C

Experimental results - 2 Experimental results - 2

Foam fluidynamicsFoam fluidynamicsModelling of foam fluidynamics and expansion

2. Modelling of foam extrusion through a can nozzle (flow of a compressible medium)

1. Modelling of single gas bubble expansion in a viscoelastic medium (void fraction evaluation)

t

3. Ice cream performance evaluation (overrun, residual mass)

Simplifying the problem by considering different steps

Bubble expansion - 1Bubble expansion - 1

8 8 atmatm

8 8 atmatm

time=0Foam inside the canEverywhere 8 atm

time>0Extruding foam through the nozzleP outside bubble<8 atm

Bubble expansion

Mechanical equilibrium at the bubble interface1

R

rr

LLL

G2 drr

3R

2PPR23RR

surface tensionP pressure at infinite distance

L liquid densityPG gas pressure inside the bubble1Bird et al., (1977), Dynamics of Polymeric Liquids, Vol.1, Wiley,

1 1 atmatmPP

- Pure bi-axial extension- Isothermal conditions- Equilibrium conditions for mass transfer

Main hypothesis

Single bubble model

RPG

r

Pinf

Bubble expansion - 2Bubble expansion - 2Rheological constitutive equations

t

33

2

Rrr 'dt

R'RR

'Rln'R'RT,'ttGdr

r

Tz

1'ttz

11TA)T,'tt(G

Weak gel model2

Linear viscoelasticity

Ideal Gas constitutive equation

TRRn

43P G3

GG

Gas-liquid equilibrium constitutive equationHenry equation ONG 2

cHP

cN2O, concentration in liquid phase

Final result

)(f)(fPG 2Gabriele et al., Rheol. Acta. 40 (2001)

GPfR

Foods Weakly structured systems

Material properties evaluationMaterial properties evaluation

*Codap S.p.A. Internal report

Surface tension*

Same value for all samples, =49.3010-3 N/m

Henry’s law parameter*

ON of g

emulsion of g 100 797.102

barHTypical value for dairy emulsions

Nozzle modelling - 1Nozzle modelling - 1Physical system

Outlet

Inlet

Outlet

Inlet

Outlet

Inlet

Outlet

Inlet

Nozzle

Actuator

Nozzle Actuator

A can having a constant volume connected to a nozzle where the emulsion flows

Nozzle modellingNozzle modelling - 2

Uscita

Ingresso

Ugello

Attuatore

Ingresso

Ugello

Attuatore

Nozzle modelling - 3Nozzle modelling - 3

Main hypothesisAngular symmetryIsothermal system

Pseudo-homogeneous approach Uniform gas distribution

“Equivalent transport properties”

Balance equations Cylindrical coordinate system (r,z, )

gρτPDtvDρ 0vρ

DtρD

Continuity Momentum

No slipNegligible normal stressesPower law fluid

DII4'kτ 21'n

D

Foam rheological constitutive equation3

εk

'k nn'

3Gardiner et al., Fire Safety J. 31 (1998)

Compressible medium)(f)(fP From bubble expansionFrom bubble expansion

density foamdensity liquid

Nozzle modelling - 4Nozzle modelling - 4

Boundary conditionsInitial conditions

Pressure= 800 kPa

Liquid mass= 250 gUn-dissolved gas mass= 2.7 g

Geometry

Dimensions [m] Nozzle N1 Nozzle N2

Total length (nozzle and actuator)

610-2 410-2

Nozzle diameter 410-3 610-3

Nozzle modelling - 5Nozzle modelling - 5Solution Method

Finite ElementsFEMLAB

Extra Fine Meshing

generation774 elements

Typical velocity field

Sample E5T=-5°C

Numerical Results - 1Numerical Results - 1Nozzle N1, Sample E5

P=8 atm; T=4°C

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 3 6 9 12 15 18 21time [s]

Resi

dual

mas

s [K

g]

Res. mass

EstimatedEstimated 37 g37 gExperimentalExperimental 27272 g2 g

0

200

400

600

800

1000

0 3 6 9 12 15 18 21time [s]

P [a

tm]

1 atm

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 3 6 9 12 15 18 21

Resi

dual

mas

s [K

g]

time [s]

Numerical Results - 2Numerical Results - 2Nozzle N2, Sample E7

P=8 atm; T=4°C

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 2 4 6 8time [s]

Resi

dual

mas

s [K

g]

Res. mass

EstimatedEstimated 3 g3 gExperimentalExperimental 27274 g4 g

Numerical Results - 3Numerical Results - 3Nozzle N1, different samples

P=8 atm; T=4°CRes. mass Empt.

time [s]

Overrun

55 g (22%)55 g (22%) 2020 72%72%37 g (15%)37 g (15%) 2121 74%74%28 g (11%)28 g (11%) 2222 74%74%

liquid

liquidfoam

VVV

Ov

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 4 8 12 16 20 24time [s]

Resi

dual

mas

s [K

g]

F1 F2 F3E3

E5

E7

Numerical Results - 4Numerical Results - 4Sample F3

Nozzle N1, different PT=4°C

Res. mass Empt. time [s]

Overrun

3 g (1.2%)3 g (1.2%) 88 74%74%60 g (24%)60 g (24%) 77 68%68%

110 g 110 g (44%)(44%)

55 56%56%

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 2 4 6 8time [s]

Resi

dual

mas

s [K

g]

800 kPa 600 kPa400 kPa

E7, Nozzle N2, different P,

T=4°C

0

200

400

600

800

1000

0 2 4 6 8time [s]

P [k

Pa]

1 atm

Numerical Results - 5Numerical Results - 5Nozzle N2, different samples

P=8 atm; T=4°CRes. mass Empt.

time [s]

Overrun

10 g (4%)10 g (4%) 88 72%72%2 (0.8%)2 (0.8%) 88 74%74%

3 g (1.2%)3 g (1.2%) 88 74%74%

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 2 4 6 8time [s]

Resi

dual

mas

s [K

g]

F1 F2 F3E3

E5

E7

Numerical Results - 6Numerical Results - 6Sample E7 (lowest freezing point)Nozzle N2, different TP=8 atm

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 2 4 6 8time [s]

Resi

dual

mas

s [K

g]

4°C -10°C

Res. mass

Empt. time [s]

Overrun

3 g 3 g (1.2%)(1.2%)

88 74%74%

10 g (4%)10 g (4%) 88 72%72%

and G=weak function of and G=weak function of TT

Rheological analysis related to “macroscopic” propertiesRelevant properties as function of ingredients“Suitable” emulsion selection

Formulation

ConclusionsConclusions

ProcessProcessSimplified fluid dynamic analysisSimplified fluid dynamic analysis

- Single bubble growth - Single bubble growth (evaluation of “local (evaluation of “local properties”: properties”: ))- Foam flow - Foam flow (evaluation of macroscopic data: P, flow (evaluation of macroscopic data: P, flow rate)rate)

ConclusionsConclusions

Simple model, sensitive to Simple model, sensitive to - change in formulation - change in formulation (F1, F2, F3)(F1, F2, F3) - operating conditions - operating conditions (P=4, 6, 8 atm, T=0°, -10°C)(P=4, 6, 8 atm, T=0°, -10°C)- Geometry - Geometry (N1, N2)(N1, N2)

Product performanceProduct performance- emptying time, residual liquid, overrun- emptying time, residual liquid, overrun

Determination of the proper conditions for each Determination of the proper conditions for each emulsionemulsion

TOOL USEFUL FOR INDUSTRIAL PROCESS/PRODUCT TOOL USEFUL FOR INDUSTRIAL PROCESS/PRODUCT OPTIMISATIONOPTIMISATION

Thank for your attention……

LaRIALaRIALaboratory of Rheology and Food Laboratory of Rheology and Food

EngineeringEngineering