membranes in bioprocessing: theory and applications

MEMBRANESIN BIOPROCESSING:

THEORY AND APPLICATIONS

Other titles in the Elsevier Applied Biotechnology Series

K. Carr-Brion (ed.). Measurement and Control in BioprocessingM. Y. Chisti. Airlift BioreactorsW. M. Fogarty/C. T. Kelly (eds). Microbial Enzymes and Biotechno-

logy, 2nd EditionT. U. R. Harris (ed.). Protein Production by BiotechnologyR. Isaacson (ed.). Methane from Community WastesA. M. Martin (ed.). Bioconversion of Waste Materials to Industrial

ProductsA. M. Martin (ed.). Biological Degradation of WastesE. J. Vandamme (ed.). Biotechnology of Vitamins, Pigments and

Growth Factors

MEMBRANES IN BIOPROCESSING:

THEORY ANO APPLICATIONS

Edited by

J. A. HOWELL

School of Chemical Engineering, University of Bath, Claverton Down, Bath, UK, BA2 7A Y.

V. SANCHEZ

Laboratoire de Genie Chimique et Electrochimie, Universite Paul Sabatier, 118 Route de Narbonne,

31062 Toulouse Cedex, France.

R. W. FIELD

School of Chemical Engineering, University of Bath, Claverton Down, Bath, UK, BA2 7A Y.

rm SPRINGER-SCIENCE+BUSINESS MEDIA, B.V

Fint edition 1993

© 1993 Springer Science+Business Media Dordrecht Originally published by Chapman & Hali in 1993

Softcover reprint of the hardcover 1 st edition 1993

ISBN 978-94-010-4954-2

Apart from any fair dcaling for the PU\}1oscs of research or private study. or criticism or review. as pemlitted umler the UK Copyright Designs and Patents Act. 1988. this publicat ion may not bc reproduced. stored. or transmitted. in any fOlm or hy any mcans. without the prior pennission in writing of Ihe publishers. or in Ihe case of reprographic reproduclion only in accoflblllce wilh the tenns of the licenccs is,uc<.l hy thc Copyright Licensing Agcncy in Ihe UK. Of in accordance with the Icnns of licenccs issued by Ihe appropriate Reproduction Rights Organization outside the UK. Enquiries conceming reproduction outside the temls statcd here should be sent to the puhlishers at the Glasgow address printed on this page.

llic publisher makcs no representation. express or implied. with regard to the accuracy of the iruonnation contained in this book and calmot accept any legal responsibility or liability for any elTors or omissions that may be made.

A catalogue record for Ihis book is available from the British LibralY

LibralY of Congress Cataloging·in-Public'ltion data

Membranes in bioprocessing: theory and applications/edited by I.A. Howell, V. Sanchez, R.W. Field.

p. cm.-(Elsevierapplied bio\echnology series) Includes bibliographical references and index. ISBN 978-94-010-4954-2 ISBN 978-94-011-2156-9 (eBook) DOI 10.1007/978-94-011-2156-9 1. Membrane separation

1. Howell, Iohn A. II. Sanchez, V. III. Field, R.W. IV. Series. TP248.25.M46M47 1993 660' .2842-dc20 92-20213

CIP

CONTENTS

List of Contributors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vll

1. Introduction1. A. HOWELL............................................. 1

2. Nature of MembranesM. MULDER............................................... 13

3. Transport Processes in Membrane SystemsR. W. FIELD....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

(Section 3.3.4. Mass transfer in pervaporation and itsmathematical description-H. STRATHMANN and R. M.McDONOGH)

4. Separation by MembranesP. AIMAR. 113

5. Design of Membrane SystemsJ. A. HOWELL............................................. 141

(Section 5.5. Case Study 1: Ultrafiltration of potable water-PoAPTEL and J.-L. BERSILLON) (Section 5.6. Case Study 2:Microfiltration of mycelial broth-Po CROCKER)

6. Fouling PhenomenaJ. A. HOWELL and M. NySTROM........................ 203

7. Flux EnhancementM. NYSTROM and 1. A. HOWELL. 243

8. Electrochemical Aspects of Microfiltration and UltrafiltrationW. R. BOWEN 265

9. The Use of Pervaporation in BiotechnologyH. STRATHMANN and R. M. McDONOGH.............. 293

Index 329

v

LIST OF CONTRIBUTORS

PIERRE AIMARLaboratoire de Genie Chimique et Electrochimie, CNRS, Universite PaulSabatier, 118 Route de Narbonne, 31062 Toulouse Cedex, France

PHILLIPE APTELLyonnaise des Eaux Dumez, 38 Rue du President Wilson, 78230 Le Pecq,France

JEAN-LUC BERSILLONLyonnaise des Eaux Dumez, 38 Rue du President Wilson, 78230 Le Pecq,France

RICHARD BOWENDepartment of Chemical Engineering, University College of Swansea, University of Wales, Singleton Park, Swansea, UK, SA2 8PP

PETER CROCKERHarwell Laboratory, Harwell, Oxfordshire, UK, OXll ORA

ROBERT FIELDSchool of Chemical Engineering, University of Bath, Claverton Down, Bath,UK, BA2 7AY

JOHN HOWELLSchool of Chemical Engineering, University of Bath, Claverton Down, Bath,UK, BA2 7AY

RICHARD McDONOGHSchleicher & Schvell GmbH, Hahnestrabe 3, J.if..3354 Dassel, Germany

MARCEL MULDERFaculty of Chemical Engineering, University of Twente, PO Box 217, 7500Enschede, The Netherlands

VII

viii List of Contributors

MARIANNE NYSTROMDepartment of Chemical Technology, Lappeenranta University of Technology, PB20, 43821 Lappeenranta, Finland

HEINER STRATHMANNFaculty of Chemical Engineering, University of Twente, PO Box 217, 7500Enschede, The Netherlands

Chapter 1

INTRODUCTION

1. A. HOWELL

School of Chemical Engineering, University of Bath,Claverton Down, Bath, UK, BA2 7A Y

1.1 WHAT IS A MEMBRANE PROCESS?

Every day over 20 million litres of brackish water are pumped out of theground near Jeddah in Saudi Arabia and passed through thin sheets ofcellulose acetate known as reverse osmosis membranes before being usedas part of the city's water supply. In St Maurice les Chateauneuf, Francethree million litres a day of ground water are ultrafiltered to supply thecity and on test sites in Australia settled sewage is being disinfected bybeing passed through microfiltration membranes.

Many of the foods we eat and beverages we drink have used membranesduring their processing. Orange juice can be concentrated by membranesto make a concentrate which retains more of the flavour than doesevaporation. Milk can be concentrated slightly by means of a membranebefore making a cheese in a process which produces no whey.

Gases rising from the ground in a waste tip can be piped away and thecarbon dioxide separated from the methane by a membrane processallowing the methane then to be used as a fuel, simultaneously savingenergy and reducing the greenhouse effect since methane is more effectiveas a greenhouse gas than carbon dioxide.

In all these processes materials are separated by a semi-permeablemembrane which allows the passage of one or more of the materials muchmore readily than the others. We have all observed that a toy ballooninflated by air or helium will slowly deflate over time. Graham in 1854also observed this and, being of a curious bent as are most scientists,decided to study the effect. He observed that some gases would leave theballoon faster than others. In each case the gases were diffusing throughthe rubber skin of the balloon due to the slight pressure difference between

2 J. A. Howell

the gases on one side and the other. Some diffused faster and as one mightexpect the light gas hydrogen diffused the fastest. A mixture of gases couldbe partially separated in this way.

In another classic experiment the French scientist the Abbe Nolletobserved in 1748 that if he stored a salt brine inside a pig's bladder andimmersed this in water the bladder would expand. This was more curioussince the solution inside the bladder was at a slightly higher pressure thanthe solution outside due to the tension in the bladder. What washappening? As most of us have already learned, this was osmosis with thewater being driven into the solution inside the bladder by its chemicalpotential gradient. This gradient of chemical potential is often called theosmotic pressure. This is not a good term since it implies that there is anactual hydrostatic pressure forcing the liquid through the membrane. Infact a pressure can be used to stop the natural diffusion down the potentialgradient.

If we set up such a cell as outlined in Fig. 1.1 we need a pump to providethe pressure, a cell to hold a membrane which is selective in that it willallow water to pass easily through it but will not allow salt to pass. Letsalt solution be on the upper side and water on the lower side of themembrane. If both sides are at the same pressure then water passes fromthe water side to the brine side. The salt is unable to cross the membrane.If the pressure on the brine side is now raised to equal the osmoticpressure no fluid flows. If the pressure is raised further to exceed theosmotic pressure then water will now flow from the brine side to the waterside separating the water and salt. This phenomenon is called reverseosmosis and is the basis of a large industry providing clean water frombrackish waters.

Retentote recycle Retentote...--_---'_--:::::"""Product

FeedTenk

Feed pump Recycle pumpMembrane Unit

Permeete

Fig. 1.1. Generalised membrane system feed and bleed.

Many membrane processes have now been developed and several ofthem share common features with the sketch in Fig. 1.1. They require asource of pressure; they circulate fluid across the surface of the membrane;the membrane is selective, preferentially passing at least one but not all ofthe components on the upstream side. The fluid may be a solution, a

Introduction 3

suspension, a mixture of gases or vapours. Not all the processes usepressure as the driving force and we shall therefore introduce the processesin common use in the biotechnology industries including pharmaceuticals,water and waste water, food and beverage as well as the major fermentation industries.

1.2 WHAT IS A MEMBRANE?

The difficulty of defining a membrane resides in the variety of uses towhich membranes can be put. In fact a simple definition may be the best.A membrane is a thin barrier between two fluids which restricts themovement ofone or more components ofone or both fluids across the barrier.A membrane may be made from a wide variety of materials, organic andinorganic, in asymmetric or isotropic form, in sheets or tubes, in thicknesses from 100 nm to over 1 mm in single component or composite form,with true pores or with regions of highly permeable solid material in a lesspermeable matrix. Polymeric membranes are discussed in detail in the nextchapter.

1.3 A LITTLE HISTORY

The use of membrane processes has been a relatively recent development in the process industries. Membranes were prepared commerciallyin the late 1920s for bacteriological laboratory use. These were symmetricmicrofiltration membranes. Large scale use did not become possiblefor reverse osmosis and ultrafiltration until asymmetric membranes wereprepared. In these membranes the resistance to permeation is concentrated in a very thin layer at the retentate side of the membrane.Sourirajan and Loeb in the early 1960s were able to synthesise anasymmetric cellulose acetate membrane by the phase inversion process.The technique is discussed in detail in Chapter 2 on membrane manufacture. Shortly after that time Michaels managed to make an asymmetric polyionic membrane for ultrafiltration and there was then awave of progress. Simultaneously gas separation membranes werebeing developed from polymer films following the pioneer work ofBarrer.

Microfiltration membranes used in a dead-end mode were verypopular for cleaning a variety of fluid streams and sterile filtration wasused widely from the mid 1960s. Electrodialysis was the first of themodern processes to develop a significant industrial base although it

4 J. A. Howell

subsequently grew more slowly than the others. Most of the earlyultrafiltration membranes were used in laboratories and industrial usedid not start becoming important until the end of the 1960s. Reverseosmosis was, however, developed much more rapidly thanks to aprogramme of demonstration projects by the U.S. Office of SalineWater. The boost which this gave to the nascent U.S. membrane industrywas extremely important in establishing them as the world leaders in thefield.

The 1970s saw rapid development spearheaded by the dairy industry forultrafiltration which bought many plants for whey protein concentration,and the electrocoat paint industry. Many new polymers were being testedand fundamental work was becoming increasingly intensive. Theoreticaldevelopments progressed in both pressure driven and gas separation fields.An increasing body of research literature was apparent. The Journal ofMembrane Science was started in 1973.

After some initial problems of poor membrane reliability manufacturerslearnt how to make robust reliable and reproducible products which thenbecame accepted by industry. Membrane lifetimes extended from monthsto years and modern R.O. membranes may last over 5 years (with a 5-yearperformance guarantee) and UF membranes over 2 years (with a 1-yearguarantee).

The beginning of the 1980s saw the announcement of commercial gasseparation by Monsanto who had been testing their Prism system on thefull scale for several years. Later in the decade Pervaporation wasintroduced and full scale plants built. The development was whollyEuropean and followed the pioneering work of Jean Neal.

The 1990s sees the membrane field with a whole variety of processes. Adivision of membrane manufacturing and use split almost three waysbetween Europe, the U.S.A. and Japan with the U.S. having the largestshare of the manufacturing. New membranes are being developed everyday. Companies are being bought and sold with great rapidity as theusually small membrane companies are traded between the chemicalindustry giants. It is likely that the end of the century will see a smallernumber of companies, a small number of well accepted membranes with atendency to move from organic to inorganic supports for the membraneswith a highly tailored surface to the membrane specific to the needs of theparticular process.

As with some of the above industries membranes will increasinglybecome the accepted separation technique for many processes. The displacement of former techniques will be due either to the quality of theproduct or to a reduction in energy.

Introduction

1.4 CLASSIFICAnON BY DRIVING FORCE

5

The major driving forces used in membrane processing are pressure, (P)activity, (a), and electrical potential (E). A thermal force, (T), is occasionallyused. These forces are of course all part of the chemical potential, (jl), thegradient of which can be written as

Vjl=RTVlna+ VwVP-SjVT-zFVE

The result of the gradients of potential are the generation of flux acrossthe membrane. For example, a pressure gradient gives a volumetric flux.A simple classification is given in Table 1.1. Sometimes the forcescouple together to produce a combined effect. Initially we shall notexamine the combined effects but review the major unit operations, briefly

Table 1.1Classification by Driving Force

Process

Pressure forcesMicrofiltration

Ultrafiltration

Reverse osmosis

ActivityGasSeparation

diffusionDialysis

Pervaporation

Membranedistillation

Facilitatedtransport

ElectricalElectrodialysis

Mechanism

Sieving0'1-10 11m

Sieving

Solutiondiffusion

Solution

Diffusion

Solutiondiffusion

Vapourpressure

Concentration

Charge andsize ofparticle

Membrane type Applications

Porous with Cell harvestingclarificationpores

Porous with Protein solution1-100nm concentrationpores Cell harvesting

Dense skin Desalting andasymmetric antibiotic

concentration

Dense skin Gas mixtureasymmetric separation

Microporous Salt removal0'1-10 11m from macro-pores molecular

solutionsDense skin Azeotropic mixture

asymmetric resolutionHydrophobic Desalination

microporesLiquid Removal of ions

membranes from solutionplus carrier

Ion-exchange Desalting

6 J. A. Howell

outline the mechanisms involved and give two examples of their use inbiotechnology.

Dealing with the simple principles for each type of membrane allowsus to introduce the nomenclature relevant to that group of operationsand also permits a basic understanding of membrane processes ingeneral.

1.5 PRESSURE DRIVEN MEMBRANE PROCESS

There are two types of pressure-driven filtration, dead-end and crossflow. Most of the membrane processes which we shall deal with in thisbook are cross-flow processes but there is a large amount of deadend microfiltration. In dead-end filtration the feed solvent to thesystem passes through the membrane which is the only exit from thefiltration chamber. A cake of retained material builds up on the surface of the membrane which restricts further flow. Cross-flow filtration causes the retained liquid to be circulated across the membranesurface.

1.5.1 Cross-flow

This is the rate at which the material flows across the membrane surfaceand is important as it generates a number of forces which tend to removethe deposited layers from the membrane surface thus helping to keep themembrane clean.

1.5.2 Transmembrane pressure

The transmembrane pressure is applied across the membrane. It is giventhe symbol tJ.P1m and must be distinguished from the cross-flow pressuredrop along the membrane control. The three measured pressures in asystem are generally the inlet pressure Pi> the retentate outlet pressure Pmand the permeate pressure, Pp'

There is a serious problem in assessing the effects of transmembrane pressure at high cross-flow pressure drops and low transmembrane pressure drops, especially with long modules. Pressuredrops vary with the process. In microfiltration they may vary froma fraction of a bar to 2 bar in conventional use, occasionally higherwith newer ceramic filters. In ultrafiltration the pressures rangenormally from about 2 to 10 bar, whilst in reverse osmosis they reachover 100 bar.

1.5.3 Flux

Introduction 7

This is the flow through the membrane. It is a velocity and is usuallyexpressed in micrometres s-1, Htres m - 2 h - 1, or U.S. gallons ft - 2 day - I,

It is also the measure of productivity of the membrane system based onthe size of the system which is directly related to capital. An alternativemeasure of productivity would be based on the energy input or runningcost.

1.5.4 Retentate

This is the solution or suspension retained by the membrane. It containsmaterial rejected by the membrane and also a considerable quantity ofmaterial that would not be rejected by the membrane but has not yet theopportunity to pass through it. In fact whilst materials rejected by themembrane will rise in concentration in the permeate under normalconditions non-rejected materials will still retain their original concentration in the feed unless diafiltration is carried out.

1.5.5 Permeate

This is the solution which has passed through the membrane.

1.5.6 Rejection coefficient

As the membrane is a separating device it is expected that some materialswill be rejected by the membrane and other materials transmitted. Ameasure of this performance is the rejection coefficient R.

R=l- Cp

Cr

Where Cr and Cp are the concentrations of cells in the retentate streamand the permeate stream respectively. It is likely that the rejectioncoefficient is not constant but changes with concentration of theretentate.

1.5.7 Diafiltration

Some of the material which is required to pass through the membranedoes not do so during a concentration of several fold. Thus, if possible, itmust be flushed through the membrane if high purities of retained productor high yields of permeating product are required. In order to achieve this,

8 J. A. Howell

pure solvent is added to the retentate and filtration proceeds until therequired purities or yields have been reached. This is very important inbiotechnology, especially for recovery of high-value proteins.

1.5.8 Membrane resistance

In the absence of cells or other constituents the membrane will offer aresistance to the flow of the solvent through it. This is the membraneresistance. It may be simply expressed as the ratio of transmembranepressure to flux. However, it is more usual to correct for the effects of theviscosity of the solvent passing through the membrane and thus the simpleratio above is divided by the viscosity. The membrane resistance maychange with use if it is fouled with particles lodged in the depths of thepores or solute adsorbed to the surface.

1.6 CONCENTRATION DRIVEN PROCESSES

1.6.1 Solution-diffusion

The major mechanism for concentration or activIty driven processes issolution diffusion. In this process the material which is to pass themembrane will dissolve into the polymer of the membrane. The dissolvedmaterial then diffuses across the membrane to leave solution on thedownstream side. Reverse osmosis, pervaporation, gas separation are threeprocesses where this mechanism is dominant. The membranes used in theprocesses are similar in concept comprising a macroporous structure onthe upstream surface of which has been deposited a very thin dense filmwhich possesses no open pores. Owing to the supporting membrane theselective layer can be very thin.

1.6.2 Permeability coefficient

The product of solubility coefficient and diffusion coefficient in theabove process is called the permeability coefficient and is given thesymbol P or Pg.

1.6.3 Plasticising

In many cases of multicomponent or binary gas separations the individualpermeabilities of the pure components are changed when the mixture isprocessed. This can easily occur if one of the components swells or

Introduction 9

plasticises the membrane creating greater opportunity for the other speciesto pass through the membrane. It is thus important when reviewing apotential separation to obtain data on the permeabilities of the components in a mixture and not rely solely on pure component data.

1.6.4 Separation factor

The ability of a membrane to separate two components is referred to asthe separation factor. It is defined as the ratio of the components in thepermeate to their ratio in the feed. It should be clearly understood that ahigh separation factor is absolutely necessary to obtain reasonably pureproducts. As the concentration of the most rapidly permeating species fallsin the feed material so it becomes progressively more difficult to remove it.

1.7 MEMBRANE SEPARATIONS: TWO EXAMPLES

The following two examples will illustrate some of the problems associatedwith obtaining pure products with membranes.

1.7.1 Diafiltration

A protein is being separated from 200 litres of a fermentation broth usinga microfiltration membrane. The protein is present at a concentration of0·5 gil and the cells at 5 gil. The highest concentration of cells which canbe readily filtered is 100 gil. It is desired that 99% of the protein berecovered.

(a) What is the minimum amount of water which must be added duringa diafiltration run in order to achieve this?

(b) How would this change if the average rejection coefficient for theprotein was 50%

(a) In concentrating the broth to 150 gil of cells and assuming the cellsare totally rejected by the membrane the new volume will be VI. A massbalance on the cells gives:

200 x 5= V x 100, thus V = 10 litres

In this 10 litres there will be 0·5 gil of protein or 5 g. Originally there was0·5 x 200 or 100 g and so a further 4 g of protein must be removed in orderto obtain 99% recovery.

If the rate of removal of liquid through the membrane is Q litres/hand the concentration of protein is c, a mass balance on the protein

10 J. A. Howell

in the retentate vessel can be calculated during diafiltration at constantvolume V.

dcV-= -Qc

dt

In order to go from 0·5 gil to 0,1 gil we must add Qt litres of water wherewe find Qt from integrating the above equation.

{0'5}Qt = 10 In 0.1 = 16·09

(b) If the rejection on average is 50% or the rejection coefficient is 0'5,then at the end of the first concentration will be Cr = 2cp from the definitionof the rejection coefficient.

A mass balance on protein after the first stage when there is 190 Iitresof permeate and 10 litres of retentate gives

190 cp + 10 Cr = 100.

Substituting for Cp we find Cr = 100/105 = 0·95 g/1.During diafiItration we must reduce this to 0·1 g/I but this time the

removal equation will be slightly different.

Vdc = _Qcdt 2 '

and integrating

{0'95}Qt = 2 x 10 x In OT = 45·03 Iitres

1.7.2 Gas separation

A mixture of methane/C0 2 (50: 50 by vol) is to be separated in a two-stagemembrane cascade. Fifty percent of the feed gas is passed through the firststage and 50% of that permeate passes through the second stage. Eachstage is to be considered well mixed on the retentate side. If the methane/C02 selectivity factor is 10, what is the composition of the finalproduct?

1st stage. Let mn mp, Cn cp be the retentate and permeate volumefractions of the methane and carbon dioxide respectively.

Assuming 100 m 3 of feed gas a mass balance on methane gives

50= 50 m,+ 50 mp so mp+m r = 1 (1.1.)

Similarly

From selectivity

But

Introduction

50 = 50 Cr + 50 C p

c=l-m

11

(1.2.)

(1.3.)

(1.6.)

Therefore substituting 1 and 3 in 2

mp/(l-mp)= 10(1-mp)/mp (1.4.)

Simplifying 9 m~-20mp+ 10=0 and solving the quadratic and requiringmp to be < 1 gives mp =0'76

In the second stage eqns (1.2) and (1.3) are retained but the mass balanceon methane equivalent to eqn (1.1) becomes

38=25m r +25mp so mr +mp=1'52 (1.5.)

Now substituting 3 and 5 in 2 we find

~= 10 l'52-mp1-mp mp-1'52

and the quadratic becomes

9 m~ +24'68 mp+ 15'2=0

leading to mp=0·93.The yield from the original methane was 76% in the first stage and only

46·5% after 2 stages.

1.8 COMMENTS

In both of the above examples it was difficult to obtain high yields andgood selectivity at the same time. Membrane processes can achieve highquality products in a single separation stage only if the separation factorsare very high. As the separation factors decline the problem of each stagebeing essentially a well stirred unit means that many units in series arerequired for good quality separation. Although stages in series are acceptable, such processes can be too expensive. The economics are morefavourable if it is the retentate which progresses from stage to stageacquiring a higher concentration in each stage. The methods of design ofcascade systems will be discussed in a later chapter.

12 J. A. Howell

Gas separation is of little importance in biotechnology but the inclusionof this example indicates that the problems are inherent in membraneprocesses generally. Diafiltration is of importance and will be consideredfurther in Chapter 4.

Chapter 2

NATURE OF MEMBRANES

MARCEL MULDER

Faculty of Chemical Engineering, University of Twente, Enschede, The Netherlands

2.1 INTRODUCTION

Separation and purification operations determine to a large extent the costof biochemical processing rather than the bioconversion itself. A numberof separation processes can be used of which (classical) filtration, centrifugation, extraction, adsorption, chromatography, precipitation, electrophoresis, crystallisation and membrane filtration are the most important ones. The application of membrane separation processes inbiotechnology is rapidly growing. Initially, mainly pressure driven processes like microfiltration, ultrafiltration and reverse osmosis were applied.However, new membrane processes such as pervaporation and liquidmembranes offer new possibilities in product recovery. In addition, thecombination of membrane separation and fermentation in a membranebioreactor leads to new concepts in bioengineering.

To determine the choice for a certain separation process the requirements for the application have to be specified first. Some specific featuresthat can be distinguished in bioseparations are:

The bioproducts must be recovered from very dilute aqueous solutions. Although the concentrations may be relatively high as in thealcohol, citric acid, and acetic acid fermentations (in the range ofmoles/liter), in the case of high value products, such as enzymes,antibiotics and vitamins, concentrations are considerably lower. Recovery and purification of these products is very expensive, especiallyin terms of energy consumption.A second characteristic is that a large variety of products are producedwhich results in tremendous separation problems. The various products differ very much in size and chemical nature. Beside suspended

13

14 M. Mulder

and colloidal solutes (e.g. yeasts, fungi, bacteria) a wide variety ofproducts are produced with different molecular weights, macromolecular solutes (e.g., proteins, polysaccharides, nucleic acids) and lowmolecular weight solutes (e.g., salts, saccharides, organic acids, aminoacids, antibiotics). Table 2.1 gives an overview of the range of dimensions.Bioproducts are very sensitive to temperature, pH, solvents, and shearrates. This means, for instance, that distillation, a technique frequentlyused in the chemical industry, cannot be used in bioseparations.The bioproducts are mostly high value products and separationtechniques are required that prevent product loss.

Table 2.1Apparent Dimensions of Small Particles, Molecules and Ions (Beaton, 1980)

Species

Yeasts and fungiBacteriaOil emulsionsColloidal solidsVirusesProteins/polysaccharides (mol. wt 104

- 106)

Enzymes (mol. wt 104-105 )

Common antibiotics (mol. wt 300-1000)Organic molecules (mol. wt 30-500)Inorganic ions (mol. wt 10-100)Water (mol. wt 18)

Range of dimensions(nm)

1000 -10000300 -10000100 -10000100 - 100030 - 3002 - 102 - 50·6-- 1·20'3- 0·80'2- 0-40·2

In order to isolate the bioproduct different separation tasks can bedistinguished:

concentration: the desired components, cells, etc. can be concentratedby removing the solvent;purification: undesirable impurities have to be removed;fractionation: a mixture can be separated in two or more desiredcomponents.

Membrane processes can be used to accomplish these basic separations.In addition, membranes can be used to enhance the biochemical conversion. Membrane processes offer some clear advantages in bioseparations:

separation can be carried out under mild conditions;energy consumption is generally low;separation can be carried out continuously;no additives are required;

Nature of Membranes 15

scale-up can easily be accomplished because of its modular structure;membrane properties are variable and can be adjusted;possibility of hybrid processing (combination of different separationtechniques).

There are also some clear drawbacks which should be mentioned:

- strong fouling tendency (especially in microfiltrationjultrafiltration);- low selectivity (for the recovery of a specific product).

Membrane processes make use of a permselective membrane to accomplish a certain separation. The nature of the membrane, i.e. themembrane material and membrane morphology, determines largelythe type and efficiency of a certain separation. In this chapter mainlythe nature of microfiltration and ultrafiltration membranes will beemphasised.

The preparation techniques of polymeric membranes will only bedescribed briefly. The build-up of a polymer chain strongly determinesthe chemical, thermal and mechanical properties. Factors which affect thestate of the polymer, such as chain interaction and chain flexibility,will be described. In addition, a list of polymers is given which arefrequently used in pressure driven processes. The choice of the membrane materials is described and it appears that the existing polymersare often not very suitable for application in bioseparations due tothe high fouling tendency. In order to improve the properties oftensurface modification techniques are applied to render the surfacemore hydrophilic. Some of these techniques will be described like thechemical reaction at the surface, plasma treatment, and adsorptioncoating techniques.

In the last part of this chapter the characterisation techniques willbe given which can be used for microfiltration and ultrafiltration membranes. Some of these methods will be evaluated critically. It will bediscussed that drying of the membrane may have a deleterious effecton the morphology. Therefore characterisation techniques using themembrane in the wet state are preferred and these techniques will beemphasised.

2.2 DEFINITION OF A MEMBRANE

A membrane can be considered as a permselective barrier between twophases. A schematic representation of membrane separation process isgiven in Fig. 2.1. Mass transport of a component across the membrane

16 M. Mulder

phase I membrane phase 2

o• 0 Ipermeate

oo

driving force~C,'~P, ~T, ~E

Fig. 2.1. Schematic representation of a two-phase system separated by a membrane.

occurs due to the presence of a driving force. The type of separation ismainly determined by the membrane morphology. Roughly, two types ofmembrane structures can be distinguished:

porous membranenon-porous membrane

A schematic drawing is depicted in Fig. 2.2. In porous membranes fixedpores are present. In order to avoid confusion the definition of pore sizesas adopted by the IUPAC (1985) will be used.

macropores, > 50 nm;mesopores, 2 < pore size < 50 nm;micropores, < 2 nm.

This means that microfiltration, ultrafiltration and nanofiltration membranes are porous membranes. Microfiltration membranes contain macropores (pore range::::: 0,05-5 ~m), ultrafiltration membranes containing

porous membranemicrotiltrlHion/ultrafiltration

polymer

• j.0 0 ()

°o 0 • 0

••0. 0o· o· 0o.

0.0 0 0

o • 0 Q ° 0• 0 • 0

nonporou membranegas separation!pervaporation

Fig. 2.2. Schematic drawing of a porous and a non-porous membrane.

mesopores (pore range~ 2-50 nm) and nanofiltration and reverse osmosismembranes containing micropores (pore range < 2 nm). The lattermembranes are in fact intermediate between porous ultrafiltration membranes and non-porous gas separation and pervaporation membranes.The term 'non-porous' is rather ambiguous because in the latter pores arepresent on a molecular level to allow transport. The existence of thesedynamic 'molecular pores' can be adequately described in terms of freevolume.

Separation in microfiltration and ultrafiltration is accomplished bymeans of a sieving mechanism. Microfiltration membranes are typicallyused to reject suspended solids (cells, cell parts) whereas ultrafiltrationmembranes, containing much smaller pores, are able to reject macromolecular solutes in the molecular weight range of about 103-106

. In thecase of nanofiltration the pores are so small that they are able to rejectmicrosolutes in the range of 200-1000 Da. These membranes are characterised by a rather low rejection for monovalent ions whereas divalent ionsare retained much better. Figure 2.3 gives an overview of the applicationof the pressure driven membrane processes in relation to the particle or

(nm)

10.000 <:: - Erythrocyte:>5000

.ei,- Cancer cell2- Saccharomyces"

~ (beer ferment).§ '" - Staphylococcus" 1000 0-e'-=

v - Tetanus2 500 E'-' - Shigella~

- Latex emulsion

100 • Oil emulsion

- Colloidal silica50 <::

0

g .ei,

2 - Japanese~

-;; encephalitis virus~

-::l

10 ~ - Polio virus~ - Hemoglobin

m''-'

- Pepsin

~m I

- Vitamin B 12.,. - Sucrose

! 0.5 .~ _Zn2+

~ . Na+ -OH-~ ~ -Hf) - C1-~ 0.2 =

~u"3

0.1c

1 nm = 0.001 !lID =10 A

Fig. 2.3. The application of the pressure driven membrane processes in relation to particleor solute size.

18 M. Mulder

solute size. The membrane morphology, as depicted schematically in Fig.2.2, is a simplication and only serves to illustrate the basic principles instructure, transport and application more readily. The morphology can beclassified further into a symmetric and an asymmetric structure, as shownschematically in Fig. 2.4. The thickness of symmetric membranes (porousor non-porous) ranges roughly from 10 to 200 11m. The mass transferresistance is determined by the total membrane thickness. A decrease inmembrane thickness results in an increased permeation rate.

I ymmetric I

]ULJO[cylindricalporous

porous

Iasymmetric I

homOReneous

~~~~~~_ loplayer

porous

....................................................~,-"""""'.",~ ....~,~....,..,

porouswith topJayer

~ dense skin layer

~porous membrane

Composite

Fig. 2.4. Schematic representation of membrane cross-sections.

A breakthrough in industrial applications was the development ofasymmetric membranes by Loeb and Sourirajan (1962). These consist of adense top layer ('skin') with a thickness of 0·1-0·5 11m supported by aporous sublayer with a thickness of about 50-150 11m. These membranescombine the high selectivity of a dense membrane with the high permeation rate of a very thin membrane. The resistance to mass transfer isdetermined to a large extent by the thin top layer.

Another type of asymmetric membrane is of a composite type. Incomposite membranes, the top layer and sublayer originate from differentpolymeric materials; each layer can be optimised independently. Generallythe support layer is already an asymmetric membrane on which a thin

Nature oj Membranes 19

dense layer is deposited. Several methods have been developed to achievethis such as dip-coating, interfacial polymerisation, in-situ polymerisationand plasma polymerisation.

2.3 PREPARATION OF MEMBRANES

A number of techniques are available to prepare synthetic membranes (see,for example Mulder, 1991; Klein, 1991). Some of these techniques can beused to prepare organic as well as inorganic membranes. The choice of thematerial limits the preparation technique employed. Table 2.2 summarises

Table 2.2A Survey of Materials for Commercial Polymer Membranes (Cabasso, 1981;

Kesting, 1985; Mulder, 1991)

Material

Polypropylene (PP)Polytetrafluoroethylene (PTFE)Polyvinylidenefluoride (PVDF)Cellulose nitrate (CN)Cellulose acetate (CA)Cellulose triacetate (CTA)Aliphatic polyamide (Nylon 6, Nylon 6,6)Aromatic polyamidePolysulphone (PSp)Polyethersulphone (PES)Polyimide (PI)Polybenzimidazole (PHI)Polyetherimide (PEl)Polyvinylalcohol (PVA)Polyacrylonitrile (PAN)Polyacrylonitrilejpolyvinylchloride copolymer (PAN-PVC)Polycarbonate (PC)Polyetheretherketone (PEEK)

Processes

MFMFMF, UFMFMF, UF, RO

ROMF, UFMF, UF, ROMF, UFMF, UFMF, UF, RO

ROMF, UFMF, UF

UFMF, UFMFMF, UF

the most important polymeric membrane materials used today in pressuredriven processes. The chemical structures of the listed materials are givenin the appendix. The preparation of inorganic membranes will not becovered and those interested are referred to a number of excellent articlesand textbooks.

A special class of polymers are the cellulosics. These are based oncellulose, a polysaccharide with 1,4-fJ-linked glucosidic linkages. Thechemical structure of cellulose is depicted in Fig. 2.5. Because of its regularlinear chain structure, cellulose is quite crystalline, and although thepolymer is very hydrophilic it is not water-soluble. This is because of the

20 M. Mulder

Fig. 2.5. The chemical structure of cellulose.

crystallinity and intermolecular hydrogen bonding between the hydroxylgroups. Cellulose (or regenerated cellulose) is mainly used as a materialfor dialysis membranes. Cellulose derivatives such as cellulose nitrateand cellulose acetate are used for microfiltration!ultrafiltration applications in particular. Despite their outstanding membrane properties, cellulose esters are very sensitive to thermal, chemical and biological degradation. To avoid such degradation, the pH must be maintained between 4and 6·5 at ambient temperature. In alkaline conditions hydrolysis occursvery rapidly. The cellulose derivatives were already used at the beginningof this century by various German investigators like Bechhold (1907),Zsigmondy (1918), and Elford (1931) and it is striking that these materialsare still used today. Other types of polymeric materials are the so-called'engineering plastics', like the polysulphones, polyimides, polyetherketonesetc. These are characterised by an improved thermal and chemicalstability.

Various methods can be used to process the polymers listed in Table 2.2into a required morphology. However, the choice of the method dependslargely on the choice of the polymer and on the morphology required.Microfiltration membranes may be prepared from a large number ofdifferent materials and Table 2.3 gives the main preparation techniquesand the effect of the preparation technique on the morphology. Most ofthe commercial (crossftow) microfiltration membranes are prepared byphase inversion techniques, either by immersion precipitation or bythermal induced phase separation. Microfiltration membranes show highsurface porosities which can range up from a few percentages to about80%. Only the membranes prepared by track-etch techniques show verylow porosities (lower than 10%).

Table 2.3Preparation Techniques for Microfiltration Membranes

Process Structure Porosity Pore sizedistribution

Sintering symmetric low/medium narrow/wideStretching symmetric medium/high narrow/wideTrack-etching symmetric low narrowPhase inversion asymmetric medium/high narrow/wide

The phase inversion process is the most versatile membrane preparationprocess. In this process the polymer is transformed in a controlled mannerfrom the liquid state (polymer solution) to the solid state. The process ofsolidification is the interplay between diffusion kinetics and solutionthermodynamics. A detailed description of the phase inversion process isbeyond the scope of this chapter and a detailed description can be foundin Mulder (1991).

The concept of phase inversion covers a range of different techniquesfrom which controlled evaporation, precipitation from the vapour phase,thermal precipitation and immersion precipitation are the most importantones. These four techniques are briefly summarised below. The basicconcept of most phase inversion processes is a ternary system consistingof polymer, solvent, and non-solvent, as depicted schematically in Fig. 2.6.Two regions can be distinguished, a one-phase region where all thecomponents are miscible with each other and a two-phase region wherethe solution is not stable and liquid-liquid demixing occurs. The initialcasting solution is a point somewhere in the one-phase-region and, byintroducing non-solvent, exchange of solvent and non-solvent occurs andthe composition shifts into the two-phase region where demixing occurs.

polymer

initial castingsolution

........_....;;..._---"L£,.e..te..~<.LoI:..L.oI:JC.LLLc..anonsolventsolvent (water)

Fig. 2.6. Phase diagram of a ternary system showing a one-phase region and a two-phaseregion (shaded area).

2.3.1 Precipitation by Controlled Evaporation (Bechold, 1907;Elford, 1931; Kesting, 1973)

This is one of the oldest techniques for preparing membranes and wasdeveloped in Germany in the early years of this century. A polymer isdissolved in a volatile solvent and a less volatile non-solvent. By evaporation (mainly the solvent evaporates) the polymer solution shifts to the

22 M. Mulder

demixing region (see Fig. 2.6) and finally phase separation occurs resulting in a porous membrane (microfiltration/ultrafiltration). Nitrocellulose (cellulose nitrate) membranes were prepared by this techniqueemploying a solvent mixture of ether and alcohol. By variation inether/alcohol composition a wide range in porosities and pore sizes wereobtained.

2.3.2 Precipitation from the Vapour Phase (Zsigmondy &Bachmann, 1918; Strathmann et al., 1975)

This method was also developed in the beginning of this century. Here thenon-solvent is introduced via the vapour phase. A polymer solution (in theearly experiments mostly cellulose nitrate was used as polymer) is cast asa film and placed in an atmosphere with water vapour. The water(non-solvent) diffuses into this film and finally demixing occurs resultingin a microfiltration/ultrafiltration membrane. Porosity and pore sizes canbe varied by the choice of solvent and the polymer concentration in thesolution.

2.3.3 Thermal Precipitation (Castro, 1980; Lloyd et al., 1988, 1991)

A polymer (e.g. polypropylene or aliphatic polyamides) is dissolved (in thecase of highly crystalline polymers above its melting point) and by coolingdemixing will take place. Three different demixing mechanisms may occur,:::rystallisation, binodal and spinodal demixing.

2.3.4 Immersion Precipitation (Strathmann et al., 1971;Koenhen et al., 1977; Reuvers et al., 1985; Wijmans et al., 1985;Reuvers & Smolders, 1987)

Most of the membranes used in microfiltration, ultrafiltration and assupport material for composite membranes are prepared by immersionprecipitation. Here, a cast polymer solution is immersed in a non-solventbath and again the composition shifts into the demixing region. Byperforming this process in a controlled way any type of morphology canbe obtained, from asymmetric membrane structures with a porous toplayer (microfiltration/ultrafiltration) or a dense top layer (gas separation/pervaporation).

Figure 2.7 depicts an asymmetric ultrafiltration polysulphone membrane. Figure 2.8 also shows an asymmetric membrane from modifiedPPO but in this case the top layer is a dense defect-free layer with athickness of less than 100 nm and suitable for gas separation.

Nature of Membranes

Fig. 2.7. Cross-section of an asymmetric polysulphone ultrafiltration membrane.

23

Polymeric ultrafiltration membranes are almost exclusively prepared byimmersion precipitation, resulting in an asymmetric membrane with a thintop layer supported by a porous support. The ultrafiltration membranesshow, compared to microfiltration membranes very low surface porositiesin the range of 0'05-1 %. Also nanofiltration and reverse osmosis membranes are prepared by phase inversion. Cellulose triacetatejcellulosediacetate and aromatic polyamides are still widely used in desalinationmembranes nowadays.

2.3.5 Interfacial Polymerisation (Cadotte, 1985; Petersen & Cadotte, 1990)

New methods have been developed to prepare membranes with improvedproperties. The most successful attempt is the development of compositemembranes (often the term 'thin-film composites' TFC is used) by interfacial polymerisation. This technique provides a method to deposit a thinlayer upon a porous support. The polymerisation occurs between two veryreactive monomers or pre-polymers at the interface of two immisciblesolvents. This is shown schematically in Fig. 2.9.

The support layer, which is generally an ultrafiltration or microfiltrationmembrane (Fig. 2.9A), is immersed in an aqueous solution (Fig. 2.9B)containing a reactive monomer or a pre-polymer, mostly of the aminetype. The film (or fibre) is then immersed in a second bath containing awater-immiscible solvent (Fig. 2.9C), e.g. hexane and toluene, in which

~ ~ ~ l: ~ ...

Fig.

2.8.

Sca

nnin

gel

ectr

onm

icro

grap

hsof

anas

ymm

etri

cm

odif

ied

PP

Om

embr

ane

for

gas

sepa

rati

on.

The

pict

ure

left

prov

ides

anov

eral

lvi

ewof

the

cros

s-se

ctio

n;th

epi

ctur

eri

ght

give

sa

mag

nifi

cati

onof

the

top

laye

r.

non-aqueousmedium

poroussuppon

~

~

~~

~~

Nature of Membranes

aqueousmedium----....,

compositemembrane

25

ABC D

Fig. 2.9. Schematic drawing of the formation of a composite membrane via interfacialpolymerisation.

another reactive monomer, often an acid chloride, has been dissolved.These two reactive monomers (i.e. amine and acid chloride) react with eachother to form a dense polymeric top layer (Fig. 2.9D). Heat treatment isoften applied to complete the interfacial reaction and to cross-link thewater-soluble monomer or pre-polymer. The advantage of interfacialpolymerisation is that the reaction is self-inhibiting by the passage of alimited supply of reactants through the already formed layer, resulting inan extremely thin film of thickness within the 50 nm range. Many reverseosmosis membranes and nanofiltration membranes are prepared by thistechnique.

2.4 STATE OF THE POLYMER

The choice of a material for membrane preparation is often basedempirically, i.e. membranes have been developed for a wide range ofapplications instead of developing a membrane for a certain class ofapplications, e.g. biotechnology. In order to develop tailor-made membranes the properties of a material and of the membrane preparedfrom this material must be studied in relation to the application. The stateof the polymer is very important relative to its mechanical, chemical,thermal and permeation properties. In addition, it does have an enormouseffect on surface effects such as adsorption and wettability. This lattereffect is of great importance in biotechnology since most of the soluteshave a large tendency to adsorption. Also the choice of cleaning agentwhich is necessary to clean the fouled membrane, is determined by thechoice of the polymer, e.g. polyamides are strongly attacked by chlorinecontaining cleaning agents.

26 M. Mulder

The state of the polymer is determined by a number of factors of whichthe most important ones are:

- chain flexibility- chain interaction

The chain flexibility, the ability to bend and rotate bonds in the mainchain, is determined by the character of the main chain (presence ofhetrocyclic or aromatic groups, saturated and unsaturated carbon bonds)and the presence and nature of the side chain and side groups. Also theinterchain interaction affects the flexibility of the chain, strong intermolecular forces reduce the mobility. The way the polymer chains are builtup determines to a large extent the properties.

The polymers can be roughly classified into glassy polymers andrubbery polymers (elastomers). When a non-crystalline (amorphous) polymer is heated, a temperature exists at which the polymer changes from aglassy to a rubbery state. Figure 2.10 shows the variation in the tensilemodulus E of a completely amorphous polymer as a function of thetemperature. The tensile modulus E is a characteristic parameter for agiven polymer and may be defined as the force F applied across an areaA ('stress') necessary to obtain a given deformation ('strain'). The unit ofE is N·m- 2 or Pascal (Pa).

rubberystate

logEglassystate I

lI -- _

T

Fig. 2.10. Tensile modulus E as a function of the temperature for an amorphous polymer.

Two regions can be distinguished in Fig. 2.10: a glassy state with a highmodulus and a rubbery state with a modulus, which is often three to fourorders of magnitude lower. The temperature at which transition from theglassy to the rubbery state occurs is defined as the glass transitiontemperature (Tg). At this temperature the thermal energy is just sufficientto overcome the restriction in rotation due to bulky side groups or toovercome the interactions between the chains. Many polymers, both glassyand rubbery, may contain crystallites and are called semi-crystalline. The


presence of the crystallites has a large effect on all kinds of polymericproperties. Crystallites act as physical cross-links and may greatly affectthe dissolution and the swelling of the polymers, i.e. they improve thechemical stability. For instance a material such as polyetheretherketone(PEEK) is chemically very stable due to the presence of crystallites. As aconsequence this material is difficult to process.

When a membrane material is used at elevated temperatures the glasstransition temperature is an important limit; the experiments must becarried out at temperatures significantly less than the glass transitiontemperature. Table 2.4 lists the glass temperature of some polymers whichare frequently used as membrane material. The presence of aromatic ringsin the main chain results in a rigid polymer with a high glass transitiontemperature (e.g. polyimides, poly(ether suIphone». A large number ofpolymers are semi-crystalline. For such polymers the glassy phase exhibitsthe same mechanical properties as would a completely amorphous polymer. However, in the rubbery state the mechanical properties will dependon the crystalline content of the polymer. Generally the modulus of asemi-crystalline polymer decreases as a function of temperature and thereis not such a large difference in the modulus at the glass transitiontemperature. As the stability of a polymer increases it generally becomesmore difficult to process. The two effects, stability and processability,oppose each other. Thus very stable polymers like polytetrafluoroethylene(teflon) are not soluble and cannot be processed by common preparationtechniques. In terms of membrane preparation, this means that the

Table 2.4Glass Transition TemperaturePolymers (Schouten & van der

Mulder, 1991)

Polymer

PolypropyleneNylon-6 (aliph. polyamide)Cellulose nitrateCellulose diacetatePoly(vinyl alcohol)Poly(vinyl chloride)PolyacrylonitrilePolytetrafluoroethylenePolyetheretherketonePolycarbonatePolysulphonePolyetherimidePoly(ether sulphone)Polyimide

of VariousVegt, 1987;

-155053808587120126145150190217230320

28 M. Mulder

polymer must be soluble in a more common solvent (the term 'normalsolvents' excludes for instance strong inorganic acids like sulphuric acidwhich are not very pleasant to handle and in addition often causespolymer degradation), in order to apply appropriate preparation techniques. An overview of a number of thermally stable polymers are givenin Fig. 2.11.

Flpmp polymm

F FI I

+C-C-+J J

polytenIJooroethylene

Amma'¥; polymm

polyphenylene polyether polyomide polyeot«

Hclemc)'Clic polymm

polyimide

I0QI8IOjc wlnna

oII H

;g:C.~1o ~- {}-N--c C

8 ~polyomideimide

polyphoophuenel polysilo......

Fig. 2.11. Overview of a number of thermally and chemically stable polymers.

2.5 CHOICE OF THE MEMBRANE MATERIAL

One of the main characteristics of bioseparations is the large variety offragile products. The commercial microfiltration and ultrafiltration membranes are not typically developed for bioseparations, i.e. many of themembranes used today do not contain the desired properties. Manypolymers are rather hydrophobic and very susceptible to protein adsorption and fouling. These aspects will be discussed later in the chapter onfouling. However, of relevance to this chapter are the several approaches


+o-@{-o-@-C--@-tSQ,H g

to render the membranes more hydrophilic and these will be describedbriefly,

using hydrophilic polymers or copolymerspolymer blends of hydrophilic with hydrophobic polymerssurface modification

2.5.1 Hydrophilic Polymers and Copolymers

The most logical way to obtain hydrophilic membranes is to use ahydrophilic polymer. Examples of these materials are the cellulosics.Another class of hydrophilic polymers are aliphatic polyamides (nylon-6,nylon-6,6, nylon-4,6, nylon-ll, nylon-12). A large variety of commercialmembranes are prepared from these materials. However, a disadvantageis their restricted chemical and thermal stability. Recently some newhydrophilic membranes have been developed based on more stable materials. These materials are intrinsically rather hydrophobic like polysulphone but by an appropriate chemical modification such as a sulphonation reaction the material can be made hydrophilic. As a result of thistreatment the polymers are still soluble in common solvents (DMF,DMAc) which enables membrane preparation by immersion precipitation.Sulphonation can be carried out by sulphuric acid, chlorosulphonic acidor by a SOrTEP complex.

CH, asoH?i.-f0-0-~-0-0-0-so, --01-':' i o-0-c-:0-0-0-so, -0}eH, CH, sO,H

PSp PSp-S03H

Since sulphuric acid may cause severe polymeric degradation the latter tworeagents are preferred. Another example of polymer modification beforemembrane preparation concerns polyetheretherketone (PEEK). This polymer has an extremely high chemical stability but is rather hydrophobic. Bypartial suIphonation a more hydrophilic polymer is obtained.

H,SO.--.

PEEK PEEKSO,H

Copolymers can also have very hydrophilic properties dependent on thecontent of the more hydrophilic part. Examples are ethylene-vinylalcohol(EVAL) and ethylene-vinylacetate (EVA). These materials are also used indialysis.

30

2.5.2 Polymer Blends

M. Mulder

Blending of two polymers, one to give the membrane sufficient chemicaland thermal stability, the other to render the membrane more hydrophilic,is another method to prepare more stable hydrophilic polymers. However,the choice of polymers is limited since only a few polymers are misciblewith each other. A survey of polymers that are compatible with each othercan be found in Krause (1978).

Polyvinylpyrrolidone (PVP) is a hydrophilic polymer (water soluble)which is compatible with a number of polymers, e.g. polysulphone (PSp),polyethersulphone (PES), polyimide (PI) and polyetherimide (PEl)(Roesink, 1990). In the case of complete mixing on a molecular level thematerial is called a homogeneous blend. Membranes from these blends(PVP/PSp or PVP/PES) can be prepared by phase inversion, sometimesfollowed by an appropriate post-treatment. Other examples are blendsfrom cellulose with other polymers such as polyacrylonitrile (PAN),polyvinylbutyrate and vinyl acetate-vinyl chloride which are soluble inaprotic solvents (DMF). Also in this case hydrophilic microfiltration andultrafiltration membranes can be prepared by phase inversion (Grinshpanet al., 1986).

2.5.3 Surface Modification Techniques

By means of surface modification the hydrophobic nature of a polymercan be changed into a more hydrophilic one. A number of surfacemodification techniques can be applied and will be discussed in thefollowing sections. These methods are in fact post-treatments of an existingmembrane which is mostly prepared by a phase inversion technique.Important surface modification techniques are chemical reaction, grafting,cross-linking, plasma treatment, in-situ polymerisation and adsorptioncoating. Much research on surface modification is carried out in researchlaboratories of membrane manufacturers, as is reflected by the number ofpatents on this subject. The objective of all these techniques is to obtain amore hydrophilic surface but sometimes, however, a modification of thestructure is also obtained. These are discussed in more detail in Chapter7.2.

2.5.3.1 Chemical ReactionModification of a hydrophobic surface into a more hydrophilic one by theintroduction of hydrophilic groups such as carboxylic, amino, hydroxylgroups or ionic groups, such as carboxylic, sulphonic and quaternaryammonium groups can be achieved by means of a chemical reaction. For


this purpose stable often hydrophobic membranes are used, such as PVDF(polyvinylidenefluoride) and PSp (polysulphone). For instance, ether oramine groups can easily be introduced onto a PVDF surface by reactionwith a hydroxyl group (R-OH) or a primary amine group (R-NH2) inthe presence of a strong base (NaOH) (Stengaard, 1988). A fluorine atom iseliminated from PVDF by the attack of the strong base and by reactionwith the reactive monomer the hydrophilic group is introduced. This isshown schematically below

NaOH+CF-CH2+-fcF2-CH2+ -R-OH I

OR

+CF2-CH2+ NaOH+CF-CH2+-R-NH2 I

NHR

Another example is the post-sulphonation of polysulphone membraneswhich can rather easily be performed by sulphuric acid or chlorosulphonicacid (see Section 2.5.1). Polysulphone can also be treated by a number ofother compounds. Examples are the surface fluorination (Le Roux et aI.,1992) and the reaction with propyleneoxide which results in hydroxylgroups at the polymer (Higuchi et al., 1990).

CH,OO

~H, • AICL, CH, -CH CH,

-£0-~-00-0-so, -G)-0J.. -. ...-t- t-Q-o-Q-so,-Q-lCH /0 ~,~ ~ ~

, CH, -clI-eH, CH,

2.5.3.2 Plasma TreatmentAnother very versatile method to modify the surface of a membrane is bymeans of plasma treatment (Stancell & Spencer, 1972; Yasuda, 1977, 1984;Kawakami et al., 1984). A plasma consist of electrons, ions, photons andneutral atoms or molecules. This plasma is very reactive and differenttypes of reactions can occur with a given chemical surface such asdeposition of a polymer layer, cross-linking, etching, degradation, andintroduction of specific groups (functionalising). In this way a number ofdifferent groups can be introduced depending on the type of discharge gasused and on the operation properties. Generally a plasma is created by anelectrical glow discharge of a gas. Often a noble gas such as helium orargon is used to initiate a plasma and a specific organic monomer is thenintroduced (or together with the gas) which will be polymerised resultingin a thin highly cross-linked polymerised layer on top of a porousmembrane. Because of the complexity of the discharge gas it is often

32 M. Mulder

difficult to know which chemical reactions occur and therefore reproducibility is one of the main problems. A simple plasma coating apparatus isshown in Fig. 2.12.

Many studies were aimed to develop reverse osmosis membranes(Yasuda, 1977, 1984), pervaporation membranes (Niemoller et al., 1988),and gas separation membranes (Stancell & Spencer, 1972; Kawakami etal., 1984). By the plasma polymerisation reaction a deposition of a plasmalayer is obtained using volatile organic monomers, such as vinyl andacrylic monomers. Introduction of specific groups can be achieved byusing as discharge gas NH 3 , N 2 and CO. A number of studies wereaimed to apply a plasma treatment to modify the surface of microfiltrationand ultrafiltration membranes (Wolff et al., 1988; Karakelle & Zdrahala,1989).

,..--------------0 Power,..- -<> supply

Tovacuum -----,pump

G115S/

VolltlleliqUid or

solid

Film Brlsselectrode

Fig. 2.12. Schematic drawing of a plasma-coating set-up.

2.5.3.3 Adsorption CoatingA very simple way to modify the surface is to coat the membrane with asurfactant or polymer by physical adsorption (Fane et al., 1985; Kim et aI.,1988). A number of different surfactants, ionic and non-ionic, as well assome polymers such as methylcellulose, polyvinylalcohol and polyvinylpyrrolidone have been applied. Since the solutes do not onlyabsorb at the surface but also in the pore a flux decline can be observedin the case of pure water as solvent. However, in the case of proteinsolutions the flux decline is less compared to the untreated membranebecause fouling is reduced. A drawback of this method is that anadditional chemical is added which is often unwanted in bioseparationsand other applications.

Nature of Membranes

2.6 CHARACTERISAnON OF POROUS MEMBRANES

33

Two different types of characterisation methods for porous membranescan be distinguished:

Characterising structure-related parameters:determination of pore size, pore size distribution, top layer thicknessand surface porosity.Characterising process (permeation )-related parameters:determination of the actual separation parameters such as flux andsieving properties by using solutes that are more or less retained by themembrane ('cut-off' measurements).

It is often very difficult to relate the structure-related parameters directlyto the permeation-related parameters because the pore size and shape arenot very well defined. The configuration of the pores (cylindrical, packedspheres) used in simple model descriptions deviate sometimes dramaticallyfrom the actual morphology, as depicted schematically in Fig. 2.13.Nevertheless, a combination of well defined characterisation techniquescan give information about membrane morphology which can be used as afirst estimate in determining possible fields of application. In addition, itcan serve as a feed-back for membrane preparation.

lOPt: lsubJayer

~IIIII

~lt~)~eon metion dead- end

porc

Fig. 2.13. Comparison of an ideal and the actual structure in the top layer of an ultrafiltration membrane.

In this section the permeation related methods will be emphasised sincethe relation between morphology and performance is more straightforward. Only the active pores are involved which are in fact the pores thatdetermine the performance. A number of characterisation techniquesavailable for porous media are summarised in Table 2.5. Some methodsuse dry membranes whereas other methods use wet membranes. Themorphology of a wet membrane may be different from a dry membranebecause capillary forces upon drying may damage the structure and often

34 M. Mulder

Table 2.5Overview of Characterisation Techniques for Porous Membranes (Cuperus, 1990)

Method

Electronmicroscopyscanning transmission field emission -

Solvent fluxmeasurements

Solute rejectionsmeasurements

Bubble-point methodCoulter porometryliquid displacement

Mercury porosimetryThermoporometry

Permporometry

Gas adsorptiondesorption

Characteristic

Pore size distribution ofcross-sectiontop layer thicknesssurface porosity

Hydraulic pore radiuspure water permeability

Membrane rejection'cut-off values'

Pore size distributionof active pores

Pore size distribution

Pore size distribution ofpore shape

Pore size distributionof active pores

Pore size distribution ofspecific surface area(BET area)

Remarks

Dry samples

Wetted sample

Wetted sample

Wetted sample

Dry sampleWetted sample

Sample changes fromdry to wetted to dry

Dry sample

the membrane shrinks considerably. In addition, swelling may occur in thewetted state and all these effects together result in a different morphologycompared to the dried state. Since the membranes are used in the wettedstate, characterization methods under these conditions are preferred.Therefore only those methods that measure a flux through a wet membrane will be described.

2.6.1 Permeability Methods

2.6.1.1 Liquid PermeationThe most widely used method in the characterisation of microfiltrationand ultrafiltration membranes is the determination of the pure water flux.If the pores are not too small transport through the membrane takes placeby convection rather than by diffusion. The flux is dependent on the poresize and pore size distribution, tortuosity and thickness of the active layer.Mostly models are used describing convective transport as a volume fluxproportional to applied pressure such as the Hagen-Poiseuille or CarmanKozeny equations

J = LpD.P/l (2.1)


For the Hagen-Poiseuille equation the hydraulic permeability is givenby

L p = nnr4/8rrr (2.2)

It can be seen that the flux is proportional to r4 which means that thelarger pores contribute disproportionately to the overall flux. However,the model cannot discriminate between a membrane with many smallpores and one with a few large pores. The convective flow through themembrane is also inversely proportional to the viscosity and the normalised solvent flux corrected for the viscosity should give the same valuesfor various solvents. This was demonstrated for different membranes andvarious solvents (Roesink, 1989; Beerlage et aI., unpublished) and anexample is given in Table 2.6. It can be seen that the normalised solventfluxes are in agreement with each other. One should be aware that swellingeffects might have a large influence on the solvent fluxes when a widevariety of solvents are used.

Table 2.6Solvent Fluxes Through Porous Polyimides Beerlage et al., unpublished

Solvent Flux J, " Normalised flux (J,''')(kg' m- 2. h - I • bar- I ) (cP)

Ethanol 120 1'125 135Hexane 681 0'303 206Toluene 248 0'581 144Acetone 513 0·315 162

2.6.1.2 Gas Flux MeasurementsAnother characterisation method is the determination of a gas fluxthrough a membrane. This method can only be applied to a dry membranebut it will be considered here because it is a permeability method measuring active pores. In addition, it is frequently used to obtain quantitativeinformation about the resistance of the sublayer in composite membranes.If the pores are larger than the mean free path length of the gas moleculethen the gas flux is linearly proportional to the applied pressure. Often thegas flow is determined at a certain pressure (e.g. difference of 1 bar). In thiscase, the ratio of permeability and effective membrane thickness can beobtained.

(2.3)

For UF membranes the values are generally in the range of1-10-2cm3·cm-2·s-1·cmHg-1. When the pore size of the membranebecomes smaller not only the viscous flow but also the diffusive flow must

36 M. Mulder

be included. In the microporous range (pore < 1 nm) surface diffusionmust also be taken into account and the description of the flow equationbecomes rather complex. However, for the rather open porous membranesthis is a very convenient method especially when the membranes are usedas sublayer for composite membranes.

2.6.2 Determination of the Relative Flux Reduction (RFR)

It is possible to prepare porous membranes from different materials with asimilar morphology. This means that measurement of the pure water fluxwould give approximately the same values. However, flux decline in actualprocess applications may differ substantially because of different surfacecharacteristics of the materials. It is known that adsorption of certainmacromolecular solutes (proteins, surfactants) at the membrane surface isan important element in membrane fouling. Adsorption already occursbefore pressure has been applied and the membrane process has beenstarted. As soon as the top surface of the membrane is in contact with the(macromolecular) solution, solute molecules will adsorb at the membranesurface due to physico-chemical interactions, e.g. hydrophobic interactions(dispersion forces), polar interactions (dipole-dipole and dipole-induceddipole forces) and charge transfer (hydrogen bonding). The nature of themembrane material, the type of solute, the solute concentration, and in thecase of proteins, the ionic strength and pH values are parameters thatdetermine the extent of adsorption. Adsorption occurs if the free enthalpychange ~G is negative

~G=~H - T ~S <0 (2.4)

The adsorption of proteins from an aqueous solution is mostly endothermic (~H > 0) which means that the adsorption is driven by an increase inentropy (~S> 0) (Norde, W., 1986). The increase in entropy is caused bythe desorption of water molecules from both the membrane surface andthe protein surface. This effect will be even stronger for hydrophobicsurfaces since the interaction between water and surface is quite low. Onthe basis of interaction forces one should expect a stronger affinitybetween proteins and polar surfaces since hydrogen bonding and polarinteractions are much stronger than hydrophobic interactions. It is goodto realise that this is not the driving force for adsorption. A very importantaspect is that the adsorption to hydrophobic surfaces (polyethylene,polypropylene, polytetrafluoroethylene) is irreversible whereas the adsorption on more hydrophilic materials (cellulose esters, aliphatic polyamides)is more reversible. Proteins can diminish their free enthalpy by a rearrangement on a hydrophobic surface which will lead to a strong interaction.

This gives a clear incentive to develop hydrophilic MF and UF membranes rather than hydrophobic ones, not only for the reduced sorptionbut also for the more effective cleaning.

The influence of the choice of the material on protein adsorption can bedemonstrated by a simple pure water flux measurement, often referred toas a relative flux reduction measurement (RFR) (Matthiasson, 1983; Aimaret al., 1986). After the pure water flux has been measured, the ultrafiltration membrane is immersed in a macromolecular solution (for instance a0'5-10% solution of bovine serum albumin (BSA) in water) for a certainperiod of time. Then the membrane is rinsed thoroughly with water afterwhich the pure water flux is measured again. The relative permeate flux(RF) is defined as RF=Ji/Jo, with Jo being the pure water flux beforeBSA adsorption and J 1 the water flux after BSA adsorption. The relativeflux reduction (RFR) is expressed as RFR = 1- RF. A small value of RFRmeans that protein adsorption hardly affects the pure water flux. Such amembrane has superior properties compared to a membrane with a muchhigher value of RFR. The method described here is a very simple anduseful method to compare various membranes and (surface) modifiedmembranes with each other. Figure 2.14 gives the relative flux reduction ofdifferently post-treated polyetherimide (PEl) microfiltration membrane asa function of the contact time in a 5 gil BSA solution (Roesink, 1989).

0.6

I • RF0.5

r 0.4

0.3

0.2

0.1

00 10 20

o

• Heal treatmento N.OCltre.bn<nt• Hell treatment aller

N.OCI tre.bnenl

30

Time (Hr)

Fig. 2.14. Relative flux reduction (1- RF) of pure water in post-treated PEl membranes asa function of contact time in a 5 gfl BSA solution (Roesink, 1989).

From Fig. 2.14 it can be seen that for each membrane after an initialsharp increase in flux reduction a kind of plateau value is reached whichfor some of these membranes already amounts to a pure water fluxreduction of almost 40%. The adsorbed BSA molecules are not removedby thoroughly washing with water which implies that more severe meansare required to clean the membranes.

38 M. Mulder

2.6.3 Permeation Related Methods Based on ModifiedBubble-Point Methods

The bubble-point method itself provides a simple means of characterisingthe maximum pore size in a given membrane. The method was used byBechold even in the early years of this century. The method essentiallymeasures the pressure needed to blow air through a liquid-filled membrane. The relationship between pressure and pore radius is given by theLaplace equation.

(2.5)

where rp is the radius of a capillary shaped pore and y the surface tensionat the liquid/air interface. Usually complete wetting is assumed whichmeans that e~0° and cos e= 1 (in practice the value of e lies between 0°and 90°, which means that cos e=1-1). The top of the membrane is placed incontact with a liquid (e.g. water) which fills all the pores when themembrane is wetted.

The bottom of the membrane is in contact with air and as the airpressure is gradually increased bubbles of air penetrate through themembrane at a certain pressure. The principle of the bubble-pointmeasurement is depicted schematically in Fig. 2.15. Penetration will firstoccur through the largest pores and since the pressure is known, the poreradius can be calculated from eqn (2.5).

Iliquid

_ membrane

o air

2r

Fig. 2.15. The principle of the bubble-point method.

This method can only be used to measure the largest active poresin a given membrane and has become the standard technique used bymembrane manufacturers to characterise their microfiltration membranes. Since the surface tension of water/air interface is high (72'3mN/m)only relatively large pores can be measured typically in the microfiltration range. Often iso-propanol is used as a liquid because also morehydrophobic surfaces are wetted and the surface tension is lower (about30mN/m).


For ultrafiltration membranes large pressures are required (more than~ 10 bar), and from eqn (2.5) it can be calculated that for a pore radius of0·1 J..lm and water as liquid a pressure of 14·5 bar is already required whichmay cause deformation of the membrane matrix. Therefore, the bubblepoint method can only be employed for microfiltration membranes(diameters larger than 0·2 J..lm).

The bubble-point method gives only limited information and anothermethod was developed that combines the bubble-point concept with themeasurement of the gas flow through the emptied pores. Here, at first, thegas flow is measured through a dry membrane as a function of the pressureand generally a straight line is obtained. Then the membrane is wet andagain the gas flow is determined as a function of the applied pressure. Atvery low pressures the pores are still filled with the liquid and the gas flow,which is determined by diffusion through the liquid, is very low. At acertain minimal pressure (the 'bubble-point') the largest pores will beempty and the gas flow will increase by convective flow through thesepores. A further increment in pressure will open smaller pores according tothe Laplace equation. At the highest pressure the gas flow of the drymembrane must be equal to the wet membrane. If this is not the case thereare still some smaller pores present in the membrane. The experimentalresult is depicted in Fig. 2.16. From the wet flow rate the pore sizedistribution can be determined.

flux

(cm3/s)

pressure (bar)

Fig. 2.16. Gas flux in the permeation related bubble-point measurement.

Another method similar to the 'bubble-point' method is the 'liquiddisplacement' method (Grabar & Niktine, 1936; Munari et ai., 1989). Sincethe interfacial tension water/air is relatively high very large pressures arerequired to open pores in the ultrafiltration membranes (pore diameters

40 M. Mulder

(2.6)

2-100 nm). By employing two immiscible liquids a much lower interfacialtension is obtained. For instance isobutanol/water has an interfacialtension of 1'85mN/m (at 20 D e) and the system water/isobutanol/methanolhas, at a certain composition, only an interfacial tension of O'35mN/m,which makes it suitable to characterise ultrafiltration membranes. Combination of this liquid displacement method with the permeation method, i.e.measuring the applied pressure and the flux simultaneously, makes itpossible to determine a pore size distribution of the membrane. At acertain pressure the liquid inside the largest pores will be displaced by thesecond liquid according to eqn (2.5) and the flux is measured. The fluxthrough these pores will increase with increasing pressure according to eqn(2.1) and a pore size distribution can be determined from the flux-pressurecurve (Munari et ai., 1989).

2.6.4 Permporometry

Permporometry is another permeation related method that can be appliedto determine the pore-size distribution of ultrafiltration types of membranes. This method is based on the blockage of pores by means of acondensable vapour, linked with the simultaneous measurement of gasflow through the membrane. The desorption out of the pores of thesecondensed liquids can be described by the Kelvin equation.

In ..f- = _ 2yV cos ()Po rk RT

Also in this method it is important that the interaction between membraneand organic vapour is small. The liquid should not swell the membranetoo much, because the pore sizes might change and erroneous results willbe obtained. Hence, the affinity of the vapour and the polymer must bevery low ('inert vapours') and also the vapour pressure should be readilyadjusted over the whole range. The choice of the organic vapour alsoinfluences the method in another way, because the thickness of the t-layer(adsorbed monolayer) is dependent on the type of vapour employed. Inorder to interpret the results correctly, the thickness of this t-layer has tobe determined (or calculated). During the experiment there is no differencein hydrostatic pressure across the membrane and gas transport proceedsonly by diffusion. The flow of one of the two non-condensable gases ismeasured (for example that of oxygen can be measured with an oxygenselective electrode). A schematic drawing of the experimental set-upemployed is given in Fig. 2.17. At a relative pressure Pr (Pr = p/Po) equal tounity, all the pores in the porous membrane (ultrafiltration) are filled with

Nature of Membranes

N2

+ °eman:~15+_~______ . 2

, membrane02 N+ 2elhanol

Fig. 2.17. Experimental set-up employed in permporometry.

41

liquid and no gas transport across the membrane occurs. On reducing therelative pressure, the condensed vapour is removed from the largest poresaccording to the Kelvin equation (eqn 2.6), and the diffusive gas flowthrough these open pores is measured. On reducing the relative pressurefurther, smaller pores become available for gas diffusion. When the relativepressure is reduced to zero, all the pores are open and gas flow proceedsthrough them all.

As a certain pore radius (Kelvin radius rk) is related to a specific vapourpressure (eqn 2.6), measurement of the gas flow provides informationabout the number of these specific pores. Reducing the vapour pressureallows the determination of the pore size distribution. During the measurement the relative pressure goes from unity to zero which implies that themembrane changes from a wet state to a dry state. In addition prior towetting the membrane has been dried already. The membrane morphologymay change very much during these transitions and the extent of theseeffects should be carefully considered. This can be done by determining thepure solvent flux and comparing this value with the calculated flux fromthe pore size distribution.

2.6.5 Molecular Weight Cut-off and Solute Rejection Measurements

In order to determine the rejection characteristics of ultrafiltration membranes many manufacturers use the concept of 'molecular weight cut-off'.The molecular weight cut-off (MWCO) is defined as that molecular weightat which 90% of the (macro)molecular solutes are rejected by the membrane. This parameter is extensively used now as being a quantitativecriterion of membrane rejection characteristics. However, it is better toconsider this parameter more critically. In this section some aspects of therejection of macromolecules will be discussed. Figure 2.18 gives a schematic comparison between a membrane with a so-called 'sharp cut-off'and a membrane with a 'diffuse cut-off'. Some factors must be consideredthat complicate the simple concept of cut-off: (i) the deformation ofpolymer chains induced by shear forces; (ii) concentration polarisation;

42

1.0

Rejection

0.5

M. Mulder

103 104

105

Molecular weight

Fig. 2.18. Rejection characteristics for a membrane with a 'sharp cut-off' compared withthose of a membrane with a 'diffuse cut-off'.

and (iii) molecular weight distribution. Since 'cut-off' values try to relatethe pore dimensions of the membrane to the size of the macromolecularsolutes in solution this aspect will be discussed first. A polymer in solutioncan be considered as a random coil. If there is a possibility of rotationabout covalent bonds in the polymer backbone there is a continuousmotion and in fact there is no well-defined shape. In solution the chain ismore coiled than stretched and therefore it is better to define coildimensions. The size of the coil can be described by the root-mean-squareof the end-to-end distance r of the chain <r 2 )o·s, the radius of gyration rg

or the Stokes-Einstein or hydrodynamic radius rho Figure 2.19 shows aschematic drawing of such a random coil with the end-to-end distance r.

Fig. 2.19. Schematic drawing of a random coil.

The conformation of the coil is determined by the length of the chain, theintramolecular forces, the type of solvent and the temperature. As themolecular weight of the chain increases the dimensions of the coil increasewith the square root of the molecular weight. The end-to-end distance isrelated to the radius of gyration and often expressed by

(2.7)

The radius of gyration can be determined experimentally by viscositymeasurements and light scattering.

The dimensions of a coil are also often expressed by the Stokes-Einsteinradius or the hydrodynamic radius rho For many polymer solutions thereis an empirical relation between the (bulk) diffusion coefficient Db and themolecular weight Mw.

(2.8)

where a and b are constants characteristic for a polymer and a solvent orclass of solvents. From the diffusion coefficient the Stokes-Einstein radiuscan be determined

(2.9)

If the empirical relations between the diffusion coefficient and the molecular weight have been determined the Stokes-Einstein can be determinedeasily. The radius of gyration and the hydrodynamic radius are within acertain ratio, 0'SS<rh/rg<0'80 (Tanford, 1961; Schmidt & Burchard,1982), which means that either one of the radii can be used to express thecoil dimensions. The dimensions are strongly dependent on type of solventand temperature. When the interaction of solvent and polymer increasesand with increasing temperature the radius of gyration increases and thecoil becomes more extended. In addition by decreasing the solvent poweror decreasing the temperature the coil becomes more compact and finallythis can result in phase separation. In the case of flexible polymers theintramolecular interactions are minimal and these polymers are able todeform under stress. In contrast to these flexible chains, proteins arecharacterised by strong intramolecular interactions (hydrogen bonding)and in many proteins there are covalent crosslinks between cysteine unitsof the various chains. The rotation of the bonds in the backbone is severelyhindered and this results in a stable globular structure with a ratherwell-defined radius.

Figure 2.20 shows the rejection characteristic of very dilute solutions ofa flexible polymer (polystyrene in toluene) as a function of the appliedpressure. The polymer concentration and the applied pressure must bevery low to avoid concentration polarisation. It can be observed that therejection of polystyrene decreases to zero with increasing pressure. Similarbehaviour was found for other flexible polymers, such as polyethyleneglycol, and polyvinylpyrrolidone and dextranes (Ngyen & Neel, 1983;Balmann & Nobrega, 1989; Meireiles et al., 1991). On the other hand, theflux increases linearly with pressure. This rejection behaviour can beexplained because of deformation of the linear molecules under stress. Inthe case of a very low shear rate (~P-+O) the polymer is still able to relax

44

100

retention(%)

M. Mulder

flux

Fig. 2.20. Rejection and flux of polymer solutions of a flexible molecule (polystyrene) intoluene (polymer concentration < I g/I). (Beerlage et aI., unpublished).

to its random coil conformation and a high rejection can be observed.With increasing pressure a critical flux value is reached where shear ratesat the pore entrance cause a chain deformation. Because of the shear-ratethe chain uncoils and snakes through the pore as has been illustratedschematically in Fig. 2.21.

" /

Fig. 2.21. Deformation of a flexible molecule caused by shear rates at the pore entrance.

By increasing the polymer concentration it can be observed thatpolymer molecules are rejected to a certain extent while the solvent fluxreaches a plateau value. This typical behaviour is caused by concentrationpolarisation and the performance is completely determined by the increased concentration of the retained macromolecules at the membranesurface and not by the membrane characteristics (pore distribution andporosity). This is depicted schematically in Fig. 2.22. Curve a gives the fluxand selectivity for a very dilute solution as a function of pressure similar tothe results given in Fig. 2.20. Curve b shows the behaviour at much higherconcentrations (~10 gil) clearly indicating that the flux is completelydetermined by concentration polarisation. A plateau value J 00 is reached

flux

100

retention(%)

pressure pressure

Fig. 2.22. Rejection measurement of solutions of flexible polymers (e.g. polystyrene) fordifferent concentrations. Curve a low concentration ( 10 gil). (Beerlage et aI., unpublished)

which is invariant on concentration. Solute rejection for membranecharacterisation should be considered with care. Two phenomena arestrongly involved, concentration polarisation and deformation of flexiblechains. For very low polymer concentrations (below the overlap concentration where the chains can be considered to be independent from eachother) the rejection behaviour is determined by the coil dimensionswhereas for higher concentrations the rejection is completely determinedby concentration polarisation. Thus, in case of a not-too-low concentratedsolution containirig two solutes with a large difference in molecular weight(for example, y-globulin, Mw = 150000) and albumin (Mw =69000), theseparation of the lower molecular weight solute is influenced by thepresence of the higher molecular weight component as a result of concentration polarisation. If the high molecular weight solute is retainedcompletely the boundary layer formed has a considerable influence on thepermeation of the low molecular weight solute. It is also possible that thesolute with the higher molecular weight blocks the pores. In addition,problems may simply arise from the fact that synthetic polymers have amolecular weight distribution. Also, here the rejection of the high molecular weight chains influences the separation characteristics of the lowmolecular weight chains.

2.6.6 Characterisation of Membrane Surface Properties

The reduction of the fouling potential of a membrane is a strong motive toprepare hydrophilic membranes rather than hydrophobic. This can beachieved by using hydrophilic polymers as membrane material or to applya surface modification to render the surface more hydrophilic. There is stilla problem to express hydrophobicityjhydrophilicity in a quantitative way.

46 M. Mulder

The hydrophilicity of a material can be described by the contact angle ofwater with that surface or in terms of the critical surface tension Yc. Themost widely used method to measure the contact angle of a liquid on asurface is a direct measurement of a sessile drop of the liquid on thesurface. Three cases can be distinguished as depicted in Fig. 2.23. In the lefthand drawing (Fig. 2.23a) the liquid is spread over the surface and wets thesurface. In this case the contact angle is zero (0=0). With water as liquidwe have in this case a very hydrophilic surface. In the second drawing (Fig.2.23b) the liquid is spread much less and the contact angle 0 lies between0° and 90°. The more hydrophilic the polymer the smaller the contactangle. Many polymers in contact with water will show such a behaviour.

~(a) (b) (c)

Fig. 2.23. Contact angles of a liquid droplet on a solid (non-porous) material.

In the third case (Fig. 2.23c) the liquid does not wet the surface and thecontact angle is greater than 90°. Hydrophobic polymers such as polypropylene (PP), polyethylene (PE), polyvinylidenefl.uoride (PVDF) andpolytetrafluoroethylene (PTFE) show this behaviour. A droplet in equilibrium with a surface can be described by Young's equation

1'1 cos o=Ys-Ysl

Zisman found for a homologous series of liquids

cos o=a-by,

(2.10)

(2.11)

The critical surface tension is defined as the surface tension at which thecontact angle approaches zero (complete wetting) or

Yc= lim 1'1(thO)

(2.12)

By measuring the contact angle 0 for two liquids or liquid mixtures (oreven better, a series of liquid mixtures) with known surface tension 1'1 andplotting the cos 8 versus the surface tension, the critical surface tension Ycis obtained by extrapolating to coso= 1 (8=0). However, in the case ofporous membranes the surface is not very smooth and large errors occurin determining the contact angle. In addition, due to capillary forces aliquid with a contact angle < 90° will penetrate into the pores of themembrane.


A method which can be used for the determination of the hydrophiliccharacter of a porous membrane is the 'sticking bubble method'(Keurentjes et ai., 1989). An air bubble is brought in contact with a surfacewhich is immersed in a liquid with a given surface tension YI' At a highvalue of Y. the bubble will adhere to the surface but by decreasing thesurface tension the adhesion ability becomes weaker. At a certain criticalvalue of YI the liquid wets the surface and the bubble will move from thesurface. In this case a surface tension of detachment (Yd) is determined andnot a critical surface tension Yc' The values are quite similar with adifference of about 2-4mN/m. This method is very simple and useful, butalso laborious, to determine the surface properties of porous membranes.

2.7 SUMMARY

The nature of membranes, the membrane material and morphologydetermines largely the type and efficiency of a bioseparation process. Inthis chapter mainly the membranes used in pressure driven processes havebeen emphasised. Since fouling dramatically reduces the flux the development of more hydrophilic but chemically stable polymers for membranepreparation is strongly favoured. In addition, post-treatment methodssuch as surface modification methods involving chemical reaction, grafting, plasma treatment or adsorption coating are also able to render themembrane surface more hydrophilic. A number of methods can beemployed to characterise the membranes obtained. Since the morphologymay alter considerably upon drying, wet characterisation techniques arepreferred involving the measurement of a flux, either gas flux or liquid flux.In the case of solute rejection measurement two effects may stronglyinfluence the results obtained, concentration polarisation and in the caseof flexible polymers, deformation.

NOMENCLATURE

c concentration (kg/m 3)

D diffusion coefficient (m2Is)J flux (m/s)k mass transfer coefficient (m/s)i membrane thickness (m)L p water permeability coefficient (kg/s' bar' m2

)

M w molecular weight (kg/kmol)Po vapour pressure (Pa)

48 M. Mulder

p saturation pressure (Pa)P pressure (Pa)R gas constant (llmol- K)R retention (-)RF relative permeate flux (-)RFR relative flux reduction (-)r (pore) radius (m)rk Kelvin radius (m)T temperature (K)V molar volume (m 3/mol)

Greek symbols:e porosity (-)p density (kg/m 3 )

1'/ viscosity (Pa -s)y surface tension (N/m)Yc critical surface tension (N/m)e contact angle (0)r tortuosity (-)

Subscripts and superscripts:b bulkf feedg gyrationh hydrodynamic

component iliquid

m membranes solidv volume

Nature of Membranes

APPENDIX

Chemical Structures of some Membrane Polymers

49

Cellulose

Cellulose acetate (CA)

Polyacrylic acid (PAA)

Polyacrylamide (PAAm)

Polyacrylonitrile (PAN)

Polybenzimidazole (PBI)

Polydimethylsiloxane(PDMS)

Polyetheretherketone (PEEK)

Polyethylene (PE)

l;C~H o.....,~OHOH OH

o 0 0-OH C~OH

i1C~~AC o~OAC

OR OR-0 0 0-

OAc C~OAc

-tC~-CH-tI

COOR

--E- CR, -CR -tI

CONH,

-tC~-IR-tCN

-E-O-@-o--@-~ --@-j-o

-tC~-CH, -t

50

Polyethersulphone (PES)

Polyhexamethylenedipamide(Nylon 6,6)

Polyimide(Kapton)

Polymethylmethacrylate(PMMA)

Poly m-phenylene isophtalimide(Nomex)

Polyphenylene oxide (PPO)

Polypropylene (PP)

Polystyrene (PS)

M. Mulder

+0-@-502 -@+o 0

H H II II-f-N -(CHJ, -N --C-(CHJ. -C~

o 0

+N~N-@-O-@+o 0

CH]

Polysulphone (PSp) +o-@-~-@[email protected]@+

C~

Nature of Membranes

Polytetraftuoroethylene (PTFE) f c~ -CF2 -t

Polyvinylacetate (PVAc) -f C~ -CH-tI

OCCHJ

II°

Polyvinylalcohol (PVA) -t C~ -CH -]-

IOH

Polyvinylamine (PVAm) +C~ -CH-t

INt!,

Polyvinylchloride (PVC) -E-C~ -CH-j-

ICl

Polyvinylideneftuoride (PVDF) -E- C~ -CF2-3-

Polyvinylpyrrolidone (PVP) +C~ -CH -j-ILJO

51

52 M. Mulder

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Ngyen, Q. T. & Neel, J. (1983). Characterization of ultrafiltration membranes.Part IV. Influence of the deformation of macromolecular solutes on thetransport through ultrafiltration membranes, J. Membr. Sci., 14, 111-28.

Niemoller, A., Scholz, H., Gotz, B. & Ellinghorst, G. (1988). Radiation-graftedmembranes for pervaporation of ethanol-water mixtures, J. Membr. Sci., 36,385-404.

Norde, W. (1986). Adsorption of proteins from solution at the solid-liquidinterface. Adv. Coli. Inter! Sci., 25, 267.

Reuvers, A. 1. & Smolders, C. A. (1987). Formation of membranes by means ofimmersion precipitation, part II. The mechanism of formation of membranesfrom the system CA/acetone/water, J. Membr. Sci., 34, 67.

Reuvers, A. J., van de Berg, J. W. A. & Smolders, C. A. (1985). Formation ofmembranes by means of immersion precipitation, part I. A model todescribe mass transfer during immersion precipitation, J. Membr. Sci., 30,2805.

Roesink, H. D. W. (1989). PhD Thesis, University of Twente.Roesink, H. D. W., Beerlage, M. A. M., Potman, W., van den Boomgard, T.,

Mulder, M. H. V. & Smolders. C. A. (1991). Characterization of new membranematerials by means of fouling experiments. Adsorption of BSA on polyetherimide polyvinylpyrrolidane membranes. Colloids and Surfaces, 55, 231.

Schmidt, M. & Burchard, W. (1982). Translation diffusion and hydrodynamicradius of an unperturbed chains, Macromolecules, 15, 1604-09.

Schouten, A. E. & van der Vegt, A. K. (1987). Plastics, Delta Press, Dordrecht,The Netherlands.

Petersen, R. 1. & Cadotte, J. E. (1990). Thin film composite reverse osmosismembranes. In Handbook of Industrial Membrane Technology, ed. M. C.Porter, Noyes Publications, Park Ridge, New Jersey, pp. 307-48.

Stancell, A. R. & Spencer, A. T. (1972). Deposition of ultra-thin coating from aplasma, J. Appl. Pol. Sci., 16, 1505.

54 M. Mulder

Stengaard, F. F. (1988). Characterization and performance of new types ofultrafiltration membranes with chemically modified surfaces, Desalination, 70,207-24.

Strathmann, H., Scheible, P. & Baker, R. W. (1971). A rationale for the preparation of Loeb-Sourirajan-type cellulose acetate membranes, J. Appl. Pol. Sci., 15,811-28.

Strathmann, H., Kock, K., Amar, P. & Baker, R. W. (1975). The formationmechanism of asymmetric membranes, Desalination, 16, 179-203.

Tanford, C. (1961). Physical Chemistry of Macromolecules, Wiley, New York.Elford, W. J. (1931). A new series of graded collodion membranes suitable for

general bacteriological use, especially in filterable virus studies. J. Pathol.Bacteriol.,34, 505-21.

Wijmans, 1. G., Kant, J., Mulder, M. H. V. & Smolders, C. A. (1985). Phaseseparation phenomena in solutions of polysulfone in mixtures of a solvent and anonsolvent: relationship with membrane formation, Polymer, 26, 1539.

Wolff, 1., Steinhauser, H. & Ellinghorst, G. (1988). Tailoring of ultrafiltrationmembranes by plasma treatment and their application for the desalination andconcentration of water soluble organic substances, J. Membr. Sci., 36, 207-14.

Yasuda, H. (1977). Composite RO membranes prepared by plasma polymerization. In Reverse Osmosis and Synthetic Membranes, ed. S. Sourirajan, NationalResearch Council of Canada.

Yasuda, H. (1984). Plasma polymerization for protective coatings and compositemembranes, J. Membr. Sci., 18,273.

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Chapter 3

TRANSPORT PROCESSES IN MEMBRANE SYSTEMS

R. W. FIELD


3.1 INTRODUCTION

The performance of membrane systems is determined by transport processes. These influence the three interdependent stages which involve: (a)convective and diffusive flows on the feed-side of the membrane; (b)permeation of material through the membrane; and (c) transfer of materialinto the permeate stream. Generally, consideration needs to be given onlyto stages (a) and (b), because the resistance associated with transfer intothe permeate stream is insignificant. Pervaporation is an exception. Forthis process, downstream pressure is of great significance, and thereforetransfer into the permeate stream needs to be analysed. The appropriateanalysis is presented in the pervaporation section. However, the processesassociated with the other two stages affect the efficiency of most membraneprocesses. The relevant transport equations are introduced in generalterms, and then applied to various membrane processes, for example,ultrafiltration, reverse osmosis and gas separation.

The next section will commence with an introduction to the concept ofconcentration polarisation and film mass transfer coefficients. After a briefreference to pulsatile flow, the discussion on surface renewal theories ofmass transfer concludes this section. Section 3.3 is concerned with permeation through the membrane. This divides principally into the development of equations for porous and non-porous membranes. The former cancontain either cylindrical pores with a narrow pore size distribution (e.g.track-etched membranes), a packed bed of submicron particles (e.g. silicabased microfiltration membranes), or a less well-defined tortuous path (e.g.asymmetric membranes produced by phase inversion). The latter arecommonly composite membranes as described in Chapter 2.

55

56 R. W. Field

In certain membrane processes there is significant coupling between theprocess transporting material to the membrane and the process of transport through the membrane. This can lead to conditions under which alimiting flux will exist. Relevant theories are included in section 3.5, whilstthe limitations caused by osmotic pressure are considered in section 3.4and towards the end of the chapter in the section on applications.

3.2 MASS TRANSFER AND MEMBRANES

3.2.1 Introduction

Fluid mechanical phenomena play an important and crucial role in theoptimisation of the mass transfer processes. It is self-evident that a consistentwell-founded transport model for each type of membrane process will provide arational basis for optimising the design and operation of the different membraneprocesses. Furthermore, attention should be paid not only to flow across themembrane but to flow into and through the membrane.

In a recent paper (Fane et aI., 1990) concluded that:

(1) For retentive UF and MF membranes, the strategies for minimisation of fouling are similar, namely, use of highly porous andisoporous membranes which are smooth and hydrophilic. Also,fouling is less and membrane recovery is easier for operation at lowto modest pressures and with low ionic strength solutions.

(2) For solute-permeable membranes, the passage of solute is alsofavoured by high porosity, iso-porosity and hydrophilicity. Similarly,low transmembrane pressure gives less flux decline, possibly because itproduces lower shear conditions within or near the membrane.

Although Fane et al. (1990) do not state directly that the flow field intoand through the membrane is important, porosity and transmembranepressure (which clearly affect the velocity field just above the membrane)were found to be influential. This will be considered later in Section 3.6.

Initially, the nature of the convective and diffusive flows on the feed-sidewill be addressed. Consideration is given to the nature of boundary layers,to the occurrence of mass transport boundary layers in membrane systemsand to models (e.g. the film model).

3.2.2 Concept of Concentration Boundary Layers

A boundary layer is that region within a fluid, adjacent to a surface,across which there is a significant change in velocity, concentration or

Transport Processes in Membrane Systems 57

temperature. Figure 3.1 illustrates typical hydrodynamic and mass transport boundary layers. Across the former there is transport of momentumand the velocity changes from the surface value of zero (no-slip) to thebulk (or main-stream) value. The mass transport boundary layer isthinner. The concentration change from wall concentration to bulk (ormain-stream) concentration occurs in the region immediately adjacent tothe wall. When the fluid is of uniform viscosity, this corresponds to aregion of constant shear rate, i.e. the velocity gradient (du/dy) is constant.The significance of this is discussed later.

~lainstream

Velocity profile

Concentration profile

Fig. 3.1. Velocity and concentration changes adjacent to the surface of the membrane.

A membrane can be considered to be a permselective barrier betweentwo phases. Figure 3.2 is a schematic representation of a semi-permeablemembrane which under the influence of an applied driving force preferentially passes component A. There is thus a convective flow of componentA to and through the membrane. Component B is also transportedtowards the membrane by the same convective flow. However, theconcentration of component B in the permeate is less than that ofcomponent B in the feed. Thus initially component B accumulates on thefeed-side of the membrane and its concentration on the face of themembrane increases above the bulk value. There is therefore a concentration gradient for diffusive back flow into the bulk on the feed-side. Atsteady-state, which is reached after a few seconds, the following equationsrepresent the relevant fluxes (flux is a vector with units of flowrate per unitarea):

convective flux of A through convective flux of Aboundary layer to membrane = through membrane (3.1)

58 R. W. Field

v - A

• B

Convective flow to and through membrane

v

v

v v• V

v

permeate

Fig. 3.2. Convective and diffusive flows perpendicular to the membrane surface. Note: (a)build-up of B at membrane surface and (b) reduced concentration of B in permeate.

(3.2)convective flux of Bthrough boundary layer =to membrane

convective flux of Bthrough membrane +

diffusive flux of Baway from membrane

The resultant concentration profile is illustrated in Fig. 3.3. Taking theconcentration at a general point within the concentration boundary layerto be C, assuming density to be constant, and applying eqn (3.2) to theelement shown, one obtains:

JC=JCp-D(dC/dy)

where D = diffusion coefficient of the solute.

(3.3)

cross-flow

• •

permeate

Fig. 3.3. Concentration polarisation. Note: concentration polarisation increases untilsteady-state thickness is reached.

If the thickness of the concentration boundary layer is taken to be {)c,

the concentration at y~ {)c is, by definition, the bulk concentration Cb •

Equation (3.3) is integrated between y={)c and the membrane surface (orwall) condition of C = Cm at y = o. Provided D is independent of soluteconcentration, this yields:

(3.4)

Transport Processes in Memhrane Systems 59

The term D/bc is a mass transfer coefficient. According to the theorypresented by Rautenbach and Albrecht (1989, pp. 78-81), it shoud beinterpreted as the mass transfer coefficient appertaining at zero flux. Asimilar analysis follows.

The mass transfer coefficient, k, for the concentration boundary layer isconveniently evaluated at the membrane surface, y = O. The net mass fluxaway from the membrane equals the mass flux towards the membrane aty=O less that which passes through the membrane. The driving force awayfrom the membrane is Cm - Cb. Hence

Also note that

k= J(Cm-C p )

Cm-Cb

(3.5a)

(3.5b)k(Cm-Cb )= -DddCI. y y=o

Although D is clearly related to the conditions appertaining at y = 0 (i.e. atthe membrane surface), k is a mass transfer coefficient that relates to theboundary layer as a whole. Nevertheless it will be affected by the flux andby variations in viscosity. It is distinguished from the value appertaining atzero flux, for which the symbol ko is used.

Equation (3.5a) can be rewritten as:

1- ~ = Cb-Cp

k Cm-Cp

Comparison of eqns (3.4) and (3.6) shows that

J1- k =exp{ -J/(D/bc)}

(3.6)

(3.7)

Rearrangement reveals the following exact and approximate solutions:

D/bc=J/ln{l +J/(k-J)}

=k-J

(3.8)

(3.9)

It is thus seen that D/bc approaches k in the limit of vanishing flux. At thiscondition the physical properties of the fluid adjacent to the membranewill approach those of the bulk fluid and so k-+ko. Also eqn (3.8) indicatesthat the overall mass transfer coefficient k must be greater than the flux, J.Of practical importance is the fact that eqn (3.8) can sometimes provide asimple method for calculating D/bc. For gas separation, pervaporation andreverse osmosis systems, k can be taken to be the value ko calculated from

60 R. W. Field

appropriate correlations. For ultrafiltration systems, D/oc should,whenever possible, be determined from experimental data using eqn(3.4).

For forced convection, the mass transfer coefficient k can be estimatedfrom the standard mass transfer correlations for forced convection. Thesecan be summarised as:

kdIi == Sh = f(Re, Sc, geometry, J.lm/J.lb) (3.10)

The mass transfer coefficient needs to be evaluated at the conditions appertaining within the boundary layer which vary from themembrane surface to the outer edge of the boundary layer. The oftenoverlooked parameter J.lm/J.lb has thus been included in eqn (3.10).Viscosity correction factors and specific correlations are included inthe Section 3.2.4. For the present we return to the matter of concentration changes in the region immediately adjacent to the membrane.

3.2.3 The Classic Concentration Profile

One of the dominant features of membrane processing is the well recognised effect of concentration polarisation. The flux of permeate throughthe membrane causes a convective flow of both permeate and retainedmaterial towards the membrane surface. The retained material close to thesurface is at a concentration greater than the bulk concentration, and so adiffusive back-flow is generated. Steady-state conditions are rapidly obtained; Howell and Velicangil (1982) have computed a time of no morethan a few seconds.

Analytically the concept of a small region of high concentrationfollows directly from the solution of eqn (3.3). For a general point,y, within the region 0 < y < oc, the concentration of the retained speciesIS:

(3.11a)

Taking k as D/oc this equation becomes

(3.11b)

According to eqn (3.11 b), concentration decreases exponentially from amaximum value of Cm at the membrane surface. The bulk value of Cb isreached at y = oc' This build-up of concentration in the region adjacent tothe membrane is known as concentration polarisation.

Exercise 3.1

Transporl Processes in Membrane Syslems 61

(a) The validity of eqn (3.4) is dependent upon two physical propertiesbeing constant. Name them.

(b) Cross-check the consistency of the above equations. Evaluate:

~~Iy=ousing eqn (3.11a) and combine with eqn (3.5b) to obtain eqn (3.5a).

(c) Show that the average concentration within the concentrationboundary layer, C, is given by:

If the membrane is perfectly rejecting (i.e. the solute is totallyretained), the concentration Cp = O. Show that under this conditionan alternative formulation for Cis:

Cb {exp(Jjk)-1}kjJ

3.2.4 Film Model

It can be argued that the solution of the full set of partial differentialequations governing fluid flow and mass transfer show that the variation of concentration with y is such that a uniform concentration isapproached but never reached. This implies that the concentrationprofile in Fig. 3.1 approaches but never actually attains a value of Cb .

However, it is clear that 99% of the concentration change occurs withina very narrow region next to the membrane. It is thus reasonable tomodel the concentration distribution on the basis that there is: (a) abulk of uniform concentration; and (b) a film on the membrane surface across which the concentration changes from the bulk concentration Cb to the wall/membrane surface concentration, Cm. Thismodel, which is known as the film model, was implicitly used in Section3.2.2.

Those not familiar with the concept of film heat transfer coefficients orfilm mass transfer coefficients should consult Field (1990a) or a standardintroductory chemical engineering textbook. Those wishing to compareand to study in depth the many correlations for mass transfer can consult

62 R. W. Field

Gekas and Hallstrom (1987). For a tubular system, eqn (3.10) is generallywritten as:

(3.12)

For a particular geometry and flow regime the indices a, b, f and g,together with E, are constants. The Reynolds number, Re( = dulv) will beless than 2000 if the flow is laminar. Under such conditions aspect ratio(Lid) is a factor, whereas for turbulent flow the Sherwood number isindependent of Lid (i.e. f = 0). The viscosity ratio will be effectively one forgas separations and pervaporation, but of significance for ultrafiltration.In particular it can influence the limiting flux (Section 3.5).

For non-viscous systems that operate under turbulent conditions, anappropriate correlation is the one due to Berger and Hau (1977):

Sh =0'0165Reo'86ScO'33 (3.13)

The diffusive flux of the rejected component away from the membrane is avital part of eqn (3.2). This flux will dominate the overall performance ofthe membrane if the resistance on the feed-side of the membrane issignificantly greater than the resistance associated with the transport ofmaterial through the membrane. Thus various attempts have been madeto improve mass transfer at the surface. One practical approach is theapplication of pulsatile flow.

Bellhouse et al. (1973) rejected the application of pulsatile flow by itselfas a means of improving mass transfer. Most of their work has concentrated on the development of membrane lungs for oxygen and carbondioxide transfer (Dorrington et al., 1985). These membranes consist of alarge number of small, part spherical dimples concave to the fluid channel.Alternatively they may be furrowed. Significant improvements in masstransfer were observed when these membranes were included in a pulsatilesystem.

They postulated that in steady flow, vortices form in the hollows butremain trapped there and little fluid exchange occurs between the vorticesand the mainstream. For effective mixing, they stated that the flow must bepulsatile and reversing. On flow reversal these vortices are ejected from thehollows and replaced immediately by a set of counter-rotating vortices. Itis the combination of vortex motion in the hollows and vortex ejectionwhich is thought to eliminate fluid boundary layers and augment masstransfer.

Mackley (1987) also looked at the combined effects of oscillatory flowand baffles on mixing. Flow reversal was again shown to be essential foreffective mixing. Under optimal conditions, the residence time distributionapproximated plug flow, and it was suggested that this type of system may


find applications in the membrane filtration field. This has been confirmedby the work of Finnigan and Howell (1989).

The coupling of pulsed flow (typically frequency is around 1 Hz) witheither baffles or a dimpled surface results in periodic removal of materialfrom the surface. The complex flow patterns (Fig. 3.4) in baffled systems givegood rates of surface renewal. This is also achieved in the rotating filterdeveloped by Sulzer AG, of Switzerland. The filter unit consists of twoco-axial cylinders to which membranes can be fixed. The inner cylinderrotates whilst the outer one is fixed. In the annular gap the rotation cancreate Taylor vortices. This secondary flow phenomenon gives good surfacerenewal. Under.these conditions a film model is inappropriate. In the future,researchers may well use the surface renewal model.

--._--- ----......--..- .._------------_...--------_...

TUIE=6 00

I:D~.'---_.>..._._------_._------_.__.~

Fig. 3.4. Fluid flow patterns in baffled tube with oscillatory flow.

3.2.5 Surface Renewal Model

The basis of these models is the periodic replacement of fluid at the masstransfer surface. Turbulent or other eddies are considered to replacematerial at the interface with fluid at the bulk concentration. Whilst thispacket of fluid is at the surface it is considered to be quiescent and of athickness that is relatively large, i.e. the concentration of the packet of fluidon the side not in contact with the interface remains unchanged as shownin Fig. 3.5. This model is frequently used for gas absorption modelling butis also used for predi\::ting heat and mass transfer from solid surfaces. The

64

membrane

R. W. Field

element in contact with membrane

concentration of this partof element does not change

L+---.......::=-------'

(3.14)

Fig. 3.5. Non-stationary diffusion into element for a limited period of time.

theory for the latter is given below but an understanding is not essential toan understanding of most of the remaining sections. Thus the theory maybe omitted by those seeking an overview.

During the period of contact with the surface (which is considered to beat a concentration Cm) diffusion away from the surface is governed by theunsteady state laminar diffusion equation:

oC = D02Cat oy2

where y is distance normal to the interface and t is the time elapsed sincethe packet arrived at the interface.

With a bulk concentration of Cb and an interfacial (membrane surface)concentration of Cm, which will be considered constant, the boundaryconditions are:

att=O C=Cb

for t>O C=Cm

for t~O C-+Cb

for all y,

on y=O

as y-+ 00

(3.15)

The above partial differential equation can be reduced to an ordinarydifferential equation by making the substitution, 1] = y/(4Dt)o'5. Thus eqn(3.14) becomes

d2Cjd1]2 +21]C = 0

C is only a function of 1]. The boundary conditions are:

for 1]=0 C=Cm

as 1]-+00 C-+Cb

Details of the solution of eqn (3.15) can be found in classic textbooks suchas Kay and Nedderman (1985). For a given time t, the rate of transport ofsolute away from the membrane can be shown to be:

(3.16)

Transport Processes in Membrane Systems 6S

Thus at time t the mass transfer coefficient is (D/nt)o,s. The average valueover a time interval from 0 to 8 is given by:

1 III {D}O'S {D }o.SK=- - dt=2-8 ° nt n8

(3.17)

Unlike the film model introduced in Section 3.2.4, the mass transfercoefficient, k, is predicted to be proportional to the square root of thediffusivity of the solute. Also, the single parameter, ~c, has been replacedby the single parameter, 8, which is the time of contact between the packetof fluid and the membrane surface. During this time of contact, theconcentration profile within the packet changes in the manner shown inFig. 3.6. The distance over which the concentration has been increasedincreases with time, and in the form of the model introduced here, thepenetration depth is assumed to be less than the thickness of the fluidpacket.

concentration

increasing time

increasing penetrationdistance

Fig. 3.6. Concentration profile as a function of time. Note: penetration distance is assumedto be less than the thickness of the element.

In the form of the surface renewal theory originally proposed by Higbie(1935), the time of contact of all fluid packets was assumed to be the same.This may be regarded as unrealistic. Danckwerts' (1951) model supposesinstead that the chance of an element of surface being replaced with a newfluid packet at bulk concentration Cb is independent of the length of timeof contact. The distribution of residence times is given by:

j(8)=s exp( -s8) (3.18)

i.e. the fraction of packets which have been on the surface for timesbetween 8 and (8+d8) is se- sll d8.

66 R. W. Field

The term s is the fractional rate of surface renewal, Le. the fraction of thesurface that is renewed per unit time. The dimensions are those ofreciprocal time. The average rate of transport away from the surface isobtained by determination of a mean value averaged over all elements.Their ages are between 0 and 00.

Ns= LX) Nss exp( -sO) dO (3.19)

=(Cm- CbHDs)OOS (3.20)

or

k=(Ds)OOS (3.21)

The distribution of residence times given by eqn (3.18) is not the onlyalternative to the Higbie assumption of a constant residence time. Someother distributions have been discussed by Davidson et alo (1959), Porter(1966) and Danckwerts et al. (1963).

In the field of membrane processes, the assumption of a constantmembrane surface concentration Cm has to be questioned if a surfacerenewal mechanism is to be assumed to be the physical process of backtransport. A modified version of the film-renewal model used by Lewis etal. (1982) is probably appropriate. In such a model, k, will be determinedby two parameters characteristic of the hydrodynamics.

3.2.6 Particle Diffusion

It might be thought that eqn (3.4) would be applicable to cross-flowmicrofiltration of particles. If all the material of interest is retained by themembrane, C p = 0, and eqn (3.4) simplifies to:

J =(D/<>c)ln(Cm/Cb)or (3.22)

J =:o:k In(Cm/Cb )

Following Porter (1972) and using the mass transfer analogues of the Graetzor Leveque solutions for laminar flow, and the Dittus-Boelter relationshipfor turbulent flow, one can estimate k from the following equations:

{UD2}0033

k= 1·62 dhL (laminar flow)

Oo8DOo67 { }0047k=0·023 U d~.2 ~ (turbulent flow)

(3.23)

(3.24)

where


L = channel length

dh = equivalent hydraulic diameter

4 x cross-sectional areawetted perimeter

and other symbols have their conventional meaning (as given in thenomenclature section). Fluid density and viscosity and particle diffusioncoefficient are assumed to be independent of concentration. An estimate ofparticle diffusion coefficient can be made using the Stokes-Einstein equation:

(3.25)

where kB= Boltzman constant = 1·380 x 10 - 23(JK - 1)T = absolute temperature (K)JJ. = viscosity (Pas)r p = particle radius (m)

With the above estimate for D, knowledge of the geometric arrangement, fluid velocity, density and viscosity, one can obtain estimates of kand hence predict values for the flux. However, for colloidal and particulate suspensions, the theoretical predictions are 1-2 orders of magnitudesmaller than experimental fluxes (Blatt et al., 1970; Porter, 1972). Forexample, Porter (1972) found that for a carboxylic modified styrenebutadiene copolymer latex (particle diameter = 0·19 Jlm), the measured fluxwas 38 times greater than the predicted flux.

Furthermore, the relationship between flux and cross-flow velocitydeviates substantially from that predicted by eqns (3.23) and (3.24). Forexample, Porter (1972) noted that for laminar flow exponents of 0·8-0·85have been found, which is over twice the predicted value of 0·33. Forturbulent flow the expected value is 0·8. However, values in excess of 1·0have been reported (Porter, 1972; Taddei et al., 1990).

The gross inaccuracy of the film model, which is reasonable forultrafiltration, suggests that Stokes-Einstein diffusion is not the only backtransport mechanism. Several explanations have been offered. In a recentcomprehensive review by Lojkine et al. (1992) the proposed explanationshave been classified into four groups:

(a) enhancement of the particle back transport by lateral movementdue to the laminar velocity profile ('tubular pinch', Porter, 1972;Green & Belfort, 1980);

68 R. W. Field

(b) enhanced particle diffusion, arising from particle interactions in ashear gradient ('shear-induced diffusion', Leighton & Acrivos,1987a; Zydney & Colton, 1986);

(c) longitudinal movement of particles along the membrane ('flowingcake', Leonard & Vassilieff, 1984); and

(d) 'scouring' of the membrane by suspended particles (Fane et aI., 1982).

3.2.6.1 Tubular Pinch in MicrofiltrationParticles suspended in a fluid undergoing laminar flow move across thefluid streamlines, perpendicular to the direction of flow. The movementmay be directed towards the axis or the wall; the direction depends uponthe relative densities of fluid and particles, and the position of the latterrelative to the walls and axis of the tube or channel.

A comprehensive review of experimental and theoretical work ontubular pinch (Brenner, 1966) confirmed that for single particles and dilutesuspensions it is generally found that:

neutrally buoyant rigid spheres migrate away from both the walls andthe axis, becoming concentrated in an annular region at about 0·6 tuberadii from the axis;for other particles, those that move at a slower velocity than the net flow(i.e. negatively buoyant spheres in upflow and buoyant spheres indownflow) are displaced towards the axis. For particles that move at agreater velocity than the net flow there is displacement towards the walls.

Those familiar with the movement of bubbles in an aerated column maybe surprised by the last sentence; in bubble columns the buoyant bubblestend to converge towards the centre of the column. The observations ontubular pinch are thus not applicable across a wide spectrum of flowregimes. Indeed, Cox and Brenner (1988) placed a severe restriction upontheir analysis. The tube Reynolds had to be significantly less than 1·0.

Porter (1972) was the first to suggest that tubular pinch might beapplicable to microfiltration. Subsequently, Green and Belfort (1980)developed a microfiltration model incorporating lateral migration. Thework of Altena et al. (1983) suggests that the motion of submicron sizedparticles is principally governed by convection, whereas particles sizedover 1 J.l.m are mainly affected by inertial forces.

Altena and Belfort (1984) have discussed some of the problems oftubular pinch theory:

the analyses do not apply close to the wall;non-hydrodynamic forces such as gravitational forces and electrokinetic effects are ignored;

(3.27)

the restrictions on Reynolds are not met;particle interactions are ignored.

Despite these problems with the theory, there is experimental evidence of thephenomenon of a lift away from the surface even in concentrated solutions.When concentrated suspensions of particles are made to flow in a tube, aparticle free zone or 'plasmatic' layer is observed near the wall of non-poroustubes. Formation of a plasmatic layer has been observed with rigid spheres(Karnis et al., 1966), blood (Porter, 1972) and spirulina (Rakow et al., 1987).Ofsthun and Colton (1987) also obtained a cell free zone adjacent to amembrane under conditions of zero transmembrane pressure. However,when a positive transmembrane pressure was applied to obtain filtration, alayer of close-packed cells was visible adjacent to the membrane surface.

3.2.6.2 Shear Diffusion in MicrojiltrationUnlike tubular pinch effects, shear induced diffusion is considered to be aparticle-particle phenomenon. The diffusion coefficients for the lateraldispersion of particles in a slurry undergoing linear shear flow were firstmeasured by Eckstein et al. (1977). For small, rigid, neutrally buoyantspheres and discs suspended in a viscous oil, they found that:

DI(r~y)=O'I<p for 0< <p <0·2 (3.26)

and

DI(r~y)~0'025 for 0'2<<p<0'5

where r p = particle diametery = shear rate of fluid<p = volumetric particle concentration.

Leighton and Acrivos (1987a) have made a useful distinction betweenself-diffusion, which takes place in suspensions of uniform concentration,and diffusion in the presence of a concentration gradient. Leighton andAcrivos (1987b) suggested that interparticle interactions are responsible forthe drift; particles experience more interactions on the high concentrationside, and so receive a net impulse which displaces them towards the lowconcentration side.

Leighton and Acrivos' analysis confirms that the diffusion coefficientsare proportional to yr~. However, they dispute the concentration dependency of Eckstein et al. (1977). In their experiments they found a dependence of DOC<p2 for dilute suspensions, and in their 1987a paper theyestimate diffusivities from:

D~0'33yr~<p2(1 +0·5 exp[8'8<p])

for particle concentrations of up to 50% v/v.

(3.28)

70 R. W. Field

Zydney and Colton (1986) compared experimental data for microfiltration with predictions from various models. Good agreement was foundwith a version which incorporated shear diffusion. This model, which wassuperior to the three that incorporated tubular pinch effects, incorporatedthe Eckstein et al. equation for D, and an expression of their own for be'Their equation for flux was:

(3.29)

3.2.6.3 Flowing Cakes and Scouring ModelsSeveral workers, including Blatt et at. (1970), Fane et al. (1982), Fischerand Raasch (1986), Leonard and Vassilieff (1984), and Rautenbach (1988),have suggested that particles may roll or slide along the membrane.However, apart from Fane et at. (1982) and Zydney and Colton (1986),there has been relatively little testing of models based upon a flowing cakeor a scouring effect. Nevertheless these models do recognise that the cakeformed by the accumulation of particles on the surface may not becompletely stagnant. Such an observation should be taken into accountwhen comparing the results of, say, latex particles and cells of about thesame size. Both cakes might behave as Bingham plastics, but one wouldexpect the yield stress of the former to be significantly lower.

Exercise 3.2

For a tubular ultrafiltration filtration system of the following dimensions, estimate the mass transfer coefficient, k, for a range of Reynoldsnumbers. It may be assumed that eqn (3.23) applies below Re = 2000,and that eqn (3.24) applies above Re=4000. It may be assumed that thephysical properties of the solution are those of water with the value of Dbeing 10- 10 m2 S-1.

Diameter of tube = 10 mmLength of tube = 500 mm

3.3 PERMEAnON THROUGH MEMBRANES

3.3.1 Introduction

If the membrane is porous, and electrical effects are absent, the mechanismis simply convective, i.e. the transmitted species flow through the mem-


brane with the driving force being the transmembrane pressure difference.Most members of the membrane research community consider that nonporous or dense membranes transmit species on the basis of a solutiondiffusion mechanism. These very different mechanisms will be introducedseparately.

3.3.2 Convective Flow of Solvent through Porous Membranes

A few membranes such as the microporous Anopore membranes, whichare formed by an electrochemical method, can be considered to havecylindrical pores as shown in Fig. 3.7. If these pores are of diameter d andlength 1, the standard Hagen-Poiseuille equation for the calculation ofpressure drop can be used. For laminar flow through a tube this takes theform:

(3.30)

If the free area in the membrane surface were e, the average velocitywould be JIe. Taking J as 500 1m - 2h - 1 (i.e. 140 Jlm s-1), e= 0,2, 1= 15 Jlmand d=0·2 j.tm, a typical value for the pressure drop would be:

32xl0- 3 x 140~.~0-6 X{0~;2 xI06}pa

=8400 Pa

~0'1 bar

This low value clearly illustrates that for this type of membrane the mainresistance to flow, during normal operation, is not the membrane itself.

Top layer consists of roughly equal~ sized cylindrical pores

E?~~~89~9~98~~H~[j 'J V[IW~ ~~WWfJW~W

/porous substructure

Fig. 3.7. Schematic representation of porous membranes of the simplest type.

The variation of flux with operating conditions is given by a rearrangement of eqn (3.30), namely:

(3.31)

72 R. W. Field

where J.l is the viscosity of the permeate and ~p is the pressure differenceacross the membrane.

The voidage can be related to the number of pores per unit area and eqn(3.31) can be rewritten as:

J= Nnd4~p

128J.l1(3.32)

where N = number of pores per unit surface area.This modelling of the pores as straight cylindrical capillaries was

challenged by Velicangil and Howell (1980) who claimed that the effectiveskin thickness of certain membranes was of the order of the pore diameter.Under such conditions it is appropriate to suggest that the pore behaves asan orifice. They proposed that:

(3.33)

(3.34)

Most porous membranes have, however, a more tortuous structure, withblind passages and a range of channel dimensions. A reasonably realisticapproximation to this structure is a packed bed of particles. This suggeststhe use of the Carman-Kozeny equation. The flow of the permeate islaminar and the relevant equation simplifies to:

e3 ~p

J= KS 2J.l1

where K is a dimensionless constant that was initially taken to have avalue of 5, but which in practice has been found to be dependent uponpore structure, and S is the surface area of the particles per unit volume ofthe bed.

For low voidages, K is close to 5. With this value and the crudeassumption of spherical particles, it will be instructive to rework the abovecalculation. Firstly a relationship between S and particle diameter isdeveloped.

For a packed bed of uniform solid particles with an equivalent diameterof dp and a shape factor A, the volume of each particle is nd~/6, andtherefore:

number of particles per unit volume=(1-e)/nd~/6)

Now S = no of particles x surface area of each particle:

(3.35)


(3.36)

The equivalent diameter of the pore space depends upon the packing, butan approximate value for the diameter of the pores is dp /6. Thus, signifyingthe equivalent pore diameter as dh and putting J.. = 1 (which would be exactfor spherical particles):

S~6(I-e)/dp

~(I-e)/dh

Using a voidage of 0·2, and taking the equivalent diameter of the porespace to be 0·2 Jlm, the value of Sis:

0·8S= 0.2

= 4 Jlm - 1 = 4 x 106 m - 1

Taking the same flowrate as before the estimated pressure drop through a15 Jlm bed with the above specific surface area is given by:

~ KS2/l1e

=(140 x 10- 6/0.2 3) x 5 x (4 X 106)2 x 10- 3 x (15 x 10- 6 )

=21000 Pa=0,21 bar

Once again a low value is obtained which confirms that membraneresistance can be expected to be small.

It is noted that for spherical particles (J..= 1) one can combine eqns (3.34)and (3.35), and with K = 5, the flux-pressure drop equation takes the form:

e3d 2 tJ.pJ= p

180(1-e)2/l1

In some textbooks this is labelled as the Carman-Kozeny equation.However, it should be remembered that eqn (3.36) only applies to laminarflow through a bed of equally sized spherical particles. Whilst thedimensions of membrane structures will ensure that liquid is in laminarflow, the structure will generally differ significantly from one which can berepresented by an assembly of equally sized spherical particles. Wheneverpossible accurate values of S should be obtained and use made of eqn(3.34).

The complicated topology of most membranes has delayed the development of realistic quantitative models. However, eqns (3.31) and (3.34) canbe used for qualitative purposes, such as the elucidation of trends. Withregard to the relationship between flux and pressure difference, both

74 R. W. Field

equations predict a linear relationship. This is indeed found to be so foralmost all membranes. (An exception is found in the case of certaininorganic membranes at high pressure - see Section 3.5.2.) Higher operational temperatures give an increase in flux and this can be attributed tothe decrease in viscosity with increasing temperature.

Exercise 3.3

The above calculations used dimensions which were characteristic ofmicrofiltration membranes. Repeat the above calculations using thesmaller dimensions of ultrafiltration membranes. Do you predict waterfluxes that are similar, an order of magnitude smaller or several ordersof magnitude smaller? Are your estimates similar to those obtained inpractice?

3.3.3 Permeation Through Non-porous Membranes

The solution-diffusion model will be introduced by considering the transport of gas across a membrane. If the concentration of gas on theup-stream side, CS1 is higher than the concentration CS2 on the downstream side, then the gas will diffuse through the membrane. If thediffusion coefficient Dm is constant and the membrane is of thickness ~y,

the flux will be given by

(3.37)

The solubility of the gas in the membrane will probably obey Henry's law,i.e. there will be a linear relationship between the gas concentration in themembrane surface and the partial pressure of the gas adjacent to thesurface. If the solubility coefficient for the gas-membrane system is S, andthe partial pressures are Pi on the feed side and P2 on the permeate side,the relationships are:

(3.38)

Combining eqns (3.37) and (3.38) gives

(3.39)


The term DmS is equal to the gas permeability P g which can be calculatedreadily from flux measurements:

(3.40)

The transport of gas through a membrane is clearly dependent upon both:(a) the diffusivity of the gas through the membrane; and (b) the solubility ofthe gas in the membrane. In most cases the membrane is a polymer andthe flexibility of the structure influences the magnitude of the diffusioncoefficient Dm , whilst the chemical nature of the polymer determines thesolubility of the gas in the polymer.

Consider a binary mixture of gases with components A and B. If thediffusion coefficient for A is that measured with pure A and if the solubilityof A remains unaltered in the presence of B, then the flux of A will be givenby:

JA=PgA(PA1-PA2)/~Y (3.41)

If likewise the flux of B is not influenced by the presence of A, then:

JB=PgB(PB, -PBJ/~Y (3.42)

The permselectivity IXAB is defined in a manner analogous to relativevolatility, a term used in distillation analysis. The relative concentration ofA to B on the permeate side is J AIJB, whilst on the feed side theconcentration ratio is PAt/PB" The enhancement (or permselectivity)gained through the use of the membrane is given as follows:

hproduct concentration ratio

en ancement = ,.feed concentratIon ratIo

(3.43)

If the downstream pressure is much less than the upstream (or feed)pressure, PA2 and PB2 are much less than PA, and PB" Under thiscircumstance, combination of eqns (3.41), (3.42) and (3.43) shows that:

(3.44)

The selectivity is, in the absence of interactions between the components,the ratio of the independently determined permeability coefficients forA and B. Recalling that P g is the product of Dm and S, we can notethat:

(3.45)

76 R. W. Field

Thus the selectivity of a membrane may arise from either a difference indiffusion coefficients and/or a difference in solubilities.

Exercise 3.4

A dynamic method for investigating the mechanism of permeation anddiffusion through polymers was developed by Pasternak et at. (1970). Inparticular, they derived a simple mathematical formula for determiningthe diffusion coefficient from a transient permeation rate, given that thedownstream concentration (i.e. partial pressure) is small. Assuming thatthe concentration is proportional to S, the signal from some measuringequipment, the diffusivity is given by:

Dm =0,176 dy2(dS/dt)/Soo

where Soo is the final steady-state value of the signal and dS/dt is thegradient of the signal (which is typically taken straight from a chartrecorder).

The above relationship and eqn (3.36) have been used to determinethe following data on diffusivity and permeability for CO 2 and CH4

through polymeric membranes A, Band C. Determine the selectivity ofeach membrane. Do the selectivities arise as a result of variations indiffusivity or solubility?

Membrane type

ABC

25·514·114·0

7·83·02·2

5·01·42·8

4·91·32·2

Values of permeability, Pg , are expressed in units of 10- 8 cm 3(stp)·cm/(s cmHg cm2

), whilst diffusivity, Dm , is given in units of10 - 6 cm3 s - 1.

3.3.4 Mass Transfer in Pervaporation and its Mathematical Descriptiont

Pervaporation may be looked at as a hybrid process. Taking a simpleview, it is similar to evaporation or distillation, in that a phase

t This section was contributed by H. Strathmann and R. M. McDonogh, authors ofChapter 9.


change occurs during the process. Before this phase change, however, thecomponents that vaporise must traverse a selective barrier. There ispermeation across the membrane and evaporation from the downstreamface of the membrane. The operating principle is illustrated schematicallyin Fig. 3.8. A liquid feed stream containing volatile components contacts asemi-permeable membrane separating the liquid from the vapour phase. Ifa driving force across the membrane is established the components thatare soluble in the membrane tend to move from the liquid side to thevapour side. The driving force for a volatile component i is the differencein the partial pressure (p~eed > pfermeate). However, the components collected on the downstream side must pass through the membrane phase.Thus pervaporation is a membrane process which combines the evaporation of volatile components with their permeation through a selectivemembrane. Therefore the separation of various components from a liquidmixture is not only determined by differences in their vapour pressures butalso by differences in their permeation rates through the membrane.

Feed Relentate

Permeate

Fig. 3.8. Schematic diagram illustrating the operating principle of pervaporation ( Pi refersto the partial pressure of a volatile component).

The actual driving force for the permeation of the different componentsthrough the membrane is the chemical potential difference between thetwo phases separated by the membrane. This difference drives the variousprocesses. Physically the mass transport of a component in pervaporationcan be viewed as a three step process (Neel et ai., 1985). This is shownschematically in Fig. 3.9. The steps are:

absorption of the component from the liquid phase at the membranefeed solution interface;diffusion of the absorbed species through the polymer matrix to thevapour-membrane interface;release of the species into the vapour phase, i.e. desorption andevaporation.

Mass transport through membranes can be described by variousmathematical relationships, varying from the rigorous to the empirical.

78 R. W. Field

fIii

Feed Mixture

x; p ~

T6y

1membrane

x~ p~Permeate

p

Ii,

Fig. 3.9. Schematic diagram illustrating the mass transport in pervaporation.

The most comprehensive description is based on a general equation whichrelates the fluxes of heat, charge and volume (mass) and individualcomponents to the corresponding driving forces (Strathmann, 1990):

(3.46)

(3.48)

where J j is the flux of each component i, X k is the driving force causing theflux, and L jk is the phenomenological coefficient relating the flux to itsdriving force.

Jj=L j grad ~i (3.47)

Expressing the chemical potential of the component ~i as a function of thestate variables temperature, pressure and composition leads to:

d -Jj=L j dy (-Sj T + ViP+RT In ajm)

where J j is the flux, L i a phenomenological coefficient, R the gas constant,T the absolute temperature, Vi the partial molar volume, p the pressure, S

the partial molar entropy, a the activity and y the directional co-ordinateperpendicular to the membrane surface. The subscript im refers to thepermeating component in the membrane.

Since in pervaporation -Si T < ViP~ RTln aim, the flux of a componenti through the membrane can be expressed, to a first approximation(Katchalsky and Curren, 1967) as:

dJ i = - L i RTdy (In aim) (3.49)

which reduces to:

(3.50)

The direction y is perpendicular to the membrane. If a linear variationof activity in the direction y perpendicular to the membrane surface isassumed, eqn (3.50) reduces to:

J.= -LiRT daimI iiim dy

(3.51)

where iiim is the average activity of the component I In the membrane, daim is the activity difference of the component i between themembrane feed and permeate side, and dy is the thickness of themembrane.

If we assume there to be local equilibria between the membrane surfacesand the corresponding phases, the activity of component i within themembrane can be related to its vapour pressure and concentration in theouter phases:

Pi <Piai= -0- =YiXi

Pi(3.52)

where Pi is the partial pressure of component i in the mixture, pi is itssaturation vapour pressure, <Pi its fugacity coefficient, Yi its activitycoefficient and Xi its mole fraction in the solution.

There are two interfaces and two expressions can be obtained. Thefeed-membrane interface is liquid-to-solid, whereas the permeate side issolid-to-gas, so it is convenient to express the activity of component i atthe different interfaces differently.

At the feed-membrane interface:

At the membrane-permeate interface:

pr><pr>ar>=_'_' =ar>, pi 1m

(3.53)

(3.54)

The superscripts f and p refer to the feed solution (side 1) and thepermeate (side 2) respectively and a~m and a~m refer to the activities of

1 1

component i within the membrane at the feed side and the downstreaminterfaces. The combination of eqns (3.51), (3.53) and (3.54) gives anexpression for the flux of component i.

(3.55)

80 R. W. Field

(3.56)

Noting that the diffusion coefficient within the membrane Dmi of component i, as defined by Fick's law (Strathmann, 1979),

D .= LiRTml C

im

and the distribution or partition coefficient, Sj, between the membrane andadjacent phases of feed and the permeate is given as

(3.57)

(this is the inverse of Henry's law coefficient, when it is expressed in termsof pressure and molar concentrations) and remembering that aim =YimCim Vi, eqn (3.55) can now be written as:

(3.58)

Equation (3.58) tells us that the molar flux of a component i through amembrane is determined by its membrane phase diffusion coefficient andits solubility in the membrane. The latter reflects the distribution betweenthe outer phases and the membrane itself. The product of the two terms,DmiSi, is the permeability Pi. The same term was met in the generalanalysis of permeation through non-porous membranes (Section 3.3.3.).

Equation (3.58) describes the mass transport in solution-diffusion membranes for a steady-state by a mechanistic model where the key parametersare the diffusivity and the solubility of the various components in themembrane polymer matrix. Thus the transport properties of the membrane depend not only on the intrinsic properties of the polymer but alsoon the conditions of the adjacent phases. Although the relations expressedin eqn (3.58) seem to be logical, it has to be kept in mind that several grossassumptions have been made in its derivation.

It was assumed that the sorption and desorption is fast compared to thediffusion in the membrane and that equilibrium is achieved at the phaseboundaries. Furthermore, kinetic coupling of the fluxes of the diffusingcomponents in membranes was neglected. It should also be noted that thediffusion coefficient and the solubility coefficient are functions of thetemperature and the concentrations of the absorbed components. Especially in permeation of organic solvents the membrane may swellexcessively and the diffusion coefficient may vary by several orders ofmagnitude with the concentration of the permeating components, (Long,1965). Thus:

(3.59)


Dmi is the diffusion coefficient of a component i in the membrane, Xi isits mole fraction in the feed solution and T the absolute temperature.For the relationship Dmi = !(Xi), different equations accounting forstructural changes of the polymer are discussed in the literature (Huangand Rhim, 1991). It should be pointed out that it is generally not possiblein vapour permeation to predict the mass transport behaviour ofvarious components in a mixture from single component measurements.This is true, for example, for both pervaporation and membrane gasseparation.

Exercise 3.5

A film of thickness 10 ~m of polydimethysiloxane (PDMS) was testedfor its permeability to ethanol. A disc, 48 mm in diameter, was placed ina membrane holder and put into the test cell. One side was in contactwith pure ethanol, the other side was held under vacuum of 10- 3 torr.The permeating species accumulated at a liquid nitrogen cold trap. Thefollowing data was collected:

Time M ass accumulated(h) (g)

0·00 0·000·25 0·200·50 0·92~75 ~05

1·00 3·481·25 5·121·50 6·971·75 8·912·00 10·962·25 13·012·50 15·062·75 17·113·00 19·15

Calculate the permeability of this film to ethanol.The limiting fluxes for other components, detailed in the table below,

were also found using the identical equipment and conditions. Calculatethe permeability of the film to these components.

82

Compound

MethanolEthanoln-Propanol

Water

R. W. Field

Vapour pressure at 35°C(bar)

0·2800·1320·053

0·055

Limiting flux(gjh)

7·84

10·1

0·564

(Answers Permeability (mol m m - 2 S - 1 Pa - 1) of PDMS to Methanol1.33 x 10- 11; to Ethanol 2.05 x 10- 11; to n-Propanol 4·8710 x 10 - 11; toWater 8·66 x 10- 12) Outline solution at end of chapter.

3.4 OSMOSIS AND OSMOTIC PRESSURE

3.4.1 Introduction

The classical trio of colligative properties, of which boiling point elevationand freezing point depression are the first two members, is completed bythe phenomenon of osmotic pressure. The phenomenon of osmosis depends on the existence of semipermeable membranes. Such membranes areof great variety but are all characterised by the fact that one component ofa solution can pass through whilst the passage of another component isprevented. Cellophane and a number of plant and animal membranes are,for example, permeable to water, but not to high molecular mass compounds.

An osmotic pressure can arise when two solutions of different concentrations (or a pure solvent and a solution) are separated by a semipermeable membrane. Osmotic flow continues until the chemical potential of thediffusing component is the same on both sides of the barrier. If the flowtakes place into a closed volume, the pressure necessarily increases.

When measuring osmotic pressure, a solution is separated from puresolvent by means of a membrane. There is a natural tendency for thesolvent to diffuse from the pure solvent chamber into the solution. Thistendency is opposed by applying pressure to the solution side. The excesspressure that must be applied to the solution to produce equilibrium (i.e.no net flow of solvent) is known as the osmotic pressure, n. This pressuredoes not depend upon the properties of the semipermeable membrane. Themagnitude of n is dependent upon the concentration of the solution andon the properties of the solvent.


In dilute solution the following equation due to van't Hoff is applicable:

IT=cRT

where c is a molar concentrationR is the universal gas constant, andT is absolute temperature.

3.4.2 Thermodynamic Relationship for Osmotic Pressure

(3.60)

(3.62)

A more exact expression can be developed by considering the chemicalpotential of the pure solvent. Let this be component A. At equilibriumthere are two opposing factors tending to cause the chemical potential ofA in the solution to depart from that of pure A. At equilibrium these are ofequal magnitude. Firstly there is the change caused by dilution (i.e. by theaddition of the solute). If the partial vapour pressure of A above thesolution is PA and the vapour pressure of pure A at the same temperatureis P~, then from use of the standard expression:

f.1'tln=f.1~+RTlnpA (3.61)

it is readily shown that the change due to dilution is:

tJ.f.1'1i1ution=RT In (PA/p~)

Exactly counteracting this is the increase in f.1A due to the imposedpressure IT. From df.1 = V dp where V is the partial molar volume,

tJ.f.1~ressure = Ion VA dp

Now tJ.f.1 '1ilution + tJ.f.1 ~ressure = 0, therefore:

(3.63)

(3.64)Ion VA dp= -RT In (PA/pA)

If it is assumed that the partial molar volume of VA is independent ofpressure, Le. the solution is practically incompressible, then

(3.65)

The significance of the above derivation is that it shows that: the osmoticpressure of a solution is that pressure which, when applied externally, willraise the vapour pressure of solvent A in the solution to that of pure A. Amore extensive discussion is given in Chapter 1 of Cheryan (1986).

Equation (3.61) is rigorous only when the vapour behaves as an idealgas. However, correction for non-ideality is usually small.

84 R. W. Field

At the practical level, the osmotic pressure of the solution is generallyrelated to the concentration of the dissolved component by expressions ofthe following type:

(3.66)

For dilute solutions, A 2 and A 3 can be neglected and a linear relationshipused. For NaCl solutions, a linear relationship is valid up to concentrations of 80kg- 3

. However, for protein solutions the relationship is highlynon-linear and dependent on pH. (See for example the data of Vilker et ai.(1984) on bovine serum albumin.) The data for other macromolecules suchas dextran is also highly non-linear.

Exercise 3.6

(A) Jonsson's (1984) data yields the following values for the virialcoefficients:

Dextran noWhey protein

0·11160·044

-0,00491-0,000 17

0·0002570·000079

Using eqn (3.66) and taking the units of c to be wt%, plot osmoticpressure as a function of concentration.

(B) Equation (3.65) can be written as follows:

RTn i= ---=-lnlailVi

Show that for ideal solutions this reduces to van't Hoff expression,eqn (3.60). An outline solution is given at the end of the chapter.

3.4.3 Transport in Reverse Osmosis

Osmotic pressure effects can be important in porous systems (see Section3.5.1) but this section is concerned principally with reverse osmosis (RO).If the osmotic pressure is exceeded on the solution-side of the membrane,there will be a net solvent flux from the solution. 'Permeation' is said tooccur. The permeation rate or flux (which can be expressed either as a


mass flux or a volume flux) is clearly dependent upon the properties of themembrane. The term 'permeation' does not imply a particular mechanism.It is indeed useful to have such a term. It should also be noted that ingeneral the mechanisms can be classed as: (a) solution-diffusion model; (b)porous capillary model; and (c) pore model. Only (a) and (b) are applicableto RO and, up to this point, we have only considered the solutiondiffusion model. However, the porous capillary model has its supporters,and this will be considered in Section 3.6. For the moment furtherconsideration is given to the preferred model.

3.4.4 Application of Solution-diffusion Model to Reverse Osmosis

This section is both more rigorous and more general than Section 3.3.3which introduced the solution-diffusion model. The reader will noticesimilarities with Section 3.3.4.

Even with reverse osmosis membranes it should be remembered thatmembranes may not be exclusively selective to just one component, and soinitially reference is made to a general component, i. With the solutiondiffusion model, the membrane is treated as a continuum and component idissolves in the membrane on the upstream side at a pressure PI' givingrise to a certain activity, ai, . This can be linked to the mass fraction of i inthe membrane phase, Wim" by means of a correlation coefficient ({Jim' Thuswith certain assumptions (Rautenbach and Albrecht (1989), p. 53):

(3.67)

(3.68)

(3.69)

On the downstream side the pressure is lower by an amount (p I - P2).Using the same correlation coefficient, ({Jim' and allowing for the pressuredecrease, the mass fraction is:

wim2 = ({Jimai2 exp{ - :~(PI - P2)}

The flux through the membrane is governed by Fick's law, and isproportional to the membrane phase diffusion coefficient and the concentration difference, and inversely proportional to the membrane thickness,~y. Thus the flux of component i is:

. pDmi({Jim { [V; ( )J}]j= ~y ai,- ai2 exp -RT PI-P2

Equation (3.69) is an expression for the flux of component i as a functionof the diffusion coefficient Dmi , membrane thickness ~y, physical properties and operating conditions.

86 R. W. Field

Organic solutions and azeotropic mixtures can be separated in principleby reverse osmosis (Kopecek and Sourirajan, 1970) but the principalinterest is in separating water from aqueous salt solutions. For saltsolutions, the transport eqn (3.69) can be further simplified. Using

RTnj = - --=-In aj (3.70)V;

The resulting exponential functions for the activity coefficients are expressedas a series expansion. If the terms beyond the linear ones are neglected, themass flux of water can be represented by the very simple equation:

(3.71)

where Kw is a constant.Equation (3.69) also applies to the transport of the essentially non

permeable salt component. The activity of the salt is not pressuredependent and so the equation simplifies to:

(3.72)

where K s is a second constant.The above equation is valid if the membrane has high selectivity, in

which case the flux of the dissolved salts is proportional to the transmembrane concentration difference. The water flux given by eqn (3.71) isproportional to the net trans-membrane pressure difference.

3.5 LIMITING FLUX PHENOMENA

The existence of limiting fluxes is both scientifically interesting and important. Two cases of limiting flux in membrane systems will be considered.

3.5.1 Limiting Fluxes in Ultrafiltration Systems

A common feature of various transport processes is the existence of alimiting flux, i.e. the rate of transport becomes independent of the drivingforce at high flux. This is illustrated in Figure 3.10. Traditional chemicalengineering science proposes a straightforward explanation for this phenomenon when the process is one of mass transfer from the bulk to aninterface which acts as a sink. This is based on the assumption that therate of reaction at the interface is controlled by the rate of diffusion of thereacting species from the bulk to the interface. Thus when the wallconcentration comes close to zero, the concentration gradient (diffusiondriving force) between bulk and wall is a maximum. It follows that the rate

J

flux

Transport Processes in Membrane Systems

Transnenbrane pressure llP

Fig. 3.10. Flux-pressure relationships.

87

of mass transfer is also at a maximum. Such a model works very well withelectrochemical reactions and with electrodialysis. For example it explainswhy limiting electric current densities are observed when the potential isincreased.

In the 1960s, the same approach was naturally considered for pressuredriven membrane processes. The steady-state mass balance for the solutewas written as:

JC= -DdCjdy (3.73)

This is the same as eqn (3.3) with Cp = o. Integration through the diffusionboundary layer leads to the now classical film equation:

(3.74)

This equation does predict an increase in solute concentration at the wallwith flux J, and a simple mass balance would allow a solute concentrationprofile to be calculated through the boundary layer, as shown in Fig. 3.11.

Water is transported through the boundary layer. If the mass fraction ofthe water is 1- Cm!Pw at the membrane surface and 1- ChiPh at the edgeof the boundary layer, the driving force for the transport of water throughthe boundary layer, Fd , can thus be expressed in a simplified way asfollows:

(3.75)

88 R. W. Field

Water concentration profile

S?~U~~ ~~~n.~~~~P~~f~!... ' .Viscosity profile

Membrane

Fig. 3.11. Schematic diagram of viscosity and concentration profiles above a membrane.

Now the transport of water from the bulk to the permeate consists of twosteps:

(1) transport through the boundary layer: J d = constant * F d

(2) permeation through the porous wall: J p = Lp t1P where Lp is thepermeability of the membrane

Under normal conditions, t1P sets J p and then Jd=J p • This mechanismworks until Jd reaches a maximum. Then further increases in t1P no longerhave any effect on the flux. The most straightforward assumption toexplain a limitation of the driving force is obviously to assume that C;",the free water concentration, has reached a physical minimum. Thissituation corresponds to the precipitation, or gelation, of the solute at theinterface. Substituting Cgel for Cm in eqn (3.74) allows a limiting fluxequation to be written:

(3.76)

where the mass transfer coefficient k = D/bc .

According to eqn (3.76), plotting lnm versus In(Cb ) should give a straightline, with k as a slope and In(Cgel ) as intercept. Such a model was proposed


in the 1960s (Michaels, 1968) and has remained popular, since it gives goodfits with experimental data. Nevertheless it does not allow predictions of flux,since the value of the 'gelling' concentration cannot be found by independentmeasurements. Also, the assumption of the gel model that the limiting flux isentirely controlled by the gel is untrue; different membranes producedifferent limiting fluxes for the same set of feed and hydrodynamicconditions. Furthermore, non-zero limiting fluxes have been observed withconcentrations larger than the gel ones obtained by extrapolation.

An alternative explanation is based on the osmotic pressure effect. It isreadily appreciated that if the concentration of a solution increases (eitheralong a tubular unit or within a batch recirculation system) the osmoticpressure will increase. If the transmembrane pressure difference remainsconstant the net (that is to say the effective) pressure difference willdiminish. Eventually the flux will decrease to zero (see for exampleJonsson, 1984).

Exercise 3.7Obtain the appropriate equations for the osmotic pressure model.Determine the dependency of the limiting flux on bulk concentration.

A review of: (A) resistance models; (B) gel-polarization models; and (C)osmotic pressure models has been given by Van den Berg and Smolders(1990), whilst in earlier work Wijmans et al. (1985) showed that in boththeory and experiment the osmotic pressure model and the boundary layerresistance model were equivalent. There is one missing element which hasbeen emphasised in an alternative approach. The alternative approachwould be to consider that when the free water concentration decreases, thetransport properties of the solution in the boundary layer are significantlydifferent from those in the bulk. In eqn (3.75) this would correspond to anincrease in the thickness of the boundary layer, (j, with decreasing freewater concentration. Such an assumption is already well established inheat transfer. When the wall temperature is very different from the bulkone, a correction factor, {J.lb/J1.m)Z is used.

Various authors have already considered the variations in transportproperties within the boundary layer in membrane processes (Goldsmith,1971; Kozinski and Lightfoot, 1972; Clifton et al., 1984; etc). Aimarand Sanchez (1986) have shown that the subsequent decrease in masstransfer coefficient can explain a limiting flux. Aimar and Field (1992)applied the theories developed and quantified for heat transfer to

90 R. W. Field

membrane processes. Their work was an exploration of the consequencesimplicit in the linking of two independently well established principles.The heat transfer work on transfer coefficient variations establishedempirically by Seider and Tate (1936) and theoretically by Field (1990b)was combined with mass transfer film theory.

Their approach to the calculation of the limiting flux was similar to thatproposed by Aimar and Sanchez (1986), but it was no longer referred tothe osmotic model. Their theory relates the dimensionless limiting flux,Jlim/ko, to the bulk conditions and a correction factor for the mass transfercoefficient. In outline their theory falls into two parts. First a viscositycorrection factor 'to the mass transfer coefficient is obtained. This is donefor an assumed concentration profile:

(3.77)

where be is the thickness of the concentration boundary layer. In developing the classical analysis, which is an extension of the classical analysis forheat or mass transfer into a linear velocity gradient that parallels Field(1990b), two main assumptions are made. Firstly it is assumed that theviscosity within the concentration boundary layer will depend uponposition in the following manner:

(3.78)

The second assumption of the analysis is that the shear stress r is constantwithin the concentration boundary layer both with respect to distancefrom the wall and also distance along the membrane surface. The assumption is reasonable because be is small compared with the distance overwhich the velocity changes.

Then following the analysis given in the Appendix, the correction factorobtained is found to be the same as that obtained for heat transfer, namely

(3.79)

In the second part no particular relationship between mass transfercoefficient and viscosity is initially assumed. Nevertheless it is shown that,given certain assumptions about the dependency of viscosity on concentration, a limiting flux exists independently of any supposed gelation effects.

Experimentally J has been found to be a function of membrane (wall)concentration, Cm' It follows that a limiting flux will correspond to a zeroof the derivative dJ/dCm . Differentiation for a given value of Cb gives:

(3.80)


The theoretical condition for a limiting flux is given by dJIdCm = 0, i.e.

91

(3.81)

This equation means that, at the limiting flux, any increase in diffusionpotential would be exactly balanced by a decrease in the mass transfercoefficient.

Substituting for k using an equation of the same form as eqn (3.79),with the index signified by z, gives a practical version of the limitingcondition:

1Z {d Ji}

- Jim dC w= - C I Cmm nCb

(3.82)

(3.83)

The membrane surface concentration that arises from this equationdepends on the bulk concentration, Cb, on the surface viscosity, Jim, andon the sensitivity of the mass transfer coefficient to the viscosity gradient(i.e. value of index z). Such an equation can be solved numerically for eachcase, provided that the variations in viscosity with respect to concentration are known.

In a previous work (Aimar and Sanchez, 1986) it has been shown thatsome functions give a relationship between viscosity and concentration,from which an analytical solution can be obtained, even though theviscosity-concentration relationships themselves do not have any theoretical meaning. For example, an assumption relating viscosity to concentration is that considered by Clifton et at. (1984), namely:

Ji=Jioexp(yC)

Three typical values of yare as follows:

whey proteins: y= 14·3 x 10- 3 if C is in glkg(after Jonsson, 1984)

albumin: y = 7 x 10- 3 (Aimar et at., 1989)gelatin (60°C): y=24 x 10- 3 (Schiiler, 1989)

Using the relationship in eqn (3.68) to relate the surface viscosity, Jim, andthe concentration at the membrane surface, Cm, the condition for alimiting flux, eqn (3.82), becomes:

Cbyz= 1/{Cmdim In Cm'lim} (3.84)Cb Cb

92 R. W. Field

The term Cbyz is a reduced concentration and there is a solution Cm. lim foreach value of the reduced concentration. These solutions have been plottedin Fig. 3.12. The polarisation factor Cm. lim/Cb decreases when the reducedconcentration increases, i.e. for higher bulk concentrations or more viscousfluids. With z = 0·27 and Y about 0,01, the polarisation factor lies between10 and 30 for bulk concentrations around 10 g/kg, which is in reasonableagreement with expectations. Furthermore, eqn (3.79) can be developed byuse of eqn (3.83) to obtain the following expression for the mass transfercoefficient:

(3.85)

The graph in Fig. 3.13 shows the variations in k against the reducedconcentration. According to the present model, the value of the masstransfer coefficient under limiting conditions would lie between 40% and80% of the standard coefficient, ko. Substituting in the film model for kand the logarithm of the polarisation factor, using eqns (3.84) and (3.85),one obtains:

Jlim=kO[eXP(YZCb)(l-CCm)] c1

.b yz m. hm

(3.86)

The limiting flux predicted by the present model has been plotted versusthe reduced concentration in Fig. 3.14. The typical decrease in flux withbulk concentration and viscosity is predicted. More surprising is theapparent linear behaviour in semi-logarithmic co-ordinates over a widerange of reduced concentrations. Therefore this part of the curve does notdisagree with the gel theory, and the numerous experimental observationswhich accord with it. However, in addition, the present model predicts an

80

Fig. 3.12. Predicted values of CW'lim/Cb as a function of Cbl'z.


1,0

0,8

0,6

0....lZ

0,4

0,2

y zCb

0,0a 2 3 4 5

Fig. 3.13. Predicted variation of mass transfer coefficient with Cb yz.

4

3

2

o+--_-...,.--~-......- .........-__,_----';;...::;:;;a.......,·3 ·2 ·1 a

Fig. 3.14. Predicted variation of limiting flux as a function of Cbyz.

upward curvature of the curve, and non-zero fluxes at bulk concentrationslarger than the supposed 'gel' ones. According to the assumptions, thecurve in Fig. 3.15 should work for any solution whose viscosity fits anexpression of the form given by eqn (3.83). For practical purposes theactual value of the equivalent limiting concentration can be calculatedif z and yare known. Details are given in the paper by Aimar and Field(1992).

Porter's data on latices, albumin and gelatin have for a long time beenseen as support for the gel theory. He reports (Porter, 1988) empiricalextrapolated concentrations of 280 for albumin in a range of (10-250) andabout 220 for gelatin at 70°C in an approximate range of (30-210). Theagreement between these data and the predictions of the present model isreasonably good. Furthermore, Cheryan (1986, p. 277) quotes a graph(Fig. 3.16) from Porter and Michaels where not only the limiting concentration but also the shape of the curve is in excellent agreement with the

94 R. W. Field

4

'Y- 0,0033 - 0,007- 0,011--- 0,0192 --- 0,029

32oL~~

oLog(Cb)

Fig. 3.15. Predicted variation of limiting flux (plotted as J/k o) with respect to log Cb.

50r-----..........,....--r---.---.--.--r--r--.-r------~-__,

0.13 sq.ft. of membrane.30-mil channels, recirculation rate of 1.600ml/min at 30 psil

10

0 1 2 5 10 20 30CONCENTRATION OF PROTEIN (WGT '%0)

Fig. 3.16. Ultrafiltration of gelatin: relationship between gelatin and flux (note the upwardcurvature of the data points in the high concentration region). Reprinted with permission

from Chern. Tech., 1,440-445, 1971. Copyright (1971) American Chemical Society.

predictions of the above model. The values reported by the same author(Cheryan, 1988) on the limiting concentration for sweet cheese whey liebetween 200 and 285 gjkg, which is in the same range as the presentresults. Further quantitative comparison is difficult because the parameters required for the calculation of the mass transfer coefficient ko werenot fully available in the papers. An interesting feature that can be noted inPorter's data is the upward curvature of the curve at high concentration


for the styrene butadiene latex experiments. In general this upwardcurvature could be hidden by fouling phenomena whose importanceincrease with time of operation and bulk concentration. An extension ofthis work has been presented by Field and Aimar (1992).

3.5.2 Solvent Fluxes through Inorganic Membranes

Water flux data for two nanofiltration membranes is shown in Fig. 3.17.The linear parts of the two curves can be described by the simple equation

(3.87)

in which Rm is the intrinsic resistance of the membrane. In terms ofpermeability, eqn (3.87) can be expressed as:

(3.88)

Lp is called the liquid phase permeability or the hydraulic permeabilitycoefficient. At high pressure the inorganic membrane displays a sharplyincreasing value of Lp and the solvent flux appears to reach a limitingvalue. Guizard et at. (1990) note that this has been observed for otherceramic membranes but not explained. They postulate the formation of ahydroxide gel layer at the membrane/water interface.

403020

organic-inorganic

L-----~10

250

200....I

""NI

'" 150

~Ii:

100

50

pressure (bar)

Fig. 3.17. Water flux data for two types of nanofiltration membrane.

96 R. W. Field

It is well recognised that the adsorption of permeating solute onto thepore walls of a membrane has the effect of tightening the pore sizedistribution. Indeed Zeman (1983) has proposed the following relationshipbetween the decrease in pore radius due to adsorption, I!.r, and theresulting decrease in water flux:

I!.r = 1- {~}O'25 (3.89)r Jm

Now a similar phenomenon may occur with inorganic membranes andwater. Some water molecules may bind onto the pore walls and it is thispressure dependent reduction in pore size that is responsible for theincreasing resistance of the inorganic membranes. This phenomenon iscurrently the subject of further research.

Exercise 3.8What is the relationship between eqn (3.87) and the Hagen-Poiseuilleequation? The latter is to be found in Section 3.3.2.

3.6 APPLICAnON OF MASS TRANSPORT EQUAnONS

The range of processes and their applications is diverse. However, almostall membrane processes are evaluated in terms of flux and separationperformance. The latter is addressed first.

3.6.1 Rejection Coefficients

The rejection coefficient is a very convenient measure of the selectivity ofthe membrane. A useful distinction has been made between the truerejection coefficient,

R= Cm-CpCm

and the apparent rejection coefficient,

R _ Cb-Cpapp- C

b

(3.90)

(3.91)

where Cb , Cp and Cm are, respectively, the concentration of solute in thebulk, in the permeate, and at the membrane surface.


Cm is greater than Cb because of concentration polarisation; Now Cm

is an average value for the surface and so if the porosity of the surface is low, the concentration will be higher closer to the pores and loweron the non-porous parts of the surface. Thus the actual concentration inthe pore entrance region will be greater, other factors being the same, formembranes of low porosity. This is detrimental to performance andexplains why Fane et ai. (1990) have observed that high porosity is ofbenefit.

Defining an intrinsic rejection coefficient for the pore region as:

1- Cp

Csp(3.92)

where Csp is the surface concentration in the region of the pore and notingthat

it is readily seen that

Rinl > R > Rapp

(3.93)

(3.94)

Clearly, Rapp is not a membrane constant; it is dependent on operatingconditions. The film model can be used to give a theoretical relationshipbetween Rand Rapp . By using eqns (3.90) and (3.91), the terms Cm and Cbcan, respectively, be written as:

Cm =Cpj(I-R); Cb=Cpj(I-Rapp)

Substitution into the film model equation,

Cm - Cp= (Cb- Cp)exp(J jk)

followed by rearrangement yields:

(3.95)

(3.96)

(3.97)R

Rapp = R+(I-R)exp(Jjk)

This confirms that the apparent (i.e. observed) value of the rejectioncoefficient is dependent upon the fluid dynamic conditions (which determine flux and mass transfer coefficient) as well as the value of the intrinsicrejection coefficient, R. Figure 3.18 shows the relationship between Rappand R for a range of Jjk ratios. With membrane developments leading toimprovements in flux, it will become increasingly important to define theterm rejection coefficient carefully. For all membranes it is good practiceto distinguish between Rand Rapp . With certain membranes, it may soonbe possible to distinguish between Rinl and R. Furthermore in all cases it isimportant to remember that membrane properties, especially rejection

98

0 ••

0.11

0.7

0.11

0.5

~pp 0.4

0.3

0.2

0.1

00

R. W. Field

0.1 0.2 0.3 0.4 0.5 0.. 0.7 0.11 0 .•R

Fig. 3.18. Theoretical relationship between apparent and intrinsic rejection coefficients

with 11k as parameter.

coefficients, may change with time. The main cause is fouling. This isdiscussed in another chapter.

The improvement in membrane properties may also encourage operation at low to modest transmembrane pressures. For example, instead ofoperating a high flux membrane at the same I1P and increasing flux, theI1P may be reduced and a smaller increase in flux accepted. This will be aparticularly attractive option if the long-term decline in flux is less.Furthermore, with solute-permeable membranes, which can be used toseparate proteins from cell debris, transmission of the solute is essential.By operating at low transmembrane pressures of less than 5 kPa,Heinemann (1987) showed that a transmission of 100% could be achievedfor whey protein passed through a polysulphone 0'2-llm cartridge filter.The transmission decreased with increasing transmembrane pressure up toa value of 40 kPa, beyond which transmission was constant and independent of pressure. This result is similar to that achieved by Papamichaeland Jula (1987). The results at higher pressure may reflect the effect offouling.

3.6.2 Mass Transport through Reverse Osmosis (RO) Membranes

3.6.2.1 Porous Capillary ModelSometimes termed the finely porous capillary model, this model is basedon the assumption that the skin of asymmetric RO membranes has afine porous structure. The supposed pores are in the nanometre (Le.molecular) range. It is assumed that the pores are coated by an adsorbedlayer of water which being bonded has no capacity as a solvent. Consequently most pores are too narrow to pass salt ions, particularly as theseare hydrated. There is thus a sharp concentration gradient in fluidcomposition at the membrane surface-feed fluid interface. This model was


developed by Sourirajan and Matsurra (1985) and is recommended byRautenbach and Albrecht (1989) for concentrations above 1 moll-I.

3.6.2.2 Characterising RO PerformancesIf the membrane has high selectivity, the flux of the dissolved salts isproportional to the trans-membrane concentration difference. The waterflux given by eqn (3.71) is proportional to the net trans-membranedifference. Transport eqns (3.71) and (3.72) are used for the design of ROplants. The parameters K w and K s are related to the membrane propertiesand thickness but are independent of the concentrations either side of themembrane. Although K s is independent of pressure, K w decreases slightlywith increasing pressure.

The rejection coefficient is a very convenient measure of the selectivity ofthe membrane. Neglecting any mass transfer resistance on the upstreamside, it can be simply defined as:

(3.98)

R is not a membrane constant. Noting that the permeate concentrationcan be approximated by:

(3.99)

it can readily be shown by use of eqns (3.71) and (3.72) that the rejectioncoefficient is given by:

(3.100)

There is potentially a strong dependency upon concentration becauseosmotic pressure is concentration-dependent.

For example, an NaCl solution with a concentration of 45 kg m - 3 hasan osmotic pressure of around 36 bar.

Lastly in this section, it is noted that the rejection coefficient for anyelectrolyte can be estimated for a given membrane without furtherexperiments, provided figures for two different salts are known. This isdone via use of energy of hydration data and the porous capillary model.

Exercise 3.9

(1) When would RO be used in preference to UF for the concentrationof protein solutions?

100 R. W. Field

(2) If, for a solution of sodium chloride, R =0'95, and the concentrationof the feed is 10 kg m - 3, what is the concentration of the permeate?

(3) If the flux associated with the data is 4·15 x 10- 6 ms - 1 at 25 bar,find the membrane coefficient K w , given that at 15°C the coefficient relating osmotic pressure and concentration is 0·77 bar(kgm- 3 NaCl)-1, provided the concentration is below 80kgm- 3 .

Also obtain a value of Ks .

(4) With regard to the above RO model, what parameters vary withtemperature? Do you expect any of these to be pressure-dependent?

Outline solutions at end of chapter

3.6.2.3 Process LimitationsIn the processing of fruit juices, early development was hampered by eitherlow fluxes or the loss of flavour components. Composite membranes witha thin active layer have brought about significant improvements andmembrane processes are now the principal technology in the concentration of fruit juices. High pressures are required because of the osmoticpressures involved. The increase in osmotic pressure with concentrationlimits the degree to which the original stock can be concentrated. Typicalvalues are given in Table 1.

Table IOsmotic Pressures of Various Juices

Juice

Sugar beet juiceTomato juiceLemon juice

Cane sugar juice

'Concentration'o Brix"

2033104544

Osmotic pressure(bar)

34·569·014·8

103·569·0

"An industrial measure related to density (10 Brix ~ I wt% sugar at20°C).

3.6.3 Further Observations on Ultrafiltration

In addition to the work of Clifton et ai. (1984) the recent work of Reismeieret ai. (1987) confirms that the flux can decrease with increasing distancefrom the inlet. The appendix outlines an extension of the well-establishedanalysis for heat or mass transfer from a solid wall into fully developedlaminar flow. The new development allows for a developing velocity


profile and the conclusion is that over the entrance length (or length of themembrane channel, if this is smaller) the mass transfer relationship is:

Sho =0·848 Reg' 5PrO' 33 (D/L)0'5 (3.101)

The prediction that the mass transfer coefficient varies with L -0,5 suggeststhat under mass transfer control the flux should vary in the same manner.The experimental work of Clifton et al. (1984), who measured the localpermeation rate at different positions along the length of a fibre bundle,would appear to meet this condition, since synthetic polymers were used.Figure 3.19 shows that the variation of local mean permeation rate forClifton et al.'s dextran data is proportional to L -0,5 as suggested by theabove equation. For their polyvinylpyrrolidone (PVP) data, the dependency upon channel length is less strong, but it is nevertheless clear thatshort filtration lengths are beneficial. Of relevance to the following sectionis the fact that, particularly in laminar flow, k is not constant along thelength of membrane channel. Thus, where appropriate, models should beused in a way which allows for this.

Data fran Clifton60 et aZ (1984)

•Flux

umls 40 0

20

-- freehand fit

0 0.1 0.2L-O• S

Fig. 3.19. Comparison of Eqn (3.101) with the data of Clifton et al. (1984).

There is an additional complexity. The local permeation flux, particularlyat low cross-flow velocities, is strongly dependent on the distance from theinlet. Clifton et al. (1984) have found that the local permeation flux at 0·5 mmay be only 20% of that obtainable close to the tube entrance. At highercross-flow velocities, but still in the laminar flow regime, the variation of fluxwith distance is significantly less. They have suggested that a possible causemay be inherent hydrodynamic instability which limits the size of the boundary layer. The instability could be caused by an inflexion in the velocityprofile as a result of viscosity variations due to the concentration profile.

Lastly it is noted that Aimar et al. (1991) have studied both experimentally

102 R. W. Field

and through modelling the phenomena of concentration build-up in hollowfibres. The build-up of the concentration polarisation layer was recordedand measurements of the amount of proteins involved in the boundary layerwere carried out before fouling had had time to alter polarisation. Using afilm model with a linear or an exponential boundary layer concentrationprofile, average values of the wall concentration and of the mass transfercoefficients are calculated, the latter being in good agreement with thepredictions of the Leveque formula. The advantage of the integral model isthe detailed picture given of what is occurring along the membrane surface.The rate of material deposition on the membrane was also measured. Themechanism offouling appears to be strongly dependent on the concentrationpolarisation. This will be discussed in later chapters.

NOMENCLATURE

aAt> A 2 , A 3

Cddp

DDm

JjkkoLL p

Ns

Pg

pR

Rm

sStTuVw

chemical activityvirial coefficientsconcentrationtube diameterparticle diametermolecular or particle diffusion coefficient in fluidmembrane phase diffusion coefficientvolumetric fluxmass fluxmass transfer coefficientmass transfer coefficient evaluated at bulk conditionslength of membraneliquid phase permeability (hydraulic permeability coefficient)flux of solute away from surfacegas permeabilitypressurerejection (retention) coefficientor gas constantintrinsic membrane resistancefractional rate of surface renewalsolubility coefficient or surface area per unit volumetimetemperaturevelocity in cross-flow directionmolar volumemass fraction

xYIX

bedydpe()

Il

nq>

pV

Subscripts:1,2

avABbegelilimmps

w


distance along membranedistance from membrane surfacepermselectivitythickness of concentration boundary layermembrane thicknesstransmembrane pressure differencevoidagetimeviscosityor chemical potentialosmotic pressurefugacity coefficientor correlation coefficient (section 3.4.3)densitykinematic viscosity

regionaveragecomponent Acomponent Bbulk/mainstreamequivalentgelgeneral component ilimitingmembrane surfacepermeatesaltor surfacewater

103

Dimensionless groups:Re Reynolds numberSc Schmidt numberSh Sherwood number

(pud/Ilb or pxd/Ilb)(v/D)

(kd/D)

APPENDIX 1: EFFECT OF VISCOSITY ON MASS TRANSFER

Following the classical approach the following concentration profile isassumed.

(ALl)

104 R. W. Field

where be is the thickness of the concentration boundary layer.As mentioned in the main text two important assumptions are made.

Firstly, it is assumed that the viscosity within the concentration boundarylayer will depend upon position in the following manner:

(A1.2)

This assumed vanatlOn of viscosity with distance from the membranesurface is not arbitrary but is parallel to that commonly assumed for heattransfer. The constant IX reflects the change of Ji with y and is equal toIn( Jiw/Jib)'

Equation (A1.2) is only consistent with Eqns (3.77) and (3.83) for smallvalues of y. Thus the numerical value of the index z of 0·27 which issubsequently obtained is only an approximation. Preliminary work suggests that the value of 0·27 is an overestimate. However, the model forlimiting flux is not dependent upon the establishment of an exact numerical value and so Eqn (A1.2) was deemed acceptable. It is also noted thatthe viscosity effects in membrane systems do not exactly parallel those forheat transfer. In the latter case the temperature profiles would be morelinear than the concentration profiles above a membrane. Also, the effectof concentration upon viscosity is more non-linear than the effect oftemperature upon viscosity.

Secondly, it is assumed that the shear stress r is constant within theconcentration boundary layer both with respect to distance from the walland also distance along the membrane. This is reasonable provided be issmall compared with the distance over which the velocity changes. (Forisothermal flow of a Newtonian fluid, in the absence of concentrationpolarisation, this is equivalent to assuming that the velocity gradient isconstant within the region of interest.)

From the above it follows that

r = Jiw exp( -lXy/be) du/dy

which on integration gives

rbe{ [IXY] }u=- exp - -1

Jiw lX be

(A1.3)

(AlA)

The expression for u can be used in the expression for 'concentration'thickness (equivalent to the standard thermal thickness)

(A1.5)


On substituting for u and C, and subsequent integration, an expression forec is obtained. This is incorporated in the mass transfer analogue of thesimple momentum equation in order to obtain an expression for the masstransfer coefficient, k. Following the standard analysis (details parallelthose of Field (1990b), the expression for the average value of k, for masstransfer across a laminar film, is found to be:

where

f = (3D c/4L)1 /3. R 1/3 (A1.6)

Introducing dimensionless groups ReD (= pumD/llb), Sc (= Ilb/pDc) and Sh(=kD/Dc) and taking the shear stress r to be equal to Ilb8um/D, which isapplicable for developed laminar flow in a pipe, Eqn (A1.6) can berearranged to give:

Sh = 1'82(Re Sc D/L)1/3 {Ilb 4(6ea-a

3-3a

2-6a-6)}1

/3 (A1.7)

Ilw a4

Equation (l.A7) is a theoretical alternative to the following semi-empiricalcorrelation for mass transfer to a fluid flowing in a pipe under laminarconditions:

(Al.8)

It is thus suggested that the Sieder and Tate correction factor could bereplaced by

(Al.9)

which can, with a high degree of accuracy, be approximated to (llb/llw)027.

APPENDIX 2: MASS TRANSFER INTO A DEVELOPINGVELOCITY GRADIENT

A number of standard texts consider heat and mass transfer into the linearpart of an established laminar velocity profile (e.g. Kay and Nedderman,1985). It is assumed that the velocity increases linearly with distance fromthe wall, i.e. u= by, where b is a constant equal to the shear stress dividedby the viscosity, ro/Il. Recognising that b is the velocity gradient at the wall

106 R. W. Field

and by use of standard boundary layer theory, the variation of b with x fora developing laminar velocity profile can be represented by:

2{ }

OOS

b-~ ~- 5·836 vx

Incorporation of this into the standard analysis, followed by integration toobtain an average value for a channel of length, L, results in Eqn (3.101).The heat transfer equation corresponding to Eqn (3.101) and the one foran established velocity profile are as follows:

For developing velocity region:

Nuo = 0'848RegsPro 33(D/L)OOs

For established velocity region:

Nuo= l'82Reg33Pr033(D/L)0033

APPENDIX 3: OUTLINE SOLUTIONS TO SELECTED EXERCISES

A3.1 Solution to Exercise 3.5

Plotting the data given as the mass of ethanol passing through themembrane with time (dm/dt) (Fig. A3.1) shows that a steady state or

2

8

4

6

o3

Mass Flow (g/h)

10

2

I I I/--0- Accumulation (g)i- ............ Flux (g/h)

••••••04 .........~ ............ :7

.' //•...II' /..'

.•' ,/.......:.. ./V

." ~..•.~

5

oo

15

10

Accumulation (g)

20

Time (h)

Fig. A3.1. Permeation of ethanol through PDMS.

limiting mass flow is achieved after 2 h of the experiment. The permeabilityis defined in the text:


The flux J j (units: mol m- 2 S - 1) is the limiting flux found from thegraph, the pressure drop ~p (Pa) is that between the vapour pressure onthe feed side and the vacuum on the permeate side, the thickness, ~y, (m) isthe thickness of the film.

~p=(0'132--o'OOl) bar

~y=lO~m

J j =4.525 kg m -2 h -1 =0,0274 mol m -2 S-1

SO the permeability coefficient is:

PE10H =2·05 x 10- 11 mol m m- 2 S-1 Pa- 1

All data required is supplied for the other components so calculation isstraightforward.

Limiting fluxes mol wt vapor press g!h g!m 2'h mol!m2'h mol!m 2 ·s Permeability(35°C) this mem

Methanol 32 2828 7-84 4332 135-4 0·03761 1'33E-11ethanol 46 1333 8·19 4525 98·39 0·027 33 2'05E-IIn-propanol 60 5315 10·1 5591 93·20 0·02589 4'87E-II

water 18 5555 0·564 311·7 17-32 0'004811 0 8'66E-12


RTn·= --lnla·1

I JIi I

where i refers to the solvent. For ideal dilute solutions, ai=Yixj~l-xj,where Xj is the mole fraction of the other components. Hence lnlad ~In(l-x) ~ -Xj for small Xj'

Let n = number of moles

... V;= V/nj

xj=n)(ni+nj)

. n.=~·ni RT•. I nj+nj V

>::;cjRT

i.e. the osmotic pressure of a dilute solution is proportional to the molarconcentration of the solutes.

108


R. W. Field

1 Either if low molecular weight molecules are required in the concentrateor if it is necessary to minimise BOD demand of the permeate2 R = 1-(cs2/csJ

0·95 = 1-(cs)10)

.·.CS2 =0'5

Concentration of NaCI in permeate is 0·5 kg m - 3

3 Volumetric flux = Kw (LlP - LlIl)

LlIl =0·77 (10-0'5)= 7·315

".Kw =4·15 x 10- 6/(25-7'315)

=0,235 x 10- 6

Membrane constant Kw =0'235 x 10- 6 ms- 1bar- 1

Ks =4'15 x 10- 6/(10-0'5)

=0-437 x 10- 6 ms- 1(kg m-3 NaCl)-1

4 Osmotic pressure coefficient, Kw and Ks are all temperature-dependent.Kw is dependent on the applied pressure whereas Ks can be taken to beindependent.

REFERENCES

Aimer, P. & Field, R. W. (1992). Limiting flux in membrane separations: a modelbased on the viscosity dependency of the mass transfer coefficient. Chern. Eng.Sci., 47, 579-86.

Aimar, P., Howell, 1. A., Clifton, M. 1. & Sanchez, V. (1991). Concentrationpolarisation build-up in hollow fibers: a method of measurement and itsmodelling in ultrafiltration. J. Mernbr. Sci., 59, 81-9.

Aimar, P. & Sanchez, V. (1986). A novel approach to transfer limiting phenomena during ultrafiltration of macromolecules. Ind. Eng. Chern. Fundarn., 25,789-98.

Aimar, P., Turner, N. M. & Howell, 1. A. (1989). Effects of concentrationboundary layer development on the flux limitations in ultrafiltration. Chern.Eng. Res. Des., 67, 255-61.

Altena, R. W. & Belfort, G. (1984). Lateral migration of spherical particles inporous flow channels: application to membrane filtration. Chern. Eng. Sci.,39(2), 343-55.


Altena, F. W., Belfort, G., Otis, J., Fiessinger, F., Rovel, 1. M. & Nicoletti, H.(1983). Particle motion in laminar slit flow: a fundamental fouling study.Desalination, 47, 221-32.

Bellhouse, B. J. et al. (1973). A high efficiency membrane oxygenator and pulsatilepumping system and its application to animal trials. Trans. Am. Soc. ArtiJ.Intern. Organs, 19, 72-9.

Berger, F. P. & Hau, K. F. (1977). Mass transfer in turbulent pipe flowmeasured by the electrochemical method. Int. J. Heat Mass Transfer, 20,1185-94.

Blatt, W. F., David, A., Michaels, A. S. & Neba, A. (1970). Solute polarisation andcake formation in membrane ultrafiltration. In Membrane Science and Technology, ed. 1. E. Flinn, Plenum Press, New York, pp. 47-97.

Brenner, H. (1966). Hydrodynamic Resistance of Particles at Small ReynoldsNumbers. In Advances in Chemical Engineering, Vol 6, ed. T. B. Drew, J. W.Hoppes Jr & T. Vermeulen, Academic Press, pp. 287-438.

Cheryan, M. (1986). Ultrafiltration Handbook, Technomics, Lancaster, PA.Clifton, M. J., Abidine, P., Aptel, P. & Sanchez, V. (1984). Growth of the

polarization layer in ultrafiltration with hollow fibre membranes. J. Mernbr.Sci., 21, 233-46.

Cox, R. G. & Brenner, H. (1968). The lateral migration of solid particles inPoiseuille flow-I. Chern. Eng. Sci., 23, 147-73.

Danckwerts, P. V. (1951). Significance of liquid film coefficients in gas absorption.Ind. Eng. Chern., 43, 1460-7.

Danckwerts, P. V., Kennedy, A. M. & Roberts, D. (1963). Kinetics of CO 2

absorption in alkaline solutions: II Absorption in a packed column and tests ofsurface renewal models. Chern. Eng. Sci., 18, 63-72.

Davidson, J. F., Cullen, E. 1. & Hanson, D. (1959). The hold-up and liquidfilm coefficient of packed towers. Trans. IChernE, 37, Part I, p. 122; Part II,p. 131.

Dorrington, K. L. Ralph, M. E., Bellhouse, B. 1., Gardez, 1. P. & Sykes, M. K.(1985). Oxygen and CO 2 transfer of a polypropylene dimpled membrane lungwith variable secondary flows. J. Biorned. Eng., 7, 87-99.

Eckstein, E. c., Bailey, D. G. & Shapiro, A. H. (1977). Self-diffusion of particles inshear flow of a suspension. J. Fluid Mech., 79, 191-208.

Fane, A. G., Fell C. 1. D. & Nor, M. T. (1982). Ultrafiltration in the presence ofsuspended matter. IChernE Jubilee Syrnp., CI-CI2.

Fane, A. G., Kim, K. 1., Hodgson, P. H., Leslie, G., Fell, C. 1. D., Franken, A. Cm.,Chen, V. & Liew, K. H. (1990). Strategies to minimise fouling in the membraneprocessing of biofluids. Front. Bioprocessing II, Colorado, June 17-21.

Field, R. W. (1990a). Introducing the concept of film heat transfer coefficients.Chern. Eng. Educ., 24, 132-135.

Field, R. W. (1990b). A theoretical viscosity correction factor for heat transfer andfriction in pipe flow. Chern. Eng. Sci,,45, 1343-7.

Field, R. W. & Aimar, P. (1992). Limiting fluxes in membrane separations:comparison of experimental and theoretical relationships, Engineering of Mernbrane Processes C01!ference, May 1992, Bavaria, Germany.

Finnigan, S. M. & Howell, J. A. (1989). The effect of pulsatile flow on ultrafiltrationfluxes in a baffled tubular membrane system. Chern. Eng. Res. Des., 67, 278-82.

110 R. W. Field

Fischer, E. & Raasch, 1. (1986). Model tests of the particle deposition at the filtermedium in cross-flow filtration. Proc. 4th World Filtration Conf, Ostend, PartII, pp. 11.1-11.17.

Gekas, V. & Hallstrom, B. (1987). Mass transfer in the membrane concentrationpolarisation layer under turbulent cross-flow, Part I. J. Membr. Sci., 30(2),153-170.

Goldsmith, R. L. (1971). Macromolecular ultrafiltration with microporous membranes. Ind. Eng. Chem. Fundam., 10,113-120.

Green, G. & Belfort, G. (1980). Fouling of ultrafiltration membranes: lateralmigration and the particle trajectory model. Desalination, 35, 129-47.

Guizard, c., Ajaka, N., Garcia, F., Larbot, A. & Cot, L. (1990). New membranes forthe hyperfiltration of small molecules: influence of the mesoporous structure onseparation and fractionation performances. Proc. 5th World Filtration Congress.

Heinemann, P. (1987). The problem of fouling in microfiltration, PhD Thesis,University of Bath.

Higbie, R. (1935). Trans AIChE, 35, 365.Howell, 1. A. & Velicangil, O. (1982). Theoretical considerations of membrane

fouling and its treatment with immobilized enzymes for protein ultrafiltration.J. Appl. Polym. Sci., 27, 21-32.

Huang, R. Y. M. & Rhim, J. W. (1991). Separation characteristics of pervaporation membrane separation. In Pervaporation Membrane Separation Processes,ed. R. Y. M. Huang, Elsevier, Amsterdam, pp. 111-80.

Jonsson, G. (1984). Boundary layer phenomena during ultrafiltration of dextranand whey proteins solutions. Desalination, 51, 61-77.

Karnis, A., Goldsmith, H. L. & Mason, S. G. (1966). The flow of suspensionsthrough tubes versus inertial effects. Can. J. Chem. Eng., 44, 181-93.

Katchalsky, A. & Curran, P. F. (1967). Non-equilibrium Thermodynamics inBiophysics, Harvard University Press, Cambridge, MA.

Kay, J. M. & Nedderman, R. M. (1985). Fluid mechanics and transfer processes,Cambridge University Press, Cambridge.

Kopecek, J. & Sourirajan, S. (1970). Performance of porous cellulose acetatemembranes for the reverse osmosis separation of mixtures of organic liquids.Ind. Eng. Chem. Proc. Des. Dev., 9, 5-12.

Kozinski, A. A. & Lightfoot, E. N. (1972). Proteins ultrafiltration: a generalexample of boundary layer filtration. AIChEJ, 118, 103-40.

Leighton, D. T. & Acrivos, A. (1987a). Measurement of shear-induced selfdiffusion in concentrated suspensions of spheres. J. Fluid Mechanics, 177,109-31.

Leighton, D. T. & Acrivos, A. (1987b). The shear-induced migration of particles inconcentrated suspensions. J. Fluid Mech., 181, 415-39.

Leonard, E. F. & Vassilieff, C. S. (1984). The deposition of rejected matter inmembrane separation processes. Chem. Eng. Commun., 30, 209-17.

Lewis, D. A., Field, R. W., Xavier, A. M. & Edwards, D. (1982). Heat transfer inbubble columns, Trans. IChemE, 60, 40-7.

Lojkine, M. H., Field, R. W. & Howell, J. A. (1992). Crossflow microfiltration ofcell suspensions: a review of models with emphasis on particle size effects. TransAIChE, 70, Part C, 149-64.

Long, R. B. (1965). Liquid permeation through plastic films. Ind. Eng. Chem.Fundam., 4, 445-51.


Mackley, M. (1987). Using oscillatory flow to improve performance, The Chem.Eng., Feb. 1987, 18-20.

Michaels, A. S. (1968). New separation technique for the CPI. Chem. Eng. Prog.,64(12), 31-43.

Neel, J., Aptel, P. & Clement, R. (1985). Basic aspects of pervaporation. Desalination, 53, 297-326.

Ofsthun, N. J. & Colton, C. K. (1987). Visual evidence of concentration polarisation in cross-flow membrane plasmapheresis. Trans. Am. Soc. Artif. Intern.Organs, 33, 510-17.

Papamichael, N. & Jula, M-R. (1987). A hydrodynamic study of the retention ofpolyethylene glyciols by cellulose acetate membranes in the absence andpresence of proteins. J. Membr. Sci., 30, 259-272.

Pasternak, R. A., Schimscheimer, J. F. & Heller, J. (1970). A dynamic approachto diffusion and permeation measurements. J. Polym. Sci., Part A-2, 8,467-79.

Porter, K. E. (1966). The effect of contact-time distribution on gas absorption withchemical reaction. Trans. IChemE, 44, T25-T36.

Porter, M. C. (1972). Concentration polarisation with membrane ultrafiltration,Ind. Eng. & Chem. Prod. Res. Dev., 11(3), 234-48.

Porter, M. C. (1988). Membrane filtration. In Handbook of Separation Techniquesfor Chemical Engineers, ed. P. A. Schweitzer, McGraw-Hili, New York.

Rakow, A. L. & Chappell, M. L. (1987). Axial migration of spirulina microalgae inlaminar flow tube. Biorheology, 24(6), 763-8.

Rautenbach, R. (1988). Ultrafiltration of macromolecular solutions and cross-flowmicrofiltration of colloidal suspensions: a contribution to permeate flux calculations. J. Membr. Sci., 36, 231-42.

Rautenbach, R. & Albrecht, R. (1989). Membrane Processes, Wiley, Chichester.Reismeier, B. Kroner, K. H. & Kula, M.-R. (1987). Studies on secondary layer

formation and its characterisation during cross-flow filtration of mirobial cells.J. Membr. Sci., 34, 245-66.

Seider, E. N. & Tate, G. E. (1936). Heat transfer and pressure drop of liquids intubes. Ind. Eng. Chem., 25, 1429-35.

Schiiler, T. (1989). Ultrafiltration et electro-ultration de solutions de gelatine.Diplomarbeit, Aachen, FRG.

Sourirajan, S. & Matsuura, T. (1985). Reverse Osmosis/Ultrafiltration ProcessPrinciples, National Research Council of Canada, Ottawa.

Strathmann, H. (1979). Trennung von molekularen Mischungen mit Hilfe synthetischer Membranen, D Steinkopff Verlag, Darmstadt.

Strathmann, H. (1990). Membranes and membrane separation, A 16, 187-263.Taddei, c., Aimar, P., Howell, J. A. & Scott, 1. A. (1990). Yeast harvesting from

cider using microfiltration. J. Chem. Technol. Biotechnol., 47, 365-76.Van den Berg, B. G. & Smolders, C. A. (1990). Flux decline in ultrafiltration

processes. Desalination, 77, 101-33.Velicangil, O. & Howell, 1. A. (1980). Estimation of the properties of high flux

ultrafiltration membranes. J. Phys. Chem., 84(23), 2991-2.Vilker, V. L., Colton, C. K., Smith, K. A. & Green, D. L. (1984). The osmotic

pressure of concentrated protein and lipo-protein solutions and its significanceto ultrafiltration. J. Membr. Sci., 20, 63-77.

112 R. W. Field

Wijmans, J. G., Nakao, S., Van den Berg, J. W. A., Troelstra, F. R. & Smolders, C.A. (1985). Hydrodynamic resistance of concentration polarization boundarylayers in ultrafiltration. J. Membr. Sci., 22, 117-35.

Zeman, L. J. (1983). Adsorption effects in rejection of macromolecules byultrafiltration membranes. J. Membr. Sci., 15, 213-30.

Zydney, A. L. & Colton, C. K. (1986). A concentration polarisation model for thefiltrate flux in crossflow microfiltration of particulate suspensions. Chem. Eng.Commun., 47, 1-21.

Chapter 4

SEPARATION BY MEMBRANES

P. AI MAR

Laboratoire de Genie Chimique et Electrochimie, CNRS, Universite Paul Sabatier,118 Route de Narbonne, 31062 Toulouse Cedex, France

4.1 INTRODUCTION

The present chapter describes the principles of separation for porousmembranes because the membrane processes mostly used in biotechnology are ultrafiltration and microfiltration. Other membrane processes inuse in biotechnology are dialysis, electrodialysis and reverse osmosis.These are not described in this chapter.

The separations achieved by membrane techniques are of two types: (a)solvent-solute separation (i.e. concentration and purification) or (b) solutesolute separation (fractionation of mixtures). Case (a) is an important stepin downstream processing, consisting of the concentration of solutions(dewatering) or of the purification from salts and small molecules (diafiltration). Case (b) is more prospective; a rule of the thumb is that twomolecules can be separated by a porous membrane at a preparative scaleonly if the larger one has a molar mass ten times larger than the smallerone. Relatively few attempts have been published yet to fractionatemacromolecules Cheryan (1986). Ingham et al. (1980) give some insightsinto the separation of PEG, BSA, iX-lactalbumin, and lysozyme. Baker(1986) proposes different cascades to fractionate PVP, and Barker et al.consider the fractionation of dextran also by cascades. Nakao et al. (1988)worked on the separation of globular proteins, and Kimura and Tamanoon the separation of amino acids. Chaufer et ai. (1988) separated wheyproteins by using polyether-imine modified Carbosep membranes.Bothorel et al. (1991) separated fractions of fish proteins. For efficiencysuch separations of bio-colloids of similar size necessarily require operation in a diafiltration mode. However, industrial applications of suchselective separations have not yet appeared, at least in the literature. Some

113

114 P. Aimar

of the reasons for this are membrane fouling which modifies both porousstructure and surface properties of the membrane, the inability to maintainsteady state during long periods, and the cost and technical difficulties ofpre-treatment of both membranes and fluids.

Another important membrane operation is the clarification (and sterilisation) of biofluids. From a separation point of view, the main objective is toretain particles, bacteria or cells, and to let proteins, enzymes or smallerbiomolecules through. The transmission of macromolecules through cleanand, especially, through fouled membranes is then of first importance.

Despite these drawbacks, ultrafiltration or microfiltration remain attractive for process engineers because they are easy to scale-up, have lowenergy demands and impose only mild chemical, thermal and mechanicalstrains upon the material processed.

The process selectivity depends upon the porous membrane structure, onthe chemical and physical properties of the membrane material, which, inturn, control membrane-macromolecule interactions. The way the membrane and the module are operated also has a determining influence on theseparation efficiency. In the present Chapter the main phenomena linked tothe porous nature of the membrane are examined. Since the driving force is apressure gradient, the role of convection with regard to diffusion through theporous medium is discussed. The influence on selectivity of chemical orphysico-chemical interactions between membranes and solutes, such asionic interactions or hydrophobic ones are presented. The last section describes engineering aspects of the separation and the purification of macromolecules by membranes. The effects of concentration polarisation and fouling on selectivity are discussed.Diafiltration is described and examples given.

4.2 SELECTIVITY OF POROUS MEMBRANES

Particular reference will be made to the transport equations for flowthrough pores. Engineering aspects are covered in section 3.

4.2.1 Membrane Porous Structures

As presented in Chapter 2, the skin layer of organic membranes can berepresented as a network of irregular, tortuous, finger-like pores in apolymer matrix. Inorganic membrane skin layers look like multilayers ofspheroids, irregular in shape and size. As discussed in the fouling chapter,the characteristics of the porous layer are modified during fluid processingby the deposition of molecules on the surface and inside the structure.

In practice, a convenient mathematical description of a porous networkshould be developed from the transport equations and a characterisation

Separation by Membranes 115

method that allows the model parameters to be measured using standardised experimental procedures. Up to now, most models have consideredthe pores to be straight, long cylinders, all of the same diameter and length(homoporous membrane). Such simplifications are popular because theyallow numerous assumptions to be set when writing the mass transportequations through the porous structure. In UF and MF, the matrix(non-porous part of the skin layer) is assumed impermeable to both soluteand solvent. The transport through the macroporous support of themembrane is neglected in general.

One refinement in such a description consists in assuming a distributionin pore size, or rarely in length. This implicitly supposes that the differentpores work independently from each other. In the absence of concentration polarisation, this is certainly true, given the average pore density. Thedescription of a transport through a membrane with a certain pore sizedistribution is then made easier, since the flow of solvent and of solutethrough the skin layer is merely the sum of the flows in each pore.

4.2.2 Flow of Solvent through a Single Pore

If one assumes cylindrical pores, the flow of solvent qw is as follows:

qw = 2nt xv(x) dx (4.1)

Whether the solvent can be considered as a continuum or not is aquestion that can be raised here. The answer is certainly yes for microfiltration membranes, where the average pore size is larger than 100 nm,when a water molecule is about 0·3 nm in diameter. The answer is tougherwith ultrafiltration membranes, where the pore diameters can rangebetween 3 and 30 nm. The assumption is probably true in the higher partof the range, but is certainly questionable in the lower part of it. Therefore,if the equations governing the flow of water through porous membranesare derived under the assumption of a continuum inside the pores, theiruse to describe ultrafiltration membranes with a fine structure might berisky. In this text we shall use this assumption, and also the HagenPoiseuille model to describe the flow through a cylindrical pore. However,other models have been discussed in the literature, as in Velicangil andHowell (1980) but no experimental evidence is yet available to decidewhich model is more appropriate.

The flow distribution across the pore is given as (Bird et aI., 1960):

v(x)=2v(l-(x/r)2) (4.2)

116 P. Aimar

where v is the average velocity in the pore and r is the pore radius. Theflow qw through the single pore is:

qw = nr2 I1Pr2/8jll (4.3)

The flux of solvent through a homoporous membrane with a poredensity n (n pores per m2

) is then:

J=nqw=(a'r 2/8)I1P/jll (4.4)

where a is the surface porosity (total area of the pore mouths/m2). Typicalvalues for n range between 1012 for a microfiltration membrane (Porter,1990) to 1016 for an UF membrane. Equation (4.4) can be compared to afiltration law:

J=Lp I1P/jl (4.5)

where Lp is the membrane permeability. Combining eqns (4.4) and (4.5)allows an expression for the permeability to be derived:

L p = ar2 /81 (4.6)

The theoretical permeability of the membrane depends on the surfaceporosity, on the square of the pore radius, and on the thickness of the skinlayer. A surface porosity of 5-15% is reasonable for organic membranes(Fane et al., 1981) whereas values as large as 40% can be expected forceramic membranes. However the skin layer is generally much thickerthan for plastic membranes.

4.2.3 Flow of Solute through a Pore

The problem of macrosolute transport through a capillary has beenextensively studied from a theoretical point of view by the groups of Brenner,of Anderson and of Deen (Deen, 1987), among others. There is a gap betweentheoretical studies and experimental works. The latter have often beenperformed using model systems such as latices or PEO on mica or Nucleporemembranes, because one can equate their pore shape and distribution withtheoretical models (Munch et al., 1979: Zeman & Wales, 1980). Also becausethe pore size can easily be measured by microscopic techniques. A few resultshave been published on the application of theories to ultrafiltrationmembranes with proteins (Deen and Smith, 1982; Jonsson and Christensen,1986). For these membranes, no technique allows the pore size and shape tobe measured, and also other forces than hydrodynamic ones can besignificant, as presented later in this chapter. The quantitative comparisonwith theoretical models is therefore more difficult for UF membranes thanfor membranes with larger pores. In such models the colloid, molecule orparticle is modelled as a rigid, solid sphere of radius a.

The retention R of macromolecules by a membrane can be defined byuse of the rejection coefficient introduced in section 3.6.1. A physical basisof retention is considered from the following: let the flow of solute in theabsence of selectivity be No whilst the actual flow is N. The retention isNo - N, i.e. the fractional retention is:

(4.7)

In the absence of selectivity, there would be a constant concentrationand hence no diffusion involved in No:

(4.8)

(4.9)

N is the sum of a diffusive flow and of a convective flow in the pore axisdirection, provided we assume (as has been done in this section) that theselectivity is only provided by size exclusion. In the simple model of ahomoporous membrane, the diffusion flux can be written as:

fr-a deNd =2mr 0 xDoK dx dx

The upper limit (r - a) ofintegration corresponds to the fact that the centre ofa particle cannot approach the wall at less than a distance equal to its radius,a. K is a coefficient to account for the effects of the pore geometry on thediffusion coefficient. Various expressions for K (usually noted K - 1) havebeen proposed, e.g. by Anderson and Quinn (1974) and also by Brenner andGaydos (1977). The values of their correction factors (Happel & Brenner,1986) are close to each other. One can use the following one, for A<O'4:

K = 1-2·1044A+2·089A3 -O·948A5 (4.10)

with

A=a/r (4.11)

Assuming that there is no radial concentration gradient across a poresection, and that the axial concentration gradient is constant, eqn (4.9) canbe integrated into:

Nd=(jDoK(~C/l) (4.12)

where I is the pore length and

=(1-A)2 (4.13)

The convection flux N c can be estimated in the same way:

N c = 2nnt-a

Gv(x)x dx (4.14)

118 P. Aimar

where G is a correction factor to account for the modification of thePoiseuille flaw by the presence of the molecules in the pore. G was initiallyworked out by Faxen (1922a,b), for a sphere travelling along the axis of thecylinder (centreline approximation). A detailed analysis of the differentversions of G is given in Happel and Brenner (1986). An expression for Gisas follows, for 2 < 0·4.

G = [1-2/322 -0'16282 3 + ...J (4.15)

Substituting for v(x) (eqn (4.2)) in eqn (4.12) and assuming this approximation is also valid for other radial positions allows the followingequation to be derived:

N c = J<101>(2 - <I»G

The retention coefficient (eqn 4.7) then becomes:

(4.16)

R = 1- {J(2 -<I»CG + <l>DoK(~C/I)}/{J· Cb} (4.17)

Diffusion and convection do not have necessarily the same importance, and eqn (4.17) can be simplified if one or the other isnegligible.

4.2.1.3 Convection or Diffusion in a Pore?The convection controls the transport of solute only if N c/N d is larger than1. According to eqns (4.12) and (4.16), one can write:

(4.18)

JI/Do is a pore Peclet number, Pel' If we assume a flux J of 10- 5 m/s (i.e.around 361/h/m2

) and a surface porosity <1 of 5%, which is reasonable forfouled membranes, the average velocity in the pore is about 2 x 10- 4 m/s.If Do is taken as 5 x 10- 11 m2/s for a protein (Tanford, 1961; Tyn &Gusek, 1990), and the thickness of the skin layer I as 1 Jlm (1 x 10- 6 m),then Pel=4. {(2-<I»G/K} is plotted in Fig. 4.1 as a function of 2. The termis always larger than 1, even for I> 0'4, as shown by Anderson and Quinn(1974). One can conclude that convection dominates mass transportprovided that C/(Cw - Cp) is not too small. If ), is little, then Cp is veryclose to Cw (no exclusion), and Cb/(Cw-Cp) is large. When 2 is large,Cw- Cp is equivalent to Cwo However, given the values calculated byAnderson and Quinn, and the Peclet number, Nc/Nd is always larger than1. In other words, convection controls the transmission of macromolecules through porous UF or MF membranes, except maybe at very low

10Nc/Nd/Pe

5

Lemde

0,50,40.30.20.1o+--.-----r-~-~-~-r_~-___,_-~____.0,0

Fig. 4.1. Left hand term of egn (4.18) divided by (i.l.IDo) as a function of A., the ratio ofmolecule to pore average radii.

transmission and high concentration polarisation, where diffusion canplaya part. In most cases, eqn (4.17) can then be simplified to:

R= 1-(2-<I»G (4.19)

Assuming, as Ferry (1936) did, that the flow through a capillary is notdisturbed by the presence of particles, a simplified but very useful formulacan be obtained:

(4.20)

A similar derivation with plug flow through the pore (i.e. the velocity ofthe solvent is independent of the radial position across the pore crosssection, and equal to the average velocity) would have given:

R=1-(1-AV (4.21)

4.2.3.2 Comments on the Sieving EquationSize exclusion, such as described in eqns (4.20) or (4.21), is a segregation ofmolecules based on their apparent geometrical size. Figure 4.2 shows thevariation in R versus the reduced molecule radius A( = air). Although thevelocity profile has some importance in the numerical value of thepredicted retention, the main feature is a progressive selectivity, verydifferent from the step function (dotted line in Fig. 4.2) that manymembrane users dream of.

However, polymer chemists or biochemists use the molar mass ('molecular weight') when talking about the size of macromolecules. Sievingrelationships such as eqn (4.20) have hence to be adapted to these customs.In a first approximation, let us consider that macromolecules have aspherical symmetry, and hence, that their volume is proportional to the

- R

• JIk=l

• JIk=2

• JIk=5

P. Aimar120

1,2

1,0

0,8

0,6

0,4

0,2

0,00,0

Retention

0,2 0,4 0,6 0,8 1,0 aIr 1,2

Fig.4.2. Size exclusion retention coefficient R (eqn (4.19» As mentioned later concentrationpolarisation modifies the shape of the curves. As J /k increases the ideal step function(dotted line) is theoretically approached. Curves for different J/k based on equation (4.32).

cube of their characteristic size (equivalent radius), noted a. Assuming thatthe molecules from a single family, such as albumins, gelatins, lignosulphonates, dextrans, polysaccharides, etc, have the same density p, onecan write an expression for the molar mass Mm:

Mm= p' N . (4/3)na 3 (4.22)

The exponent of 3 is a theoretical one. In practice, we have obtained thefollowing empirical relationships for dextran Stokes radii from Granathand Kwist data (1967)

Mm=6'10 x 1022a(2'17)

The PEG Stokes radii from Tam and Tremblay (1991) is:

Mm = 1·46 x 1021 (a)2

Whilst the radius of giration radius of proteins according to Tyn andGusek (1990) is:

Mm=3'1 x 1025 Rg(2'72)

However, for the sake of simplification, we keep the exponent of 3 for therest of the development, since it is close to the one found for proteins.Accordingly, the solution of the following equation:

Mco=p'N'(4/3)nr3 (4.23)

gives the molar mass of the spherical molecule having the same radius asthe average pore radius of the membrane. Mco is a theoretical definition ofthe cut-off of the membrane. In practice, membrane manufacturers provide


a value for Mco that has been experimentally determined by extrapolation ofretention measurements of solutes of different size. This value is thereforedependent on the type of solute and on the conditions under which themeasurements have been carried out and do not necessarily match the abovedefinition.

Substituting for r and a in eqn (4.20) would then lead to:

R =(1-(1-(MmjMco)(l/3l)2)2 (4.24)

Equation (4.24) is plotted in Fig. 4.3 and experimental data reported byPorter (1990) are also presented in Fig. 4.4. The impression one could havehad of a poor selectivity in Fig. 4.2 is even worse here, particularly in therange of molar masses around the theoretical cut-off of the membrane.This graph illustrates how there is little difference in partition coefficientseven for molecules having molar masses in a ratio of 2. This is also ajustification for the rule of the thumb presented at the beginning of thechapter. As for example, from the curve in Fig. 4.3, one can estimate that a10-kDa protein should be retained at 50% by a 100-kDa nominal MWCOmembrane.

1,0 .----------:;:::::::::iit=""'I!I'-----1j1Retention

0,8

0.6

0,4

0,2

Mm I Meo

0,0 ~-.....--____,.-------.---.--.,...---.--...,...-....-----l

0,0 0,2 0,4 0,6 0,8 1,0

Fig. 4.3. Retention coefficient according to size exclusion (eqn 4.24) plotted as a function ofmolar mass, if macromolecules are assumed hard spheres. Mco is the molar mass of a

molecule having the same radius as the pore.

However, one of the achievements of chemical engineering is the designof efficient ways to separate components with boiling points or partitioncoefficients of which are very close. Therefore, curves such as those shownin Figs 4.2 and 4.3 should be considered with some optimism, since theygive evidence of, at least, a little segregation between macromolecules thatare different in their size. Section 3 of this chapter illustrates how this littledifference can be exploited to give a sharp separation, at the cost of someextra operating time, solvent volume or membrane area.

122

1,0

0,8 'ic:0-c:Q)

0,6-Q)

a:

0,4

P. Aimar

UM-05

UM-2

PM-10

PM-30

• XM-50

0,2 -+--.......---.----..----...---...--...-- --1

2 3 4 5 6

Log (Molar mass)

Fig. 4.4. Retention of a series of globular proteins for several Amicon Ultrafiltrationmembranes.

4.2.3.3 Selectivity and Ionic InteractionsAmong the various interactions a molecule can experience when travellingthrough a pore, the non-specific charge interactions are the most probable,together with the van der Waals ones. Not all macromolecules areconcerned by this sort of interaction, because they are not charged.However, most of the macromolecules coming from the major fields ofapplication of ultrafiltration and microfiltration (food, beverages, biotechnology, pharmaceutical, paints) carry net charges and this section particularly refers to these applications. Evidence of such interactions withcharged ultrafiltration membranes have been shown in earlier studies byBhattacharyya et at. (1980), for the repulsion of sulphate anions in water,by Kimura and Tamano (1986) and by Nakao et at. (1988) in separation ofmyoglobin from cytochrome.

Talking about the net number of charges of a macromolecule is again anoversimplification, since this net value is the result of the combination ofthe relative charges of the different amino acids constituting the molecule.This net charge depends on the pH if the molecule has amphotericproperties. A similar remark can be made about membrane materials. Ingeneral, membranes in cellulose acetate or sulphonated polysulphone havea negative zeta potential (measured across the membrane) for pH largerthan 3 (Nystrom et at.) (see Chapter 6). Chemically neutral materials such

as PVDF or polyether sulphone can show negative zeta potentials, due tostrong adsorption of anions from the buffer or the electrolytic solutionused to dissolve macromolecules. Zirconia has an isoelectric point aroundpH 5 (Rollin, 1991).

When interactions between membrane material and macromolecules areattractive, the latter adsorb on the pore walls, generally at a large numberof interaction sites per molecule, which stabilise the molecule on thesurface. The shear forces induced by the filtration are generally not strongenough to overcome this attraction, and the macromolecules remainattached to the pore walls. This is typically one of the several foulingmechanisms, soon leading to a pore size narrowing or, even worse, to theblocking of the pore. For this reason, attractive interactions can provide aselective way of separating molecules only until the interacting sites aresaturated (just like in chromatography) which is expected to come early,given the small specific surface per unit area of membrane.

On the other hand, interactions can be repulsive when both the wallsand the macromolecule surface bear the same charges. Such a situationtheoretically corresponds to a clean membrane and a macromoleculehaving the same sign of charge. In practice, proteins adsorb most of thetime on membrane material, even if their global charges are oppositebecause other forces than electrostatic attractions lead to adsorption, suchas hydrogen bonding and hydrophobic interactions. If a pore becomes toonarrow after adsorption for another protein to pass through, its retentionbecomes equal to 1. Otherwise, the proteins passing through this pore areexpected to experience electrostatic interactions, as modified by theprotein coating of the pore wall. If the coverage is important, which seemsto be true in most cases, the interactions are repulsive, whatever the initialcharge of the membrane material. Influence of repulsive interaction onmembrane selectivity has received considerable attention from a theoretical (Malone & Anderson, 1978; Smith & Deen, 1980; Smith & Deen, 1983),and from an experimental point of view (Munch et al., 1979; Deen &Smith, 1982). If membrane and solution were at equilibrium, the freeenergy due to repulsion inside the pores would create a partition betweenporous structure and bulk (Cpor• < Cb). From a size exclusion point of view,the situation can be sketched as follows: repulsion creates a depletion atthe wall, and is balanced by diffusive transport from the centre of the poretowards the depleted zone. A distance of minimum approach, e, betweenthe pore wall and a molecule is defined, beyond which the probability tomeet a charged macromolecule is very low. e depends on the charge of themolecules, of the pore wall, on the position and size of the molecules, andon the ionic strength of the medium. In eqn (4.14), the upper limit of theintegral should then be (r-a-e). Using the Ferry approximation, one can

124 P. Aimar

derive a modified version for the retention in the presence of electrostaticrepulsions:

R' = 1-2(1-(a +e)/r)2 -(l-(a +e)/r)4

Assuming a new definition of the reduced radius A.':

A.'=(a+e)/r

Equation (4.20) changes into:

R'=(1-(1-A.')2)2

(4.25)

(4.26)

(4.27)

The distance of interaction e is equivalent, from the size exclusion model,to an apparent enlargement of the macromolecule radius by a term e.However, the molecule is actually not larger, as the Debye length does notcorrespond to a mechanical or geometrical boundary as some interpretations might lead us to believe. It is merely a distance where interactionenergy has a specific value [kT within the Debye HUckel approximation(Probstein, 1989)].

The DLVO theory (Vervey & Overbeek, 1948 or the textbook ofHiemenz, 1986) provides a good description of electrostatic interactions atthe particle scale. In particular, this theory has often been used withsuccess to interpret the phenomena of aggregation or flocculation, i.e. therepulsion/attraction balance between particles or colloids. Within theassumptions of such a theory, flocculation is observed when the freeenergy due to electrostatic interactions between two particles is equal to(or smaller than) kT. This condition is achieved when the distance betweenthe two particles is equal to (or smaller than) the characteristic Debyelength, ld (Hunter, 1988; Probstein, 1989).

Rollin (1991) considers that the distance of minimum approach of acolloid from a pore wall is equal to ld' Munch et al. (1979) assume that thisdistance is 21d , which seems more reasonable in order to avoid that van derWaals attractions overcome electrostatic repulsions. However, the definition these authors take for the reduced radius ),"=(a+ld)/(e-1d), is notconsistent with the solute and solvent transport equations as written byFerry (see eqn (4.20». The distance of interaction e is then probably largerthan ld' say twice as large. The Debye length depends on the saltconcentration as follows, for a 1: 1 salt Hiemenz (1986) gives:

ld = 3/mO /2) (ld in Angstroms) (4.28)

m: salt concentration in mOl/I. The apparent radius (a + 21d ) of a moleculeis not significantly different from its actual one (a), if 2ld/a is smaller than,say 0'1; i.e.:

m>[60/a]2 (4.29)


By way of example, consider the influence of repulsive interaction for BSA(a = 36 A). It should be negligible only if m is larger than 2·8 M, which is aquite high salt concentration.

One should then expect that charged molecules are more rejected thanneutral ones by charged membranes, unless the value of e is negligiblecompared to the molecule radius. This result, although obtained underseveral simplications points out the role of ionic strength on selectivity ofporous membranes as observed by several authors (Munch et al., 1979;Deen & Smith, 1982; Fane et al., 1983). Changes in pH should also have aninfluence on retention, but in a more complicated manner since forexample, a globally neutral molecule at its IEP is also poorly soluble andthen prone to adsorb on the pore walls, thus reducing the pore radius.However, Nakao et al. (1988) showed that for myoglobin, BSA orcytochrome C, retention was always smaller at the IEP.

The measurement of the surface charge of pore walls and the study of itschanges with ionic strength, pH, and adsorption on different materials isthe purpose of several recent studies (Nystrom et al., 1989; Bowen & Gan1991; Hernandez et al., 1991). This information can be a key factor forfouling control and also solute transmission.

4.2.3.4 Influence of Physico-chemistry of Colloids on TransmissionAs commented before, the size of molecules is often referred to theirmolar mass (also molecular weight). This is a characteristic of theamount of matter constituting a molecule, but does not inform preciselyon the overall dimensions and shape of the molecule or the colloid.Such 'geometric dimensions' would help to describe the retention. TheStokes radius of colloids, derived from diffusion coefficient throughthe Einstein law, is therefore used extensively since it allows a descriptionof the colloid in terms of an equivalent hard sphere. Stokes radii ofdextran (Granath & Kwist, 1967), of PEG (Tam & Tramblay, 1991)and of various proteins (Tanford, 1961) are available in the literature.However, a protein, a polymer or a colloid in general is not a solid,rigid sphere, and more realistic dimensions are obtained by introducingthe radius of giration [a good definition of which is given in Hiemenz(1986)] instead of the Stokes radius. A hydrodynamic volume of thecolloid, proportional to the product of Mml1, is then involved. Suchvolume has been successfully used in size exclusion chromatographyto obtain universal calibrations for a column and various classes ofpolymers (Grubisic et al., 1967). It probably provides a better statisticaldescription of the apparent size of a molecule as compared to a poresize. The giration radius (and the hydrodynamic volume) is currentlynot used much, but this could change at least for membrane calibration

126 P. Aimar

purposes. A comprehensive list of giration radii of proteins has beencollected by Tyn and Gusek (1990).

The size and shape of macromolecules is dependent upon externalparameters. For flexible polymers, such as PEG, dextran or PVP, therandom coil can be stretched by the shear stress created by the flow ofpermeate through a pore. This was described in Chapter 2 and 6 byNguyen and Neel (1983) and de Balmann and Nobrega (1989). Thepolymer would then have a linear shape, meant to crawl through a poremore easily than the equivalent random coil. In the case of most proteins,although some flexibility can be allowed, the shape should not change thatmuch under shear stress, unless a denaturation occurs. In the latter case,several molecules aggregate to each other to form a precipitate. Such aphenomenon, also dependent on pH, ionic strength and temperature,fundamentally changes transmission, concentration polarisation and protein transmission (Twineham et al., 1984; Meireles et al., 1991). Selectivethermal, mechanical or chemical aggregation have often been used in thepast to enlarge the difference in species sizes, before performing a membrane separation (clarification).

At a pH different from the isoelectric point, intra-molecular repulsionsdominate, and tend to enlarge polyelectrolytes at least if the ionic strengthof the medium is small enough not to shield these repulsions. At theisoelectric point, the proteins are expected to be more compact in theabsence of charge repulsion. However, their transmission through porousmembranes is often not better than that obtained far from the IEP. At theIEP they are also at a minimum of solubility, and therefore have amaximum potential for adsorption: being prone to adsorb on the membrane surface and on the pore walls, thus creating self rejecting membranes(Fane et aI., 1983).

A very important phenomenon in the assessment of separation potentialis the possible interactions between the colloids to be separated, which canovercome the basic sieving mechanism, particularly if a small proteinsticks to a large one. Such interactions must be considered in each case.Ingham et al. (1980) provided convincing evidence of such interactionsbetween proteins of similar or of opposite charges (e.g. (X-lactalbumin andlysozyme shielded in the presence of 0·15 M KCI.)

4.3 PROCESS ENGINEERING

The selectivity principles discussed in the previous section only describemass transport through porous membranes. The mass balance of aseparator has not yet been considered. The performances of a membrane


separation unit depend not only on the membrane properties, but also onthe way the process is operated. In a similar manner distillation dependsnot only on the different boiling points of a mixture, but also on thecolumn operating parameters.

Two major points need to be discussed. The first one is the modificationof the theoretical sieving curves due to concentration polarisation andfouling. The second one is the design of separation processes in order toobtain the most efficient separation possible.

4.3.1 Influence of Concentration Polarisation

The retention coefficient, as defined in eqn (4.7) is the difference created bythe membrane between the concentration of two solutions, relative to oneof them (Fig. 4.5a). As convective transport is dominant, the retentioncoefficient can be written as:

(4.30)

Cp can be considered to be the average concentration in the pore. Thisequals the average concentration in the permeate only if all the pores areequal in size.

Cb Cw

(a)

Cpt R 'Xl

Cb

Cw

l'ol__CP---:.l_R

_(%_)_1 R'P' (Xl

(b)

Fig. 4.5. Retention (Rapp) and intrinsic retention (R) without (left) and with (right)concentration polarisation.

However, as shown in Chapter 3, the wall concentration Cw is differentfrom the bulk one Cb (Fig. 4.5). Since the overall mass balance of amembrane plant is based on the bulk concentration, then the retentioncalculated using the bulk concentration is somewhat different from the onegiven by eqn (4.30):

(4.31 )

In other words, eqn (4.30) tells us how the membrane performs, whereaseqn (4.31) tells what the operation achieves; it is related to the massbalance. Both are equally important, and must be linked if possible.

128 P. Aimar

Using eqn (3.97) in Chapter 3, one can work out an expression for Rappas a function of R, of the flux J, and the mass transfer coefficient k. Arearrangement of eqn (3.97) gives

In«1- Rapp)/Rapp)= In«l-R)/R) +J/k (4.32)

Relationship (4.32) is a theoretical link between the separation observed ata macroscopic scale and the local mass transport phenomena at theinterface and inside the porous skin layer. This relationship predicts thatthe selectivity of the process varies with the flux (pressure, permeability)and the mass transfer coefficient (geometry, cross flow velocity, viscosity,diffusivity, etc.... ). In general a good agreement is obtained betweenexperimental data and this relationship, provided that no other phenomenon, such as membrane fouling, occurs. For example, eqn (4.32) is used todescribe the retention data of macromolecules such as PEG or dextrans,which do not produce significant fouling of the membrane porous structure (e.g. Goldsmith, 1971; Jonsson, 1986). During filtration of proteins,the decrease in retention with flux predicted by eqn (4.32) is balanced by amodification of the pore size distribution of the membrane by thedeposition of fouling material.

4.3.2 Effects of Membrane Fouling

As shown in Chapter 6, there are numerous reasons for a molecule, acolloid or a particle to settle on the membrane surface or inside the pores,and to stay there. The main consequence is a change in flux, but also achange in the apparent porous structure of the membrane. The generaltrend reported is an increase of retention by fouled membranes ascompared to clean ones (Zeman, 1983; Hanemaaijer et ai., 1988; Taddei etai., 1989). The change in pore size from a clean to a fouled membrane canbe dramatic. Adsorption of (X-lactalbumin on a SPS membrane changesthe average radius from 7 to 2 nm (Meireles et ai., 1991). Ultrafiltrationmembranes fouled with ovalbumin showed a significant retention forsugars. Microfiltration membranes with nominal pore sizes as large as1 Jl.m can retain plasma proteins after fouling. The interpretations mightdiffer from one author to another one, but eqn (4.4) suggests twostraightforward ways to describe the effects of fouling:

- a reduction in the number of pores, n;- a reduction in the average pore radius, r.

Although the truth certainly lies between these two options, they arefrequently used in the literature under the names of pore blocking modeland pore narrowing model. However, they are not often discussed in terms


of solute retention. According to eqn (4.21), a reduction in pore size (fromrl to r2) corresponding to an increase in retention (R 1 to R 2) should satisfythe following equation:

(4.33)

(4.34)

At the same time the solvent flux should be changed from J 1 to J 2

according to eqn (4.3) (Zeman, 1983):

J 2IJ 1 =(r2/r l)4

Combining eqns (4.3) and (4.20) gives:

J 2/11 = {I- [[1- R\1/2)](l/2)]/[I_ [1 - R~1/2)](l/2)]}4 (4.35)

For example, if R 1 =0'5 and R2 =0'9, one should have J 2IJI=0·12.Normally, both eqns (4.34) and (4.35) should be satisfied by flux andretention, if the effect of fouling is a pure pore narrowing mechanism.Otherwise pore plugging can be suspected. With a homoporous membrane(all the pores of the same size), pure pore plugging should not change theretention. With a membrane showing a pore size distribution (this beingtrue of most actual situations), the blocking of some of the pores modifiesthe balance between solvent and solute transport and therefore theretention.

A more detailed analysis of fouling would be obtained if the variationsin pore size distribution with fouling could be studied. This was achievedin a study by Meireles et al. (1991) (Fig. 4.6). It was shown that both the

4.0

-G clean membrane..... BSA fouled membrane.. Ovalbumin fouled membrane~ a -laclalbumin fouled membrane

00 L.f,IlI",&to-l;]_I!L..---.:::II!!iilIll:IlllIlC_-'..=..J~~oDool!-"

o 20 40 60 60 100 120 140

Pore radius (A)

Fig. 4.6. Estimation of pore size distribution of an IRIS sulphonated polysulphone membrane 40 kDa (Tech-Sep), either clean or fouled after ultrafiltration of different protein

solutions.

130 P. Aimar

average pore radius and the distribution function vary, most probablybecause the fouled membrane has a composite structure made of the initialone modified by internal fouling, and of a layer deposited on its surface.

The choice of a membrane to solve a given separation problem shouldanticipate the above-mentioned phenomena. The cut-off of a membranecan be considered as a first clue to make a choice from a catalogue. Usingeqn (4.24) can be helpful to make a first rough estimation of the selectivityto be expected, if the molecule one is interested in has a standardbehaviour. However, experimental tests carried out at a laboratory scaleare necessary to validate and to improve the estimation, and to study theinfluence of operating parameters.

The actual performances in terms of separation depend on the type ofsolute (foulant or non-foulant), on concentration polarisation (i.e. geometry, hydrodynamics, pressure, etc.... ) and on the average pore sizethat can be expected for the membrane in operation, i.e. after fouling, andin some cases, on the flexibility of the solute.

4.3.3 Diafiltration

We have seen how a sieving membrane can achieve a separation fromamongst a series of molecules. This segregation is chiefly based on the sizeof molecules, but non-specific, and in some cases specific interactionsshould be accounted for. A more or less straightforward relationship henceexists between retention and molar mass as a function of membranecut-off. As commented before, the major conclusion from the previoussection is that the difference in intrinsic membrane selectivity for twodifferent molecules is generally small. However, the same exclusionprinciple is used in SEC chromatography or gel electrophoresis, withvery good resolutions. So if such a separation principle works with a

Dlaflltrat ion~'+---I~solvent

Permeate

Fig. 4.7. Diagrammatic view of a continuous diafiltration system.


chromatographic gel, what is the process design that would be efficient fora porous membrane?

Somehow, the permeate passing through a membrane and carryingsolutes, can be considered as a stripping phase, in the same way as inextraction. The more solute permeates through the membrane, the deeperthe extraction. From a practical viewpoint the extraction of a largeamount of solvent leads to a high concentration of the rejected solutes.This has the following drawbacks:

increase in concentration polarisation;- increase in fouling;- decrease in flux, hence increase in time and membrane surface.

If the required purification is important, such an operation will certainlygive poor results including a heavily fouled membrane, long residencetimes, and high operational costs. The usual remedy is to avoid overconcentration of rejected species by replacing the permeate with fresh solvent.This constant volume filtration technique is called diafiltration.

4.3.3.1 Mass Balance Equations in DiafiltrationTaking C as the retentate concentration the two basic equations are:

d/dt=O

d(C)/dt= -(l-R)JC

(4.36)

(4.37)

After combination and integration of eqns (4.36) and (4.37), we obtainan expression for the retentate concentration Cd' at the end of thediafiltration:

(4.38)

where Vp and Vo are the volume of filtrate and the volume of solution tobe purified respectively. Equation (4.38) is derived under the assumption ofR being constant during the run. The decrease in concentration of anyspecies is directly dependent on its retention by the membrane, and on thevolume of solvent filtered. From eqn (4.38), the volume of solvent can beworked out:

(4.39)

Vp/Vo is a reduced volume, characteristic of the diafiltration, and denotedV.

In Fig. 4.8, substituting for R given by eqn (4.24), Cd/CO has been plottedversus the reduced molar mass (Mm/Mco) in Fig. 4.8, with the volume Vas a parameter. As discussed before, the separation is eased if the difference

132

1,2

0,8

0,6

0,4

0,2

Cd I Co

P. Aimar

- V=O,OI

• V=1.0

• V=5

0 V=20

• V=50

~ V=I00.. V=200

~-- Step Function

0,0~--....-=II~.........-j~"",~4----r-""""---;/--'----,0.0 0,2 0,4 0,6 0,8 1,0 1,2

MM I MeoFig. 4.8. Theoretical composition of the retenate after diafiltration. Volume V is the ratio

of the permeate volume to the initial volume of concentrate. (Vp/Vo in eqn (4.38».

in retention between two molecules is large. One of the main features ofFig. 4.8 is that this difference increases when the volume filtered increases,i.e. the resolution of the separation increases with V. The best separationcan be expected at the inflexion point of the curve. The other characteristicof the separation is the location of this inflexion: the higher V, the higherthe molar mass at the inflexion point. This figure shows that a diafiltrationcan provide a good separation for a range of molar masses close to thecut-off of the membrane. The limit curve is the step function. Theselectivity of the process is improved by the use of large amounts ofsolvent.

The design of a separation plant should account for a balance betweenthe desired selectivity and the price to pay for it in terms of time,membrane area and volume of solvent. A wise approach would be to makesome preliminary tests even with low values of V, on laboratory cells inwhich polarisation could be significantly changed from one run to thenext, and where fouling can be assessed.

4.3.3.2 DesignWhen operating an UF or MF plant, the usual task is to concentratemacromolecules or colloids from Creed to Cproduct, and to eliminate salts orsmall molecules (from mCeed to mproduct). A question is then how to organisethe different operations (concentration, purification):

(a) at which stage of the concentration would it be optimal to carry outthe diafiltration?

(b) once the more appropriate concentration Co has been found, whichsystem of diafiltration is the less demanding in time or membranearea?


The general idea considered in this part is to start the concentration first, up to a certain level, to carry out the diafiltration atconstant concentration, and then resume the concentration. This leadsto the question: at which colloid concentration is it interesting todiafiltrate?

One generally tries to perform diafiltration as fast as possible, with thesmallest membrane plant possible. In order to find an optimum, weminimise the product of membrane area and time. The product St isreadily derived from eqn (4.39):

(4.39)

Where J is the average flux in diafiltration mode, assumed constant andRm the salt or small molecules retention. If Rm is constant during thediafiltration, St is minimum when Vo/1 is minimum.

(a) If the flux J is concentration independent, the minimum for St isobtained for the minimum of Yo: i.e. once the concentration inmacrosolute has been achieved. But one does not meet this casevery often in practice.

(b) If the flux J is concentration dependent, the minimum for St is foundwhen Vo/1(Co) is minimum.

Case (b) can be solved if a simple function is known for J as a functionof Co. As an example, the gel layer relationship (Chapter 3) is used in thepresent section to illustrate this dependence on the design of a diafiltrationplant. The separator is assumed to work in batch mode.

(4.40)

Co is the macrosolute concentration, constant during the diafiltrationstep. It is given by the mass balance:

(4.41)

R is the macrosolute retention. Substituting for Co in eqn (4.40) wouldgIve:

(4.42)

J is now a function of Yo. The optimum for St (i.e. the minimum for VoIJ)is obtained for Vo(opt), solution of equation:

d(Vo/1(Vo))/dt=O (4.43)

in which J(Vo) is given by eqn (4.42). The solution of eqn (4.43) is:

Vo/Vr= exp(l)' [Cr/Cg](l/R) (4.44)

134 P. Aimar

(4.45)

Substituting for Vo/Vr in eqn (4.41) leads to:

Co (optimal) = Cg exp( - R)

if R = 1 (total retention of the macrosolute) then

Co (optimal) =0,37 Cg (4.46)

The following table gives some optimal values for the concentration:

R Cg 100 200 300 400 5001 CoPt 37 74 110 147 1840·8 45 90 135 180 225

If Cg is known from preliminary tests, eqn (4.45), although derived undersimplifying assumptions, provides an estimation for the optimal macromolecular concentration at which diafiltration should be performed tominimise the time and membrane area.

4.3.3.4 DiafiltrationDiafiltration can be operated in batch or in continuous modes. In batch,the volume two modes can be considered: cross-current and countercurrent (Fig. 4.9 and 4.11).

4.3.3.4(a) MULTI-STAGE CROSSED-CURRENTS

A schematic flow sheet is given in Fig. 4.9. Assuming all the fluxes andrejections constant from stage to stage, if N is the number of stages, V the

Permeate Permeate Permeate

Feed

Diafi ltrationso Ivent

Diafiltrationsolvent

Diafiltrationso Ivent

Fig. 4.9. Schematic view of a cross current continuous diafiltration.

ratio (total solvent flow/feed flow) and Co/Cr the required purificationfactor, V is given by:

V=N/(I-R)[(Co/cd- 1/N)-I] (4.47)


Equation (4.47) is plotted in Fig. 4.10. For comparison, the volume of solventnecessary in batch mode has been plotted. The conclusion is that diafiltration in continuous mode is not economic in solvent unless a great number ofstages is used; then the demand for solvent tends towards that for one batch.However, the membrane area, which is proportional to the number ofstages, dramatically increases whereas it is constant for batch mode.

III Cross current

• Counter current

• Batch

• Batch· CC

Number of Btages

100Vp I Vo

80

60

40

20

00 2 4 6 8 10 12

Fig. 4.10. Volume of diafiltration solvent required to reduce the bulk concentration by afactor of 1000, for different configurations.

4.3.3.4(b) MULTI·STAGE COUNTER-CURRENT DIAFILTRATION

The flow sheet is given in Fig. 4.11. Again, a simplified mass balance canbe written, assuming Rand J constant at each stage. V must satisfy thefollowing equation:

CO/CN =(1 +V(I- R)+ V(I- R)2 + V(I- R)3 + ... + V(I- R)N) (4.48)

Solutions of eqn (4.48) are plotted in Fig. 4.10, and compared to the otherconfigurations. The counter current continuous diafiltration shows an

2 n

Solvent

Fig. 4.11. Schematic view of counter current diafiltration.

136 P. Aimar

interesting feature: it is less demanding in solvent than batch diafiltration,provided that the number of stages is high enough. Despite the highdemand in membrane area, such a configuration could be advantageous incases of diafiltration with expensive solvents such as some buffers ororganic solvents.

NOMENCLATURE

a molecule radius (m or A)Cb bulk concentration (gil or kg/l)Cp concentration in the permeateCw wall concentrationDo Diffusion coefficient of a molecule in the bulk (m 2Is)e Distance of minimum approachJ Flux of solvent through a membrane (m 3/m 2/s)k mass transfer coefficient (m/s)I skin layer thickness = pore length (m)Id Debye characteristic length (m)Lp membrane permeability (macroscopic)Mm molar mass (g/mol or Dalton)Mco molar mass cut-off (g/mol or Dalton)n pore density (11m 2

)

N Mass flux (diffusive or convective) of molecules through a pore(kg/m 3

)

i1P Pressure drop through the membrane (Pa or bar)qw Volumetric flow through a pore (m 3/s)r pore radius (m)R Retention coefficient (-)S Membrane area (m2

)

T Temperature (K or DC)v Average velocity in a pore (m/s)v Volume of fluid (m3

)

V Reduced volume in diafiltration: the ratio of the volume ofpermeate to the volume of solution to be diafiltered.

Greek symbols partition coefficientA. reduced molecule radius (air)J.l viscosity (Pa· s)'1 intrinsic viscosity(1 surface porosity (%)

Separation by Membranes

REFERENCES

137

Anderson, J. L. & Quinn, J. A. (1974). Restricted transport in small pores. Biophys.J., 14, 130--50.

Baker, R. W. (1969). Methods for fractionating polymers by ultrafiltration. J.Appl. Polym. Sci., 13, 369-76.

de Balmann, H. & Nobrega, R. (1989). The deformation of dextran molecules,causes and consequences in ultrafiltration. J. Membr. Sci., 40, 171-9.

Barker, P. E., Poland, K., Till, A. & Alsop, R. M. (1989). The development of adiafiltration cascade system for the fractionation of a dextran hydrolysate.Chem. Eng. Res. Des., 67, 262-6.

Bhattacharyya, D., Balko, M. G., Cheng, C. & Gentry, S. E. (1980). Use ofnegatively-charged ultrafiltration membranes. In Ultrafiltration membranes andApplications, ed. A. R. Cooper, Plenum Press, New York, pp. 605-8.

Bird, R. B., Stewart, W. E. & Lightfoot, E. N., Transport Phenomena, Wiley, NewYork, 1960.

Bothorel, M., Jaouen, P. & Quemeneur, F. (1991). Couplage ultrafiltrationdiafiltration pour Ie fractionnement de proteines solubles de poisson. In'Recents progres en genie des Procedes', Vol. 5, ed. G. Antonini & R. Ben Mm,pp. 111-16.

Bowen, W. R. & Gan, Q. (1991). Properties of microfiltration membranes:adsorption of bovine serum albumin at polyvinylidene fluoride membranes. J.Colloid Interface Sci., 144, 254-62.

Brenner, H. & Gaydos, L. 1. (1977). The contrained brownian movement ofspherical particles in cylindrical pores of comparable radius. J. ColloidsInterface Sci., 58, 312-55.

Chaufer, B., Grangeon, A., Dulieu, 1. & Sebille, B. (1988). Separation de proteinespar ultrafiltration sur des membranes inorganiques modifiees par depot depolymere. Filtra 88, Paris, 1988.

Cheryan, M. (1986). Ultrafiltration Handbook, Technomic Publishing Company,Lancaster.

Deen, W. M. (1987). Hindered transport of large molecules in liquid-filled pores.AIChE J., 33, 1409-24.

Deen, W. M. & Smith, F. G. (1982). Hindered diffusion of synthetic polyelectrolytes in charged microporous membranes. 1. Membr. Sci., 12,217-37.

Fane, A. G., Fell, C. 1. D. & Waters, A. G. (1981). The relationship betweenmembrane surface pore characteristics and flux for ultrafiltration membranes.J. Membr. Sci., 9, 245.

Fane, A. G., Fell, C. J. D. & Suki, A. (1983). Ultrafiltration of protein solutionsthrough partially retentive membranes. J. Membr. Sci., 16, 195-210.

Faxen, H. (1922a). Der Widerstand gegen die Bewegung einer starren Kugel ineiner zuhen Flussigkeit, die zwischen zwei parallelen ebenen Wanden eingeschlossen ist. Ann. Physik, 68, 89-119.

Faxen, H. (1922b). Die bewegung einer starren Kugellangs des Achse eines mit zaherFlussigkeit gefiillten Rohres. Arkiv Mat., Astronomi Och Fysik, 17, 1-28.

Ferry, 1. D. (1936). Ultrafilter membranes and ultrafiltration. Chem. Rev., 18,373.Goldsmith, R. L. (1971). Macromolecular ultrafiltration with microporous mem

branes. Ind. Eng. Chem. Fundam., 10, 113.

138 P. Aimar

Granath, K. A. & Kwist, B. I. (1967). Molecular weight distribution by gelchromatography on sephadex. J. Chromatogr., 28, 69-81.

Grubisic, Z., Rempp, P. & Benoit, H. (1967). A universal calibration for gelpermeation chromatography. Polym. Letts, 5, 753-9.

Hanemaaijer, J. H., Robbertsen, T., van den Boomgaard, T. & D. G. Oliemen P.Schmidt (1988). Characterisation of clean and fouled ultrafiltration membranes.Desalination, 68, 93.

Happel, H. & Brenner, H. (1986). Low Reynolds Number Hydrodynamics, Martinus Nijhoff Publishers, Dordrecht.

Hernandez, A., Calvo, J. I., Martinez, L., Ibanez, J. A. & Tejerina, F. (1991).Measurement of the hydraulic permeability of microporous membranes fromthe streaming potential decay. Sep. Sci. Technol., 26(12), 1507-18.

Hiemenz, P. C. (1986). Principles of Colloid and Surface Chemistry, 2nd Edn,Marcel Dekker, New York.

Hunter, R. J. (1988). Zeta Potential in Colloid Science, Academic Press, London,1988.

Ingham, K., Busby, T. F., Sahlestrom, Y. & Castino, F. (1980). Separation ofmacromolecules by ultrafiltration: influence of protein adsorption, proteinprotein interactions and concentration polarisation. In Ultrafiltration Membranes and Applications, ed. A. R. Cooper, Plenum Press, New York, pp.141-58.

Jonsson, G. & Christensen, P. M. (1986). Separation characteristics of ultrafiltration membranes. In Membranes and Membrane Processes, ed. E. Drioli & M.Nagasaki, Plenum Press, New York, pp. 181-90.

Kimura, S. & Tamano, A. (1986). Separation of amino acids by charged ultrafiltration membranes. In Membranes and Membranes Processes, ed. E. Drioli &M. Nagasaki, Plenum Press, New York, pp. 191-7.

Malone, D. M. & Anderson, J. L. (1978). Hindered diffusion of particles throughsmall pores. Chem. Eng. Sci., 33, 1429-40.

Meireles, M., Aimar, P. & Sanchez, V. (1991). Effects of protein fouling on theapparent pore size distribution of sieving membranes. 1. Membr. Sci., 56 13-28.

Meireles, M., Aimar, P. & Sanchez, V. (1991). Albumin denaturation duringultrafiltration: effects of operating conditions and consequences on membranefouling. Biotech. Bioeng., 38, 528.

Munch, W. D., Zestar, L. P. & Anderson, J. L. (1979). Rejection of polyelectrolytesfrom microporous membranes. J. Membr. Sci., 5, 77-102.

Nakao, S., Osada, H., Kurata, H., Tsuru, T. & Kimura, S. (1988). Separation ofproteins by charged ultrafiltration membranes. Desalination, 70, 191-205.

Nguyen, Q. T. & Neel, J. (1983). Characterisation of membranes, Part IV. J.Membr. Sci., 14, 111-28.

Nystrom, M., Lindstrom, M. & Matthiasson, E. (1989). Streaming Potential as atool in the characterisation of ultrafiltration membranes. Colloids Surfaces, 36,297-312.

Paine, P. L. & Scherr, P. (1975). Drag coefficients for the movement of rigidspheres through liquid-filled cylindrical pores. Biophys. J., 15, 1087-91.

Porter, M. C. (1990) Handbook of Industrial Membrane Technology, Noyes, ParkRidge, N.J.

Probstein, R. F. (1989). Physicochemical Hydrodynamics, an Introduction. Butterworth, Boston.


Rollin, M. (1991). Concentration et extraction hautement selective de proteines etd'antibiotiques par des membranes minecales d'ultrafiltration fonctionnaliseespar depot de polyvinylimidazole quaternise. Dissertation thesis, UniversityParis XII, 19 December.

Smith, F. G. & Deen, W. M. (1980). Electrostatic double layer interactions forspherical colloids in cylindrical pores. J. Colloids Interface Sci., 78, 444-64.

Smith, F. G. & Deen, W. M. (1983). Electrostatic effects on partitioning ofspherical colloids between dilute bulk solution and cylindrical pores. J. ColloidsInterface Sci., 91, 571-90.

Taddei, C, Daufin, G., Aimar, P. & Sanchez, V. (1989). Role of some wheycomponents on mass transfer in ultrafiltration. Biotechnol. Bioeng., 34, 171-9.

Tam, C M. & Tremblay, A. Y. (1991). Membrane pore characterizationcomparison between single and multicomponent solute probe techniques. J.Membr. Sci., 57, 271-87.

Tanford, C (1961). Physical Chemistry ofMacromolecules, John Wiley, New York.Twineham, M., Hoare, M. & Bell, D. 1. (1984). The effect of protein concentration

on the break-up of protein precipitates by exposure to shear. Chem. Eng. Sci.,39(3),509.

Tyn, M. T. & Gusek, T. W. (1990). Prediction of diffusion coefficients of proteins.Biotech. Bioeng., 35, 327-38.

Velicangil, O. & Howell, 1. A. (1980). Estimation of the properties of high fluxultrafiltration membranes. J. Phys. Chem., 84(23), 2991-92.

Vervey, E. J. W. & Overbeek, 1. Th. G. (1948). Theory of the Stability of LyophobicColloids, Elsevier, Amsterdam.

Zeman, L. (1983). Adsorption effects in rejection of macromolecules by ultrafiltration membranes. J. Membr. Sci., 15,213-23.

Zeman, L. & Wales, M. (1980). Steric rejection of polymeric solutes by membraneswith uniform pore size distributions. Sep. Sci. Technol., 16, 77.

Chapter 5

DESIGN OF MEMBRANE SYSTEMS

1. A. HOWELL

School of Chemical Engineering, University of Bath,Claverton Down, Bath, UK. BA2 7A Y

5.1 FUNDAMENTALS

5.1.1 Introduction

The design of membrane systems for the separation of liquids depends ona number of features which have to be incorporated into an overall system.The major aspects of the system which are important are its performanceand its cost. The cost is influenced by three major factors; the capital costwhich is mainly dependent on the membrane area required; the runningcost which depends on the power consumption of the system, the cost ofreplacing membranes, and the cleaning cost; and finally the loss of productthrough the membrane. The performance is intimately related to the costsand is dependent on the flux which can be achieved through the membrane and the degree to which components in the liquid can be separatedor in other words its rejection behaviour towards the solutes in the liquidfeed.

A good membrane system designer will strongly influence both performance and cost of the system. It is the purpose of this chapter todemonstrate the theoretical background and practical nature of the designprocess and how the myriad of design decisions can be made effectivelyand efficiently.

5.1.2 Experimental Trials

When starting to design or select a membrane system the designerrequires certain basic information which cannot be calculated but mustbe obtained from experimental trials. There is currently no known

141

142 J. A. Howell

method of predicting the performance of a membrane system fromknowledge of the membrane and purely physical measurements to bemade on the fluid mixture to be processed. There must always beavailable some results obtained by actually filtering the fluid to beused through a membrane.

In order to carry out such trials the designer must restrict their scopeor else the trials will last too long and be too expensive. In restricting thescope of the trials as much as possible the designer will have to make aseries of choices which will have the effect of, at least partially, closingdown many options. The trial systems must be chosen empirically.

In deciding on a choice of system for trials the designer may approacha vendor or manufacturer of membrane modules for help, restrictingchoice to the systems or modules offered by the vendor. Knowledge ofsome degree should precede this selection and often an independentconsultant will be approached to help make such a selection. Heuristicmethods are likely to be used.

Later in this chapter we will review the choices available, but first wewill assume certain information, relevant to the systems under consideration, is available.

Before making a final design firm information is required on:

the effect of concentration on flux;the effect of pressure on flux;the effect of cross flow rate on flux;the rejection characteristics of the membrane;the effect of temperature on flux and rejection;the rates of fouling;the cleaning regime to be adopted;the likely lifetime of the membrane itself.

5.1.3 The Effect of Concentration and Pressure on Flux

In earlier chapters the fundamentals of membrane processing have beendealt with in detail and here they are reviewed very simply so that theirrelationship to design can be seen more clearly.

Concentration polarisation occurs when solutes are rejected by themembrane and solute passes through thus leaving solute accumulated onthe surface of the membrane or polarised. As polarisation increases so thedegree to which it interferes with the membrane surface and flux alsoincreases. The accumulation may cause a deposit on the surface of themembrane such as a cake which can restrict flow and even alter therejection characteristics of the membrane. This is fouling.

Design of Membrane Systems 143

5.1.3.1 UltrafiltrationFor the case of ultrafiltration a simple equation is often used to relate theconcentration at the membrane surface (Cm) to the flux through themembrane (J) and to the concentrations of solute in the bulk liquid (Cb),

at and in the permeate stream (Cp) respectively.

Cm=Cp+(Cb-Cp)eJkl (5.1)

where k. is the liquid phase mass transfer coefficient at the membranesurface.

As has been discussed in earlier chapters the mass transfer coefficientmay vary with operating conditions and concentration. The variation offlux with concentration is so marked that it dominates the overall designof an ultrafiltration membrane system. The various types of system whichare available are discussed later in the chapter. They can be single ormulti-stage, continuous (feed-and-bleed) plants or alternatively batchoperated. Their basic design uses only eqn (5.1). However, more complexconsiderations are necessary for full designing of the individual membranemodules.

As the concentration Cm increases so the osmotic pressure exerted at thesurface of the membrane increases. The flux through the membrane is thenrelated to the transmembrane pressure and the osmotic pressure throughthe simple Darcy relationship

(5.2)

where Rm and Rr are the resistances of the clean membrane and the foulinglayer respectively, while the osmotic pressure is given by eqn (5.3)

(5.3)

where the aj are virial coefficients. The osmotic pressure given by thisequation deviates progressively further away from the Van't Hoff law that

(5.4)

as the concentration increases. This can lead to quite high osmoticpressures at the membrane surface even when high molecular weightsolutes are being processed.

Equations (5.1) to (5.3) can be solved for the flux at any given appliedtransmembrane pressure and bulk concentration if the various coefficientsand resistances are known. The results can be plotted as flux versus bulkconcentration at different applied pressures as in the example below.

144 J. A. Howell

For the fundamental designer the first measurements which need to bemade on the system are thus the relationship between osmotic pressureand concentration and also the resistance of the clean membrane. Theother solution properties are the relationship of viscosity to concentration,the density of the solution and the molecular diffusivity of the solute ofinterest.

5.1.3.1(a) AN EXAMPLE

The properties of dextran T500 were given by Da Costa et al. (1991) asfollows:

J.l = 0·0019 exp(2'45 C) Pa'sp= 1013+330Ckg'm- 3

D=(0'1204+2'614C-4'167C2 +2'132C3)x to-tO m2's- t (5.5)

where

and

Lln=37·5Cw+0·75C;'+0·00764C~Pa

These properties can be used to determine the fluxes through the membrane if one also knows the mass transfer coefficient which is prevailing inthe absence of any fouling.

It is interesting to examine this case. The value of Cwwhich is achievedby the system at a given applied transmembrane pressure is of course thevalue of Cw which gives a value of the osmotic pressure equal to theapplied pressure. This is shown in Fig. 5.1. As the pressure rises so doesthe value of Cwo However, the flux hardly rises at all as is shown in Fig.5.2. Traditionally it has been thought that the value of Cwwas fixed as itis possible to obtain a straight line relationship between the flux and the

800,-------------------,

.~14800 ~ .

i 320 / .. .... . .

1~0(

252010 15Pre.,ure (blr)

O'"--------------------Jo

Fig. 5.1. Plot of concentration at the membrane surface as a function of transmembranepressure for the osmotic pressure model.


120~-----------------,

252010 15Pr...ure(ar)

0'------------------'o

96

24

Fig. S.2a. Plot of flux versus pressure for the osmotic pressure model.

3 ----------- _

-------,.. /-.

i"(LJ

II

10 15P....u.. (ba,)

20 25

Fig. S.2b. Plot of the log of concentration at the membrane surface versus pressure_

\\\\\

-"-

50

o0.1 - 10 100 1000

CONCENTRAliON

Fig. 5.3. Plot of the flux versus the bulk concentration for ultrafiltration.

10

20

40

log of the applied bulk concentration which is linear and gives a value ofCb at which the flux is zero (Fig. 5.3). In fact in Fig. 5.2 is also plotted thelog of the concentration against pressure and it is clear that beyond asmall value of the applied transmembrane pressure the value of thelogarithm of the intercept (Cw ) will scarcely change no matter what thepressure is within a reasonable practical range so long as the value of themass transfer coefficient remains constant. The slope of the curve in

60

146 J. A. Howell

Fig. 5.3 is the mass transfer coefficient. In practice the changes inconcentration cause a change in physical properties which changes themass transfer coefficent and the above method is reliable as a determination of the mass transfer coefficient only in the immediate region wherethe data is gathered.

5.1.3.2 MicrofiltrationIn microfiltration the relationship between flux and concentration of aparticulate suspension is less regular. Several varieties of curve are foundwhich depend on the behaviour of the particular suspension, cross-flowvelocities and transmembrane pressure (Fig. 5.4). Generally transmembrane pressures are low and fluxes tend to be constant over a region ofintermediate concentrations, declining sharply only when the viscosity hasrisen so that flow becomes laminar at the design feed pressure which isoften less than 100 kPa.

If a multistage plant is used it may be advisable to operate a final highconcentration stage at much higher feed pressures to gain turbulentcross-flow at the higher viscosity. (Pritchard, 1990).

5.1.4 Factors Influencing Design

There are four module geometries currently in use: the tube; the hollow fibrebundle; the flat sheet, thin-channel; and the spiral. In each of these geometries except the hollow fibre it is possible to insert turbulence promoterswhich obstruct the flow, increase the pressure drop but also increase themass transfer coefficient at the membrane surface. In introducing thefundamentals of design we will deal with the unobstructed tube and thethin-channel. The same approach can be used in dealing with inserts and thedata can be used in a similar design to the membrane module.

5.1.5 Pressure Drop

The pressure drop in a tube in which there is well developed flow is givenby the Blasius correlation.

The relevant equation for the pressure drop is

Af= Re n

where f is the friction factor and Re is the Reynolds numberThis equation can be rewritten

!1P oc urn

(5.6)

(5.7)

Porter (1972)

so

~ Gelatin

e. 40

><~

Ii 30

i=!

I20

10

0

2 5 10 20 30

CONCENTRATION OF PROTEIN (WT ")

Porter «Michaels (1977)

0010

0 III00,; """" '"~ -",00 IV,0010

~~IV V

000; \

~ (~"0 " , I~ 10 70 '00 100 ~

10 70 100

Blatt et al.( 1970 )

'I Ovalbumin10 "-1100 em/s

"- ItIa

70'

'0...

'0'

Wheat starcb diluent

Nakao et al.(1979)ol---'----'----''---'-_...............---''----'-...J

0.2 .4 .6 I. 2. 4. 6. 10. 20.

SOLIDS CONCN. (wt. ">

Fane « Fell (1977)

Fig. 5.4. Different forms of the flux versus concentration plot for microfiltration ofmicro-organisms. (Pritchard, 1990).

148 J. A. Howell

(5.8)

Whilst for laminar and turbulent flow in an empty channel the index m is 1and 1·75 respectively it can be slightly different in a spacer filled channel.

5.1.6 Mass Transfer Coefficient

It is possible to estimate the mass transfer coefficient from a Sieder-Tatetype correlation corrected for the viscosity difference between the bulkfluid and the wall as discussed in Chapter 3. The Sieder-Tate correlationapplies to a thin channel or empty tube configuration. Many membranesystems do not have this configuration but include turbulent spacers. Themass transfer coefficient correlation for these has been shown by DaCosta et al. (1991) to be similar to the Sieder-Tate but varies in theexponents. These should be determined for any given membrane packingsystem.

The important consideration in choosing a spacer or turbulence promoter is the trade-off between the increase in the pressure drop versus theincrease in the mass transfer coefficient. The mass transfer coefficient isobtained from a correlation of the form.

Sh=cReaScb (?Ywhere

Sh= kmdD'

Re= pVd, Sc=!1Jlm D

It turns out that the value of the parameters A and n in the pressuredrop correlation vary considerably with different spacers whilst theparameters for the mass transfer coefficient a, b, c, d remain moderately constant (Table 5.1). Costa et al. have determined values for severalspacers. In order to obtain this information for any new system theindividual mass transfer coefficient can be obtained using eqns (5.1-5.3).In this case the product flux is measured, the clean membrane pure

Table 5.1Parameter Values for Equations 7 and 8

a b c d m A n

Spacer filled channel 0·5 0·6 0·0096 0 1·77 0·5 0·15-4,5 -0,3

Empty channel -laminar 0-43 0·33 1-86 0·33-entry region 0'5 0·33 0·66 0·5-turbulent 0·89 0·3 0·023 1·75


water permeability is measured and then the osmotic pressure is calculatedusing eqn (5.2) assuming that the membrane resistance R has remainedconstant between the two measurements. From this and the equation ofstate (eqn 5.3) the value of Cw can be calculated. Knowing the flux and thewall concentration the mass transfer coefficient is easily obtained from eqn(5.1) if the permeate concentration Cp is measured.

5.1.7 Reynolds Number

The cross-flow velocity affects the Reynolds number and thus the pressuredrop along the module, the pressure drop at each point of the module andalso the mass transfer coefficient as described by eqn (5.8). These varyalong the channel for a laminar flow system and can be corrected for bythe entrance region correlations as described in Chapter 3.

5.1.8 Entrance Length

The length of the entrance region itself is of interest. This has been thesubject of an investigation by Clifton et al. (1984) who showed that at highmembrane resistance as in a fouled membrane the entrance length wasquite long with flux dropping slowly over lengths as long as 1m. On theother hand, high flux membranes have entrance lengths as short as a fewcentimetres. This change of flux with length is important for the membranedesigner as it introduces a scale effect into membrane performance whichis relevant over typical experimental channel dimensions. It is not practicalto consider correcting for entrance length effects and so experimentalmeasurements for design purposes must be conducted on full lengthmodules where empty channels are being used. The effect is less importantwhen spacers are involved as they introduce a break-up of the boundarylayer on the spacer dimension which makes data gathered on a smallerscale still valid.

5.1.9 Surface AreafVolume Ratio

The degree to which membrane area can be packed into a given volumeis of some importance to users as very inefficient designs are not usefulif large membrane areas are required. The compactness of a systemaffects its economics but also creates some difficulties of managing flowpatterns across the membrane surfaces. Nearly all really large scalesystems use compact geometries which are either hollow fibre or spiralwound.

150

5.1.10 Fouling of the Membrane

J. A. Howell

There are two types of fouling which need to be identified. The first isinherent in the process solution or suspension, the second occurs becauseof the use of unsuitable water supplies or other raw materials which leadsto wholly avoidable fouling. This latter form should be eliminated by theproper design of pretreatment systems, or by the selection of suitable rawmaterials. Two common problems are the use of improperly treated waterfor cleaning and rinsing streams, and the use of poorly chosen antifoamagents in fermentations.

Water should not have any colloidal silica or iron which can contaminate the membrane. Nor should it be hard enough to promote calciumprecipitation on the membrane. All o( these problems are extremelydifficult to cope with and are much better avoided. Suitable treatment canbe provided by specialist companies and often a reverse osmosis unitfollowing sand filtration and chlorination proves to be effective. The use ofchlorinated water needs to be controlled because of its possible damagingeffect on some types of membranes. Many source waters can now betreated directly by UF or RO membranes without any pretreatment. Thisis especially true of some ground waters.

The rate of fouling of the membrane is a crucial consideration in design.It cannot be predicted a priori and must be determined by experiment onthe material of interest using the membrane of interest. So many factorsaffect fouling that as has been discussed earlier in the volume it isimportant to use the solution to be treated as close to its normal conditionas possible. In the treatment of fermentation broths Taddei and Howell(1989) have shown that the simple storage of the broth will drasticallychange the degree of fouling which occurs in the system. For exampleFig. 5.5 shows the flux as a function of time for the cross-flow microfiltration of cider broth after being stored for different lengths of time. At the

Iretentate product I

[Membrane I

Ipermeate waste I

Fig. 5.5. Schematic diagram of a simple feed and bleed plant.


moment it is not possible to predict fouling exactly although the work ofTaddei and Howell showed that reproducibly controlled fermentations ofcider at least resulted in reproducible microfiltration behaviour. It is thusbelieved that a given system can be characterised and a model for foulingdeveloped.

Howell and Wu (1991) have shown how the flux time curve can belinearised to give two parameters which describe fouling rates empirically.Other models exist in the literature and are discussed in Chapter 6.3.Although each has a physical description describing its derivation eachshould be regarded as an empirical technique until more verification hasbeen obtained of their general applicability. Whatever model is used thedesigner will want to test the system to be used at the full scale anddetermine the fouling rates and the parameters which are applicable.

5.1.11 Cleaning and Membrane Lifetimes

The cleaning of a membrane mayor may not be simple. There is littlepublished on the fundamentals of cleaning. The practical side of cleaningis that there are at least two levels of clean which can be practised on agiven membrane, a mild clean and a vigorous clean. The latter is moredamaging to the membrane and may affect membrane life. The aim of acleaning regime is to maintain optimal performance without shorteningmembrane life too drastically. The main measure of whether a membraneis clean or not will be the Clean or Pure Water Flux (CWF or PWF).This is measured for the new membrane and for the membrane afterfouling and after a subsequent clean. The total resistance of the membrane is defined as the applied pressure divided by the flux. This is madeup of the fouling resistance and the clean membrane resistance. However,it is not a foolproof measure of cleanliness and it is often found that aftera clean has achieved a original PWF the rate of subsequent fouling isfaster than with a new membrane. This is not a feature isolated tomembranes. Cleaning of stainless steel plant in the food industry doesnot usually result in a totally clean steel surface afterwards. It is in facthard to restore the membrane to its virgin state although it is possible toremove all macroscopic soil leaving an adsorbed layer of molecules onthe membrane surface. This occurs after a vigorous clean. Less vigorouscleans often result in a membrane slowly losing performance over time.Economic considerations should be used to determine when this loss ofperformance has become intolerable and a vigorous clean is to beinstituted.

The difficulty which the designer or operator has with this policy is thatthe lifetime of the membrane depends on the decision, the lifetime is

152 J. A. Howell

measured in years, and there is not usually time to collect the necessarydata before designing building and starting to operate the plant.

The solution usually adopted is to follow the membrane manufacturersrecommendations as to a cleaning regime. These organisations may havelong experience of similar materials, and they can usually be persuaded togive a lifetime guarantee of 12 months or more if their instructions arefollowed. This situation is intellectually unsatisfactory and further fundamental work on cleaning of membranes is urgently needed.

The cleaning regime will vary from membrane to membrane andsolution to solution. A typical approach is to use a simple causticdetergent at around 50°C followed by an acid sanitising rinse. Somemembranes are able to stand a mild hypochlorite or peroxide solutionwhich is effective at oxidising the deposit as well as having a sanitisingaction. Other membranes such as polyamide materials and cellulosics arehighly sensitive to chlorine and suffer permanent damage of a progressivenature. These solutions may be used if drastic cleaning action is necessary.Polysulphones on the other hand are very resistant to these cleaners andare consequently favoured by the food industry. Cleaning agents may alsoaffect the resins and sealants used in the construction of the membranemodule. If proteinaceous materials are being filtered an enzyme detergentis sometimes used although the higher cost of this leads to it being anoccasional use only in most systems.

Inorganic membranes are more easily exposed to strong cleaners andare generally believed to be almost totally resistant to most commoncleaners. They will also withstand much higher temperatures and can ifnecessary be heated in an oxidising atmosphere to remove all organicdeposits. The only difficulty with general use of this approach is thedifficulty of exposing the sealants and gaskets etc. to these high temperatures. Generally modules cannot be exposed to temperatures much above250°C although the membranes themselves may be calcined above 500°C.

5.2 OVERALL DESIGN

In the detailed considerations of the plant design the designer will decideon:

the process to be used; UF, MF, etc.; batch, continuous;type of module and its geometry; spiral, hollow fibre, flat sheet;material of the membrane; which polymer, ceramic;pore size of the membrane;number of stages;

Design of Membrane Systems

whether washing or diafiltration is required;how water is to be added; continuously or batchwise;the operating pressure;the flowrate through the modules;the operating temperature;the control strategy.

5.2.1 Process Selection for Membrane Processes in Biotechnology

153

5.2.1.1 Cell SeparationCell and cell debris separation from fermentation broths is a majorapplication of membranes using cross-flow microfiltration. There are anumber of different configurations of the membranes which have beenproposed but the majority of the current applications limit the use ofturbulence promoters within the channels of the membrane modules toeliminate blockages. Unfortunately microfiltration membranes have notproved to be absolute when used in the cross-flow mode and it isnecessary, for the complete removal of cells, to add a polishing filterdownstream of the cross-flow device. These filters acting in dead-endrather than cross-flow mode have a limited capacity for cells. They canonly be used in a polishing role. Recent advances in such devices haveincluded the use of variable voidage filters which allow large capacities atthe upper large voidage portion of the filter and finer gaps lower downtowards the absolute rejecting surface. Installations of cross-flow filters forcell separation have already been applied on the large scale, displacingcentrifuges. However, in many critical applications such as removal ofrONA cells from broths centrifuges have still been preferred in spite oftheir complexity. The advent of ceramic filters for cell and cell debrisseparation shows considerable promise and there are several Europeanmaufacturers of ceramic membranes including Techsep on the large scaleas well as several smaller companies such as Ceramesh which hasdeveloped a ceramic membrane based on coating a separating surface on ametal mesh that has a highly uniform pore size. These membranes havenot yet been produced for large scale use but show extremely interestingproperties.

Where cells or cell debris are to be separated from broth in which thedesired product is a smaller molecule it is often preferable to use ultrafiltration membranes rather than microfiltration membranes as they oftenshow less tendency to foul irreversibly. Although there are currently fewinorganic membranes which show low molecular weight cut-offs (belowloo000Da) membranes which show such characteristics are being developed. Inorganic materials being generally preferable for use with rONA

154 J. A. Howell

organisms because of the need to have absolute sterilisation (preferablywith steam) of the downstream processing equipment.

5.2.1.2 Protein ProcessingThe processing of proteins has long been carried out with membranes.One of the major application areas of UF membranes has been in thedairy industry where first whey proteins were concentrated with UF andthen RO and UF were used to concentrate milk prior to making cheese,yoghurt and other fermented products such as fromage frais. The processing of proteins in the laboratory has also been widespread and so use ofUF to concentrate protein products in biotechnology is naturally attractive. The problem with proteins is their ability to foul the membranes.Much research has been devoted to elucidating the fouling problem anddevising ways around it. Several of these techniques are discussed elsewhere in this book. They can be categorised broadly into hydrodynamic,surface modification and electrical field methods.

5.2.1.3 Product RemovalIn fermentation plant the products of the fermentation are often toxic tothe organism or important enzymes carrying out the desired transformations. In these cases it is desirable to remove the products as they areformed, or at least before their concentration becomes excessive. It is oftenuseful to circulate the fermentation broth through a membrane separatorto remove unwanted or toxic products before recycling the broth back tothe reactor. It has been suggested that the permeate now cell free may betreated by selective adsorbents before it recycles itself back to the fermented now free of contaminant.

One example of this technique which has received some attention hasbeen the removal of ethanol from fermenters as it is generated removingthe inhibitory effect of high ethanol concentrations. Although manymethods of achieving this are known membranes have been included insome of the techniques. Membrane distillation has been proposed, as hasthe use of pervaporation. Usually the value of the pervaporation technique, however, is in the final dehydration of the product alcohol withoutthe necessity of azeotropic distillation. This technique will be discussed indetail in Chapter 9.

5.2.1.4 SterilisationFour major streams require sterilisation especially with the new rONAfermentations. Air has always required sterilisation before entering thereactor and membrane filters offer an absolute removal of microorganisms from the incoming air with low pressure drop and high


efficiency compared to absolute depth filters traditionally used. The lowloadings that can be achieved by membranes mean that pre-filtration withdepth filters is desirable but they do not have to achieve such perfect performance if they are backed up with a membrane. This can result in considerable energy saving on the plant. Similarly the sterilisation of the exitgases can be efficiently performed by membranes.

The sterilisation of media and final broth by membrane techniques ispractised in many small scale applications using dead-end filters becauseof the lack of a need to heat the media which can cause changes in thebroth composition or damage valuable heat sensitive products. Althoughsuch techniques are not often going to be applied to large scale fermentations it must be remembered that many biotechnology products aregiven to patients in microgram quantities and very small production rateswill satisfy the annual market. These products may well be produced inquite different technologies from the very large industrial fermentationsused in the antibiotic industry for example.

5.2.1.5 Gas RecoveryThe gases leaving an anaerobic digester contain carbon dioxide andmethane amongst other gases. Recent developments in gas separationmembranes have produced commercial membranes which can be used toseparate these gases from landfill, or digester gas leaving a high calorificvalue methane. It is also possible to remove the hydrogen sulphide usingmembrane technology. There are already plants producing 800 tonnes/annum of methane from a landfill site.

The separation of nitrogen from oxygen on a small scale is alreadyefficiently done with methane plants which are the most economical for99·5% nitrogen. As methane plants do not tend to have economies of scaleit is still more economic to use cryogenic plant for very large scaleapplications but the methane plants are becoming efficient at higher andhigher scales as their performance improves. As yet high purity oxygen isnot economic with membranes but this will be developed. Nitrogen is ofvalue in anaerobic environments although the really high purity nitrogenis still made by alternative techniques. The use of membranes to enrich theoxygen in aeration of fermenters is unlikely to occur in the short term asthe pressure losses in the membrane plant will more than offset the savingsin compression resulting from feeding less air to the fermenter.

5.2.1.6 Membrane ReactorsA number of applications of membrane to biological reactors have beenreported recently. It has long been possible to cultivate cells in hollow fibremodules with the cells in the shell side and nutrient fed through the lumen.

156 J. A. Howell

Recent research in this area has focused on developing new applicationsfor the technology and increasing the cell density achievable in thedevices. It is now commonplace to feed oxygen and nutrients withseparate membrane fibres leading into the device. High cell densities oftissue cells can be grown but as the cells become starved whether ofoxygen or nutrients they appear to become more susceptible to the highpressures that can be induced by the still growing cells nearby. Breakagecan then result and very high cell densities of starved cells can beobserved.

In addition to the use of membrane reactors to cultivate tissue cellsthey are also used for immobilised enzyme systems. It has recently beenreported that by co-immobilising glucokinase and acetatekinase insidethe shell of a hollow fibre module and feeding the lumen with glucoseand ATP, glucose 6-phosphate can be produced continuously with theco-enzyme being regenerated continuously by the dual enzyme system.This system can show advantages over a dual membrane system wherethe regeneration takes place at a distance from the original reaction.

Two-phase systems can also benefit from membrane technology. Theenzyme may be placed in the membrane which is the interface betweentwo phases. Reaction can be carried out on a reactant in the organicphase whilst regeneration takes place in the aqueous phase. This can bebeneficial where the product of the reaction is unstable in the aqueousphase. Liquid membranes can be used to achieve the same result whereregeneration is not required and the enzyme can be immobilised in areverse micelle of surfactant emulsified in an organic phase.

Membrane reactors integrating separation and reaction will developrapidly. The benefits of such plant are very clear but they have not yetbecome commercial on a large scale. It is likely that this is going to bethe next most rapid area of growth for membranes in biotechnology.

5.2.1.7 BiosensorsA large number of biosensors now use membranes to immobilise theactive enzymes. There are three major types of biosensor which use themembrane. The traditional type uses a potentiometric or ampiometricsensor against which the enzyme is immobilised. The enzyme may bedirectly attached to a solid state device within the sensor body. Itcatalyses a reaction which has a measurable redox potential. The secondtype uses a fibre optic sensor and relies on the reaction modifying colouror fluorescence of a material also present within the membrane envelope.The third directly attaches the enzyme and membrane to an ISFETsensor which will detect particular ions released during the enzymeaction.

5.2.1.8 Medical ApplicationsOne of the oldest established uses of membranes is in kidney dialysismachines and it still figures as one of the largest users of membranes withover 350000 patients on long-term dialysis and perhaps 70000 on shortterm dialysis. The development of membranes for artificial organ usecontinues with a continued search for materials which have improvedcompatibility with the blood. The problems with dialysis have led to about20% of the patients opting for peritoneal cavity dialysis using the naturallining of the peritoneum to carry out the dialysis against fluid passed inthere from 2-litre bottles. This technique can, however, lead to bouts ofperitonitis which is uncomfortable, however, the technique is ambulatory.There remains a challenge to membrane engineers to develop ambulatorytechniques which are patient friendly.

Membranes are also used in processing blood especially with regard toplasmapheresis or separating plasma from erythrocytes. Many developments have occurred in this area and it has been learned that operating atlower trans-membrane pressure reduces haemolysis significantly(< 70 mmHg). Membrane pores must be less than 0·6 11m to eliminate theforcing of cells through the membrane. With these precautions fairly highshear rates are possible within the membrane channels. The higher shearrates promote the movement of the cells away from the walls of thechannel reducing polarisation. The local effective diffusion coefficient forthe cells is proportional to the shear rate to the 0·6 power. Previously ithad been thought that shear rate on its own promoted haemolysis.

5.2.1.8 Food IndustryLong uses of membranes in food processing have included the dairyindustry where whey protein, milk and other materials are concentratedby UF and RO. A recent development has been the production of cheesewithout whey by preconcentration of the milk. Soft cheeses such asMozzarella are relatively easy but the South Australian Dairy Board hascollaborated with APV of the UK in developing such a process for hardcheese with a product said to be indistinguishable from Cheddar. This willhelp to increase output and reduce environmental problems of theindustry.

More recently a large industry has grown up concentrating fruit juicesby RO. These juices are quite viscous when concentrated and in fact it isthe viscosity which limits the ultimate concentration which can beachieved by membranes alone. Unfortunately for the membrane manufacturer standard products have become adopted in the industry from earlierevaporative methods of concentration. Although these methods produce alower quality of product organoleptically and at higher price the innate

158 J. A. Howell

conservative nature of the industry means that often a small supplementary concentration by evaporative methods has to follow the main waterremoval by RO.

In the beverage industries membranes are used to remove protein beerhaze, to pasteurise beers without heat, and to recover extra product fromthe concentrates in the bottom of the tanks. The clarity of wine has beenenhanced by membrane filtration and claims are made for its use inspeeding the maturation of bulk wines by removing some of the smallerprecipitated tannins and tartrates. The development of ceramic membranes has allowed high velocities to be used in these processes and veryhigh throughputs have been reported.

5.2.2 Module Configuration

5.2.2.1 SpiralSpiral wound devices are one of the two most popular configurations forcommercial use. The major advantage is the large surface area per unitvolume that can be achieved in these modules. Essentially they consist ofmembrane envelopes with the open end sealed to a porous pipe. The~nvelope contains a thin spacer to keep the two sides apart and theseparating surface is on the outside of the envelope. The envelope is then::oiled around the central pipe with a spacer incorporated to keepsucceeding layers of the spiral apart. This tight spiral coil is then placed ina tube into which it will fit very tightly so that as fluid passes along thetube it is forced betwee the coils of the spiral under pressure. This pressureis the force which derives fluid through the membrane envelope to be::ollected in the porous pipe.

Aspects of the design which are important are of course the design of theturbulence promoting spacers, their thickness, pattern, and open area bothtowards the membrane and across the channel through which flow isoccurring. High pressure drops along the channels can be induced whichalso reflect local turbulence and higher mass transfer coefficients to keepthe membrane surfaces clean of foulants. Detailed aspects of the design ofthese spacers have been considered by Da Costa et al. (1991) who::ompared the efficiency of several designs in generating pressure drop:undesirable) and improving mass transfer coefficient (desirable). Optimumdesigns were recommended which involved the polymer fibres making upthe mesh being aligned to the flow at approximately 60 degrees.

Another practical aspect to the design is the anti-telescoping devicewhich must be included at the ends of the spiral modules within the tubeso that the spiral is not distorted by the fluid flow pressures. This deviceallows several modules to be inserted in a single tube with simple


connectors between the permeate tubes. Typical installations will have 3 or4 modules of 4 m2 each within a single tube of about 150 mm diameter.Packing densities are then of the order of 150 m2/m 3 although muchhigher for reverse osmosis and gas separating modules where the channeldepth is much smaller.

The disadvantages of the spiral configuration are the narrow spaces andthe space filling turbulence promoters which can become blocked with thewrong type of feed, especially where there are suspended solids which areeither large or may agglomerate. As with any membrane system seals are aproblem and the material used to seal the edges of the envelope can causedifficulty because of the effect of cleaners on the adhesives over time. Caremust be taken to use the correct materials. At the outer edges of the spiralthere are regions where dead spaces can be created because of the gapbetween the edge of the spacer and the outer region of the membrane. Ifcare is not taken to bring the spacer right to the edge of the outer tube thedead space created can be a source of bacterial contamination since it isextremely difficult to clean.

Spiral modules are operated at high flow rates with pressures up to 10bar at the inlet and 2-5 bar at the outlet for ultrafiltration. The systems arerobust and are easy to link together with other modules in parallel or insenes.

5.2.2.2 Hollow FibreHollow fibre modules are the other major system used on really largeapplications. With spiral wound modules they share the large reverseosmosis desalination market and the gas separator market. In each casethis is because it is easy to build modules which resist large transmembrane pressures of over 100 bar and also to have extremely narrowchannels and thus pack large areas into moderate volumes.

For gas separation and reverse osmosis the hollow fibres are ofdiameters of several micrometres whilst for ultrafiltration and microfiltration diameters of around 1 mm are more common. It is feasible toestablish turbulent flow within the fibres for low viscosity solutions butmore frequently the flow is laminar. The hollow fibres are easy tomanufacture and are embedded into an epoxy or other resin at each end.Normally flow is from the inside to the outside for ultrafiltration as thefibres are relatively weak at these larger diameters whilst the thinner gasseparation or RO membranes may be used in either direction at highpressures, and microfiltration membranes can be used at moderate pressures with a higher pressure backflush being used from the inside out.

The fibres are normally assembled together and placed inside tubes of10-500 mm diameter depending on the application. Permeate is removed

160 J. A. Howell

from the shell or tube side depending on the application. It has provedfeasible to use air or liquid backflushing with some designs and these havebeen quite successful. The patented Memtec air backflush system isperformed on a frequency of about 10-20 min and is able to cope at thatfrequency with forward flow in a dead-end configuration. As with thespiral systems several modules can be interconnected in series or inparallel to provide a full system and very large systems are now possiblewith the larger diameter modules which reduce the need for excessivemanifolding. Plants with areas in excess of 1000 m2 are now beingdesigned with packing densities of the order of 300 m2/m 3 for UF and MFand around 8000 m 2/m 3 for gas separation plants.

A disadvantage of the hollow fibre designs is that the fibres may breakbeing relatively weak and may therefore cause a loss of rejection in one ofthe single tubes which might be very hard to detect unless the membranemodule is removed when it is actually quite simple to plug a single tube.The removal of the membrane results in downtime and unless theprobability of breakage is minimised a high labour cost will result. In viewof this difficulty it is important that pressure surges which would endangerthe membranes are not permitted and the fluid control system is set up toramp pressures gradually to the operating level. It is also necessary thatmanufacturers' recommendations as to the maximum operating pressurebe rigidly adhered to even if brief experience may indicate that higherpressures can be occasionally resisted by one or more test modules.Another problem with the large number of individual parallel channelspresent in a hollow fibre module is that if a small blockage develops in asingle channel the flow through that channel is reduced and there is areduced 'cleaning force' down the channel. Blockage once started will tendto be permanent for the channel affected. This restricts their use to quiteclean feeds on the tube side although the shell side may cope with moreparticulate matter.

5.2.2.3 TubularWhilst hollow fibre membranes are strictly speaking tubular, this term isreserved for the slightly larger diameter tubes from about 3 mm to 25 mmwhich are operated generally in turbulent flow mode for a wide range offluid viscosities. These units are assembled from a wide variety of materialsand are the smallest diameter modules currently in use for ceramicmembranes and other inorganic materials.

There are two major types of system. In the first the single tube units areattached in groups inside a larger shell tube through the use of a tube plateinto which the individual tubes are separately sealed with discrete grommets or gaskets. The other major group of units are blocks of tubes formed


into a single unit. This is the most common system used for ceramicmembranes and is often found in the form of hexagonal blocks or coarseIX-alumina into which are moulded the individual tubes with their separating surfaces often of zirconia being formed in situ. These individual tubesvary in inner diameter from just over 2 mm to 6 mm.

The larger diameter tubes are most useful when the fluids being treatedhave a high content of particulates, especially when they are fibrous or oflarger size, or when they can agglomerate easily. If the fluids have highviscosity and need to be processed to low levels of water content, thenagain the larger tubes are most useful.

The smaller diameter monolithic type structures are developing intodevices which contain greater and greater areas of membrane per unitvolume. The greatest drawback of the large diameter tubular systems isthat they are expensive in both energy and space per unit volume ofmaterial treated. They are thus used primarily when they offer otherfeatures which cannot be met by the other systems. They are easy to clean,they withstand high pressures, especially for the ceramics, they are easy toassemble and individual tubes can be replaced relatively easily in cases ofbreakage thus permitting a longer overall system lifetime before completeremembraning is required.

The larger diameters means that it is less likely that individual tubes willbecome blocked. Packing densities for tubular systems are quite low beingof the order of 40 m21m 3 even for the smaller diameter tubes.

5.2.2.4 Plate and FrameFlat sheet membranes are assembled in plate and frame assemblies ofwhich there are many different designs. The difficulty with these designs isthe edge sealing for the membrane and thus many designs includepreformed cartridges, or alternatively flat sheets of membrane bonded to abacking sheet containing the permeate channels. These units are thenmounted between other sheets which have the retentate channels formedwithin them. The gaskets between the retentate sheets and the permeateunits can alternatively be used to control the height and geometry of thechannels. Assembly of several layers of membrane with the preformedchannels into closely packed cartridges is an excellent method of assembling units but at the moment it is only being done on a small scale.

These cartridge units and the smaller single sheet units are excellent forlaboratory use as the fluid flow paths are defined and the units can accepta wide variety of different membranes for testing purposes. As a result a lotof data is accumulated for the flat sheet configuration. On the larger scalethe plate and frame system has a major disadvantage of complexity. It is,however, very robust, technically easy to remembrane individual sheets

162 J. A. Howell

although labour intensive, and the membrane can be cleaned physically ifnecessary making it useful for heavy fouling high value product situations.The problem with sealing has bedevilled many would be manufacturers asthe high pressures across a flat sheet create enormous deformation forceson the units and tend to cause edge leakage. Many ingenious solutionshave been developed to solve the problem and where this has been donethe units will perform extremely well. Modern designs impregnate the edgeof the membrane with resin or polymer to seal it and form the sheets intopresealed units containing from 1 to 50 membrane sheets. Spacers areincluded between the sheets but mayor may not incorporate turbulencepromoters.

5.2.3 Simple Design Examples

Equations from these theory chapters will now be introduced to show howfirst a simple, and then a more complex design can be developed.

5.3 SYSTEM CONFIGURAnON

The first choice of the designer is the plant system. The choices are for:

1. a simple batch concentration in a single stage;2. a multiple stage batch concentration;3. a single stage continuous feed and bleed plant;4. a cascade of such feed and bleed plants; and5. any of the above with a diafiltration facility

The simplest of all to design is a single stage feed and bleed plant becauseit operates under constant conditions.

EXAMPLE 1: BLEED AND FEED PLANT

In a simplified process design the membrane area is required for theconcentration of 10 m3 of 0·1 % glucose oxidase solution to 5% by weight.Constant flow conditions will be maintained over the membrane. Experiments have shown that using a thin channel flat sheet system or a tubularsystem the flux is given by rewriting eqn (5.1) when Cp=O or the enzyme istotally rejected by the membrane.

(5.9)


where: for the flat sheet system

km

= 141m - 2 h - 1Cm = 30 weight percent

C = weight percent protein over the membrane

and: for the narrow tubular system

km = 8 1m - 2 h - 1

Cm = 80 weight percent

In a one pass system using the configuration shown in Fig. 5.5 whatareas would be required using each module assuming that Cm is constant?

Assume also that the recycle rate is fast enough to make the membraneoperate at a completely mixed mode.

Mass balance on enzyme

(5.10)

therefore

(5.11)

Overall mass balance

(5.12)

Combining

(5.13)

(5.14)

As

Qp=lO(l- O~1)=9'8m3h-1

The flux through the membrane is occurring at CF 5% and all thepermeate must pass through the membrane. Evaluating eqn (5.1) at 4-5%

For the flat sheetnarrow tube

Js=22'21m -2 h-IJ T =27'2lm- 2 h- 1

Thus the areas required are

As= Qp 1000 m 2 =442 m 2

Js

AT =390m 2

(5.15)

(5.16)

164 J. A. Howell

It is evident that the simple feed and bleed design has several flaws. Themost obvious is that the whole of the permeate is passed at the lowestpossible flux for solutions between the feed concentration and the finalproduct concentration.

EXAMPLE 2: A TWO STAGE FEED AND BLEED PLANT

A simple improvement is obtained by using a cascade of more than onefeed and bleed unit of the same basic design. If two such units are usedthen it is possible to design a system whose total area is minimised.

Dealing with a flat sheet or plate and frame system with the sameperformance characteristics as in Example 1. The new set-up is shown inFig. 5.6.

Feed Tank

Retentate

tst Stage 2nd Stage

1st Permeate 2nd Permeate

Fig. 5.6. Schematic diagram of a two-stage feed and bleed plant.

The first unit operates at CR1 the second at CR2 . A mass balance onenzyme over stage 1 and stage 2

(5.17)

therefore

(5.18)

As a total mass balance over stage 1 shows

(5.19)

using eqn (5.9)

(5.20)

Design of Membrane Syslems

A total mass balance over both stages similarly yields

QPl +Qp2 +QR2 =QF

substituting for QPl and QR2

[CF CFJQp2+QF 1---1+-CR2 CRi

The required areas are obtained using eqns (5.1) and (5.7)

A_ Qp2

2-km{ln Cm-In CR2 )

Combining eqns (5.17) and (5.18),

1 1 1--- ---

A1+A 2=QF Cr CF CR1 + CRI CR2km In Cm-In CRI In Cm-In CR2

165

(5.21)

(5.22)

(5.23)

(5.24)

(5.25)

(5.26)

The Minimum Area is found by taking the first derivative of the abovesum of areas w.r.t CR1 , or by a search technique on CRI.

With modern desktop computers the latter process is now very straightforward. Figure 5.7 shows a plot of the total area as a function of theinterstage concentration. There is a sharp minimum at 0·6% of 210 m2.Initially it may seem strange that the minimum is so close to the feedconcentration, but consider the volume of permeate passing in eachchannel. The first stage passes 8·33 m3 h -I the second 1·47 m3 h -I. Eventhough the majority of the permeate passes through one stage it is doingso at a reasonably high flux as the concentration of the retentate is high.The overall area is only 60% of the single stage requirement.

166 J. A. Howell

4O<f.---------------------,350~-------------------_=-""""=__..j

* 3OOit----,=:===,----------~=--! jrotalarea L ---j*200 __] First stage L _::J

g-150.s

! 100++_-,,-.-::---_-_=.J Second stage [=~=-_- --j

o ------------ -------·50+---,---,----,-----,---,.---1

o 234 5 6Intermediate Concentration

Fig. 5.7. Total required membrane area as a function of intermediate concentration for atwo-stage membrane cascade.

More complex designs, as we shall see later, incorporate even morestages in a cascade.

5.3.1 The Simple Single Stage Batch Plant

Another approach is the batch concentration when one concentrates10m3 in 1 h in a batch from 0·1 to 5% reducing to VE =0·2m3

•

d(VC) =0dt

dV=JAdt

vC = constant

= VOCF

C= VOCF

V

Thus the overall permeation rate is

dvdt = km[ln Cm-In VOCF +In V]A

(5.27)

(5.28)

This can be integrated using Simpson's Rule and a BASIC program or aspreadsheet with say 200 intervals.

h1=3(Yo+ Y200 +2~Yeven +41:Yodd ) (5.29)


As A is unknown the integration uses the time variable t' = At then usingthe following values for the parameters and system concentrations

Cm =30kgm- 3 (5.30)

the filtration time required is:

75A"h so that A=76m 2 (5.31)

This is significantly less than required for a cascade of two stages.Another consideration concerns the degree of concentration which

occurs in a single pass through the membrane unit. A typical ratio offorward flow to recycle is 1:5 Le. Qc = 5Q R.

Let us assume the system is working with a single membrane stage. Nowas CR= Cc = 5 kg m - 3 the feed concentration C~ into the membranechannel is given by solving the mass balance over the junction between thefresh feed and the recycle stream as they combine to form the feed to themembrane channel itself.

QFCF+QCCC=(QF+QdC~ (5.32)

Now

CFQR=C

RQF

Thus

5CF (5.33)QC=QF x CR

and

(5.34)

(5.35)

(5.36)

168 J. A. Howell

Checking this ratio for a range of degrees of concentration we obtain a setof values for the ratio CR/Cr: the concentrations at either end of themembrane channel when the recycle flow is various multiples of the feedflow and various degrees of concentration are obtained in the overallsystem (CR/CF ). The degree of concentration within the loop is alreadyhigh when a factor of 5 in concentration is achieved during a single passthrough the overall system. It would not be accurate to assume acompletely mixed model for the membrane under such circumstances. It isof course possible to increase the recycle rate.

Table 5.2 also shows the effect of changing the ratio of QclQ R' Very highdegrees of recycle are unacceptable owing to the energy costs. However,this particular aspect of membrane design works to the designers advantage. In order to achieve high fluxes through the membrane high crossflow rates are desirable. This is achieved more easily at lower concentration when viscosities are lower and if concentrations along the membranechannel are not uniform slightly higher fluxes are obtained due to theconcentration effect than if the channel were completely mixed. The detailsof how to account exactly for this difference are more complex and requirea complex design procedure. If the majority of the water or other solvent isremoved under high flux conditions the total membrane area required isreduced. Optimisation of the whole system design normally requires acascade of feed and bleed units rather than a single stage.

Table 5.2Values of CF/CR

CR/CF 2 5 10andQR/QF

0 2 5 101 1·5 3 5·52 l-3 z.3 45 1·2 1·7 2'5

10 1·1 1-4 1·8

The design of a cascade system requires the use of a computer but againa spreadsheet is ideal as the following example shows.

5.3.2 Mathematical Approach to Design of a Cascade

5.3.2.1 Maintain the Well-Stirred Assumption for each ModuleIn many stage design problems in chemical engineering where there is nocountercurrent flow it is possible to simplify the design process by workingbackwards from the end of the cascade. Assume total rejection.


Let each black box be a full stage. Stage n. Area AnNow the operating situation for the final stage (N) is known since the

discharge retentate concentration must meet the design specification andthe flow is determined by an overall mass balance:

Since there is total rejection

therefore (5.37)

The permeate flow through the Nth stage is,

and the flux

with the areas for the two end stages being

(5.38)

(5.39)

(5.40)

Given a value of CN _ 2 there will be a value of CN - 1 that will yielda minimum value of AN + AN _ 1. Conversely for a minimum area systemif we assume a value for CN _ 1 if we can calculate the value of CN - 2

for which that value of CN _ 1 minimises the area of the two stages. Thisthen provides a back calculation algorithm. If we assume a value forCN - 1, then we can calculate the starting concentration for which wewould have that value of CN - 1 in a minimum area system. Iteratinguntil we find a starting concentration to match CF we can determinethe concentration profile and hence the areas for a minimum areasystem.

The total area for the last two units is

(5.41)

170 J. A. Howell

Differentiating with respect to the intermediate concentration

(5.42)

+CNl_12ln~ [+(c:_, -C:J In'~ ct]CN - 1 CN - 1

and then equating the numerator to zero

(5.43)

(5.44)

(5.45)CN-2= ()2Cm Cm CN CmIn--In--In-+ In--

CN CN- 1 Cm CN- 1

By extrapolation one can use this solution fairly easily to generate theconcentrations in each stage and hence the fluxes by guessing CN - 1 anditerating. This can be done for a number of stages to generate theminimum area recalling that for each stage n.

(5.46)

and

(5.47)

Actually the areas calculated and displayed in the last line in Table 5.3 donot make practical sense although they may be optimal. In a real systemthere will be a minimum standard module for the system. In such a casethe areas will need to be rounded to the nearest unit on each area and thesystem recalculated. If the minimum unit is 4 m2 then it makes little sense

Tab

le5.

3E

xit

Con

cent

rati

ons

from

Stag

esin

Cas

cade

sw

ithD

iffe

rent

Num

bers

ofSt

ages

Tot

alT

otal

Exi

tco

ncen

trat

ion

from

each

stag

enu

mbe

rar

eao

fsta

ges

12

34

56

78

910

11~ ~

139

050

cEo '"

221

05·

7850

~

318

42-

8810

·95

a:: '"4

174

2·11

5·22

15'4

50:I 0

-

516

91·

783-

497·

719

·150

... '" '"6

166

1·59

2·71

5·0

10·1

22'1

50'" ""

716

41-

482-

33·

786·

6212

-424

·650

~

1016

11·

31·

732-

363-

334·

837·

2611

·318

·230

·150

~ :I11

160

1·26

1·64

2'16

2-92

4·04

5·76

8·46

12,7

819

·86

31-4

550

'"St

age

30·1

26·7

22-9

19-4

16·2

13-3

10·8

8·6

6·7

5·3

Are

asfo

r10

tota

lst

ages

.....

172 J. A. Howell

to use a cascade of one more membrane stage to save less than 4 m2 . Infact owing to the cost of the pumps and control and instrumentationrequired on each stage it makes little sense to go beyond 3 stages.

If the above calculation is repeated to achieve a final concentration of200 kgjm3, then the required areas are:

Stage area Min Nearest 4 m 2

per stage

I 1752 17522 320 3203 236 2364 209 2125 196 1966 188 188

10 175 176

Having obtained a minimum area. New areas are substituted to thenearest 4 m2 on each stage to achieve nearly the same performance. Theconcentrations in each stage can be back calculated using the revised areasfrom eqn (5.48) and the entrance concentration checked against the designfeed.

therefore

CN-1QN-I=QNCN

JNAN=QN-I-QN (5.48)

CN- 1= QNCNQN+JNAN

In fact for a six-stage plant the required area is almost exactly the same forthe following design:

Optimal area Stage conc. h Modularised areastage conc. h

8·5 200 8 20011·6 102 12 104·818·6 36·5 20 36'130·7 12·2 28 11-648.2 4·6 48 4·770·8 2·0 72 2·0

188 ~188

We must now check on the flow through the system and the degree ofconcentration per pass. Let us take the modularised design just developed.


Table 5.4Flows through Six-Stage Cascade

Stage Feed flow Permeate flow Exit flown Qn-l Pn Qn

1 10000 50624937·5 4937·52 4937·5 2814 21223 2122 1256 866·24 866·2 589 276·75 276·7 181 95-46 95-4 45 50

First the overall mass balance: on a six-stage plant the flows are as shownin Table 5.4.

Let the ratio of flows within a module be given by the ratio of therecycle flow rate in a stage Qcn to the forward retentate flow from that unitQn

(5.49)

A stage mass balance gives

(5.50)

where CnO is the concentration of the feed to a stage after mixing with therecycled stream. Using eqn (5'50) one can calculate the ratio of theconcentrations in and out of a given module and thus the ratio of fluxesalong the module. These are given in Table 5.5.

Table 5.5Flux Ratios From Inlet to Outlet of a Channel

Stage Concentration ratio,

2 5 10

I 1·08 1·06 1·03 1·022 1-12 1·09 1·05 1·033 1·17 1·12 1·07 1·044 1·34 1·25 1·14 1·085 1·63 1·47 1·26 1·156 1·92 1·65 1·35 1·2

One effect of the increased recycle is to reduce the average flux across astage since it makes the concentration experienced by the unit closer to thehighest concentration in the unit. On the other hand, increased cross-flowincreases flux, as well as pressure drop. The net benefit must be calculated

174 1. A. Howell

for any design to establish an optimum cross-flow velocity. This will nowbe done for another simplified design.

5.3.2.1(a) MEMBRANE SYSTEM OPERATION/DESIGN

A spiral wound membrane system is available with 1'5-mm channel depth.Pilot experiments have determined the following information for a feedcontaining 5 kg m - 3 dextran.

Using a cross flow velocity of 0·5 ms -1 the flux was 25·8 1m - 2 h - '.The flux was proportional to the mass transfer coefficient which was in

turn found to be proportional to the cross flow velocity to the 0·5. Thepressure drop along the channel which was 1 m long was found to be2 kPa and was further found to be proportional to the 1·7 power of thecross flow velocity.

It is desired that a feed of 1000 m3 h -1 be concentrated by a factor of 2in a single unit. It is necessary to find the membrane area required. Thesystem will be operated at the optimum cross-flow velocity.

If the complete Membrane system costs £1000/m 2 installed and isreplaced every 2 years at a further cost of £2oo/m2 what cross-flow velocitywill yield the minimum cost if the plant operates at design for 6000 h perannum. Assume the annual cost of the capital is 10% of the capital cost.Power costs fO·95/kW.

The area of membrane required will depend on the flux J which we willcalculate in the usual units of 1m - 2 h - '. Then as the permeate flow will be500 m3 h - " the area

A = 500000 m2J

Now the flux can be assumed to be proportional to the mass transfercoefficient and at cross-flow velocity of u, and concentration of 5 kg m - 3

dextran.

where

so

( )

0.5

J = (25'8) 0~5

a=36'48

A = 13706 UO' 5

(5.52)

(5.53)


the area A = 2BL where B is the width and L is the length of themembrane sandwich used to form the spiral.

The cost of the membrane system is £200 A per annum, but the powercost is dependent on the cross-flow velocity sd, th'e~:pressure drop

(5.54)

For a length L

(5.55)

and the power consumed W will be u' tlp· S where S = 1·5 B x 10- 3 is thecross-section of the cross-flow channel in m 2.

Thus

W=_2_ x 1O- 3 u2 ' 7AkW0·5"7

= 1·004 x 1·5 x 103 B.L.U 2-7 kW

= 7·5 X 10- 4 Au2 ' 7 kW

The cost of power will be

W6000 x 0·15 £y-' =0·675 AU2 ' 7 £y- '(kW)(hy-' )(£(kWh)-')

=2'1'5·0'15'6 2'7A=bA 2·70'51'7 U u

where

2·1 . 5·0· 15·6b= 0'15"7

(5.56)

(5.57)

The Annual cost is thus membrane cost plus power cost or

A [200+0'675u 2'7] = 13 706 [~~.~ +0.675u2'2] (5.58)

This cost will be a minimum when

Differentiating

~ [200 +bO'675U 2'2]=0du UO' 5

_1~~+1'485u"2=0U

(5.59)

176

or

giving

J. A. Howell

(5.60)

u=4·75 m S-l

The required area is then 6285 m2 with a flux of 79·5 1m -2 h- 1

The next part of the design demands organising this area to provide theright cross-flow velocity.

The feed-flow is Q= 1000 m3 h -1 if the recycle ratio is y the cross-flowvelocity is:

Q(y+1) (l+y)QU= 1.5 x 10 33600B 5·4B

and as

B=~2L

therefore

l'5uAyL=-

Q

y~ 1 what are the options for L?

5.4 OTHER PARTS OF THE OVERALL SYSTEM

(5.61)

(5.62)

(5.63)

(5.64)

As experiments are often carried out by users on systems supplied bycontractors for general applications they may not provide universallyoptimal conditions for individual users who may wish to redesign thesystem configuration to suit their own situation. Some comments aremade here which may help a user to set up a pilot system for a particularapplication that can use several types of membrane module but whichallows proper evaluation of each system under near optimal conditions.

5.4.1 Pump

The feed pump used in a membrane system is generally chosen bythe system supplier. The choice will depend on the pressures to beused and the cross-flow velocities required. The use of ultrafiltration


membranes generally needs feed pressures of 600-1000 kPa andcross-flow velocities of 1-8 m s- 1 depending on the fouling propensityof the process fluid. Lower velocities are used in hollow fibre systems.Higher pressures can be used in ceramic membranes which allowhigher viscosity materials to be pumped at reasonable cross-flow rates.The choices are then usually centrifugal or diaphragm pumps forlarge scale moderate viscosity applications. High viscosity applications will use a positive displacement pump which may be a mono typepump on low volume applications or otherwise a gear or diaphragmpump.

The recirculation velocities will be higher than the feed rates in mostsystems and so will the pressure head required from the recirculatingpump. This will therefore usually be a centrifugal pump or diaphragmpump where the contact materials need to be sanitary and leak-free suchas in some biotechnological applications.

5.4.2 Cooling

The pumping energy being supplied to large membrane units can be highand so cooling is necessary in the circuit. The choice of where the coolingis applied depends on the application. If heat is really damaging to theproduct the temperature should be reduced immediately after the pump.However, as fluxes are generally higher at higher temperatures and as asingle pass through the membrane is completed in a few seconds it may bemore efficient to allow the flux to occur at the higher temperature withboth permeate and retentate cooled immediately afterwards. Standardheat exchangers can be used.

5.4.3 Holding Vessels

The use of holding vessels is necessary for batch applications or wherediafiltration is done in a semi-batch manner. In small scale applications the design of the holding vessel and indeed the whole circuit iscrucial to the success of the system if large concentration factors arebeing sought. The use of conical bottomed vessels is traditional andcare must be taken in the placing of return loops if excessive foam isnot to be generated during the concentration cycle if proteins or similarsurfactive materials are being pumped. Air should not be entrainedin the recirculating fluid which may become difficult to avoid whenvolumes become low. Baffles are important to minimise swirl in the catchpot.

178

5.4.4 Instrumentation

J. A. Howell

Instrumentation on many small systems is quite basic. The absoluteminimum requirements are temperature indication, as well as pressureupstream and downstream of the membrane module and flow measurement of the permeate. It is useful to have a flow meter on the recirculatingfluid. The next level of sophistication is some means of measuring theconcentration of the retentate which is often difficult owing to the complexand often turbid nature of the stream. Viscosity, refractive index, andturbidity have been used as gross measures of concentration.

If batch concentration is being practiced it may be important not to let aretentate concentration get too high or it will become likely to form a gelor immobile paste should either the fluid become too hot (proteinsolutions) or sould a recirculating device fail through possible overloadand the flow become stagnant in the narrow membrane channels. Somefluids exhibit significant yield stresses and flow may be hard to restart.

5.4.5 Control Software

As a result of some of the problems outlined above most units which arecommercially supplied for specific applications use control software whichprevents, as far as possible, malfunctions of the system and takes care ofcomponent failures by bringing the overall system to a safe holdingcondition. PLC type controllers are often sufficient using comparatortriggers when certain conditions have been exceeded to initiate a newmode of operation. The types of situation which are catered for are:

start-up with a slow ramp up of delivery pressure;shut down if high feed pressure reached as this may indicate blockedmembrane or over concentration;temperature control with shut down if temperature is exceeded;shut down cycle which first flushes the membrane with solvent andmay then leave it full of a cleaning or sanitising solution dependingon the application;automated monitoring of the flux so that if fouling has becomeexcessive cleaning regimes can be initiated. These may be as simpleas permeate backflushing or surface flushing or as complex as fulldetergent cleans;detection of membrane failure tl1rough sudden pressure drops on thefeed side or of off-specification turbidity or other measurement onthe permeate side;detection of feed flow failure with automated shutdown;


detection of final concentration possibly by pressure drop along themembrane module or by other concentration measurement;initiation of certain actions on a timed basis such as regularbackflushing or flow reversal.

The following two sections of the chapter discuss two different casestudies directed at the design of membrane systems. The first assumes anavailable membrane material and determines the optimum operatingconditions and choice of alternative tube diameters for a particularapplication which is the clarification of an antibiotic solution from afermentation broth using a ceramic tubular membrane.

The second case study treats a complete project from the statement ofthe problem through the development of completely new membranemodules to the use of the new modules on a large commercial scale. Itconcerns the application of hollow fibre polymeric membranes to theproduction of potable water from ground water supplies inter alia.

5.5 CASE STUDY 1: ULTRAFILTRATION APPLIED TODRINKING WATER TREATMENTt

This case study reports the development of an ultrafiltration system for afield where the product has a very low added value: the production ofpotable water. In order to comply with all the technical and economicrequirements of the field, all the aspects of the membrane filtration processwere researched, from the nature of the best polymer for the membrane, tothe process itself. This was made possible by a major R&D programme,with the help of the Commission of the European Community and theEureka Programme framework.

5.5.1 Project Definition

5.5.1.1 Background Information on the Main Unit OperationsUsed in Potable Water Treatment

In taking water from rivers or underground reservoirs (the resource) tothe tap, water companies must ensure its compliance with health standards as well as producing an acceptable quality in terms of taste, odour

tThis section was contributed by Philippe Aptel and Jean-Luc Bersillon.Acknowledgments: The authors wish to thank Mr. J. F. Rosado and Dr. P. Thebault (or

making available data on their plants. The research and development work was madepossible by the contribution of the EEC through the BRITE Programme No 1566 andthe contributions of the French Ministry of Research and the French Ministry ofIndustry and International Trade for the Eureka programme EU5 MEMBRANE.

180 J. A. Howell

and visual characteristics such as turbidity and colour. The differentprocesses are chosen and designed so as to remove the following types ofpollutants:

- particulate material (sand, silt, bacteria, viruses);- colloidal material (clays, hydroxides, organic matter);- undesirable dissolved material (nitrate, nitrite, iron, manganese,

pesticides).

Other treatments are aimed at the modification of the ionic quality of thewater so that it can be distributed without corroding or scaling thedistributing network, and ensuring a suitable sanitary quality at the end ofthe distribution network, or at the point of restitution to the environment.

The basic principles used in .the traditional treatment operations includegravity, separation, capture and biological, chemical and physical-chemical reactions. The unit operations include:

screening and straining;coagulation, flocculation and precipitation;biological treatments for the removal of specific nutrients (nitrogen,carbon, phosphorus compounds);settling and sand filtration;activated carbon adsorption and ion exchange;ozonation and chlorination.

A special place is occupied by reverse osmosis which is the first membraneprocess to be used on the large scale for water treatment where it is usedfor desalination of brackish or salt waters. The technique competes withmultistage flash distillation.

5.5.1.2 Limitations of the above Techniques and Trends inWater Quality Regulation

Most of the above processes suffer from one or more of the followinglimitations:

the addition of a chemical product at a rate that depends on theincoming water quality;formation of undesirable chemical by-products;lack of specificity or insufficient yield;formation of sludges containing undesirable compounds;

- reliability which varies with load.

Even where the quality of the treated water has been considered acceptable for a long time this can change through improvements in analyticaltechniques and consumer and media pressures which require an ever


improved quality that is more and more difficult to reach. The samefactors act on legislators leading to the setting of ever more stringentstandards. (Fiessinger et al., 1986).

5.5.1.3 The Technical ChallengeAmong the separation processes, membrane filtration offers advantagesthat overcome the major drawbacks of conventional water treatmenttechniques:

A membrane is an absolute filter. Provided that its cut-off isproperly chosen, it will reliably separate pollutants from water.If properly chosen, membrane filtration does not need the additionof coagulating agents.The waste stream of a membrane separation unit contains onlypollutants removed from the water. It will not contain reactionby-products, nor other added materials.

The major drawback of this technique was the cost of the membranes andtheir frequency of replacement, and the relative inadequacy of the membrane material with respect to the conditions and constraints of watertreatment. The challenge in this project was the adaptation of themembrane manufacturing and operating technologies to meet watertreatment quality and cost objectives.

5.5.1.4 The Technical Objective

5.5.1.4(a) RAW WATER QUALITY AND ITS CONSEQUENCES

In the regions selected for the building of the first ultrafiltration plants, andwhere they have since been operating, the raw water quality is generallygood, save after rainy periods which give rise to an increase in turbidity andorganic content. This is illustrated in Fig. 5.8, where the turbidity of the

AMO COURT LE BAIZIL DO CHY

25.3

I_ 0·1 NTU D 1-5 U fI'JI 5·20 NTU En 20-100 NTU IFig. 5.8. Turbidity frequency diagram on 3 ground waters.

182 J. A. Howell

resources is represented on a time frequency diagram. The high rate atwhich this deterioration occurs means, as the coagulant dosage is seldomappropriate and cannot be easily changed quickly (especially on unmanned plants), that these resources are difficult to manage. This then impairsthe quality of the distributed water. In the case of ultrafiltration theprocess parameters are physical and an automated control system canrapidly increase the operating pressure or the backwash frequency in orderto maintain the permeate flux. Figure 5.9 illustrates the response of theultrafiltration plant at Douchy during a transient deterioration of theresource turbidity. Wherever the deterioration of the resource quality isrelated to particulates then the quality of the UF permeate will remainunchanged.

TransmenbarnePressure (bar)

1.0

Turbidity(NTU)

20

0.8 16

8

4

o

12

3025

0.6

0.2

0.4

10 15 20Time (days)

Fig. 5.9. Pressure response of the ultrafiltration process to a turbidity surge on the rawwater (Site of Douchy).

5.5.1.4(b) TREATED WATER QUALITY: VALIDATION OF THE TECHNICAL CHOICES

As would be expected the water quality produced by the ultrafiltrationprocess is constant and is way beyond current European standards forturbidity and microbiological quality. This is illustrated by Figs 5.10 and5.11, and Table 5.6. In Fig. 5.4 it is worth noting the consistency of thedistributed water quality as compared to the situation before the start-upof the ultrafiltration process.

This type of response of the product water quality was expected as themembranes constitute an absolute filter. This contrasts with deep bedfiltration for which the particulate removal is influenced by the upstreamtreatment efficiency as well as the time which has elapsed since the lastbackflushing cycle.

The main effort of the research work was aimed at the resolution of twoproblems related to improving the overall economics and system designfor ultrafiltration of water.

Raw water turbidity._- Direct filtration treated water turbidity-- Permeate turbidity

lOO.--------,-------,----~---_.,..---...,

183

IO

0.01l------I.------I.------I.---.........---......o 50 100 150 200 250

Time (days)Fig. 5.10. Comparison of the turbidity of treated waters and raw water on the Douchy

plant (ultrafiltration long term piloting).

Turbidity(measured by DDASS and Lyonnaise on municipal main))

2.0 t- .;;I'M.;;.;.;;;C_"La=w.;;O.;.lo..;89;;... _

Maximal monthly value

1.5

1.0

0.5

12 1 2 3 4 5 6 71989

Fig. 5.11. Time evolution of the turbidity on the Douchy potable water distributionnetwork, before and after ultrafiltration implementation.

Table 5.6Water Qualities at Douchy

Raw Treated Raw Treatedwater water water water

Turbidity (NTU) 0·28 0·06 3 0·06Fe (jlg/l) <0·28 <20 40 <20Mn (jlg/l) <5 <5 <5 <5AI (jlg/l) <10 <10 195 <10Total coliform (lml) 44 0 10 0Fecal strept. (lml) 0 0 364 0Total germs (lml) 6 300 <1

the choice of a suitable polymer compatible with water treatmentconditions and with the techniques of fabrication including spinning,bundling, potting and conditioning;the study and the control of fouling relating to the use of ultrafiltration in water treatment and the techniques that can be used tominimise its detrimental effects on both capital and operating costs.

184 J. A. Howell

5.5.2 Step 1: Choice of the Membrane Type and Configuration

5.5.2.1 Ultrafiltration us other Membrane ProcessesTo comply with particle removal requirements, one must either choose atight membrane, or pretreat the suspension in order to aggregate theparticles so that they are retained by the chosen membrane. This isillustrated by Fig. 5.12. There are a large number of solutes found insource water, some of them likely to adsorb on the membrane materialand contributing to fouling. (Bersillon, 1988; Lahoussine-Tucaud et al.,1990).

I

I Organic ITl8cromolecules II Colloids I I Organic I

compounds

I Bacteria I I Vlru_ I DI:O~ved II Pollens 18

JU'l 10 1 0,1 0,01 0,001 0,0001

0 0 0 0 ;:> IReverse osmosishair visible Red Smallest P)lio

to naked globule microorganisms virus INanofmralion Ieye

I Ultrafillration II Microfillration I

ISand filler I

100

Fig. 5.12. Pollutants and separative techniques comparative size diagram.

5.5.2.2 Hollow Fibres and other GeometriesMembranes are available in four different geometries of module (plate andframe, spiral wound, tubular and hollow fibres), each adapted to specificfiltration applications. For water treatment the following requirements areimportant:

pretreatment of the source;easy to clean by backwashing;low specific energy consumption;compactness.

Fluid dynamic calculations were used to estimate energy consumption. Ithas been reported that permeate fluxes increase with tangential velocity(Bourdon et al., 1988). This increases energy costs as shown in Table 5.7.In this table the energy requirements were calculated assuming the


Table 5.7Energy Requirements as Calculated by Fluid Dynamics Laws as a Function of

Feasible Operating Conditions

Ultrafiltration M icrofiltration

1. Membrane characteristics-Length (m) 1·2 0·850-Int. diameter (mm) 0·93 4·0-Stabilized flux (m 3. h - I. m - 2) 0·100 0·87

2. Operating conditions-Operating pressure (kPa) 70 40-120

Calculated energy requirements(kWh'm- 3)

-Transfer through the membrane 0·019 0'109-Tangential velocity (m's - 1)

0·5 0·043I 0·1725 0·950

3. Total required energy on 0·019---0·191 1·059the modules

185

requirements to overcome head loss in a smooth pipe. In practice losseswould be greater due to the transport through other parts of the systembesides the membrane fibres. There are also other energy costs in acomplete process system.

Hollow fibre systems rank high against all requirements when comparedto the other geometries and have the additional advantage that they areeasy to manufacture and were chosen for this project.

5.5.2.2(a) NATURE OF THE MEMBRANE MATERIAL

Many polymers are used to manufacture commercially available hollowfibre membrane modules including polysulphone (PSf), polyvinyl difluoride (PVDF), polyvinyl alcohol (PVA) and polypropylene (PP). Most ofthese were tested for their performance in spinning trials and also ascomplete membranes in field trials.

The final choice of the polymer was made quite early in the course of theproject with the code name BCDA.

After the choice of the polymer was made the study was geared towardsthe improvement of the chemical and mechanical resistance of the fibre. Asof today membranes developed from this project have a life expectancyaveraging 5 years under normal water treatment conditions:

temperaturepHresistance to chlorine

o-30°C5·5-8·575000 ppm' h.

186 J. A. Howell

5.5.3 Step 2: Process Definition and Validation

5.5.3.1 Large Modules for Large ApplicationsWater treatment is an application where relatively large volumes ofproduct are handled (2 to several thousands m3 •h -1) and where themarket value is very low (a few FF· m - 3). All the elements of the processmust be robust, resistant to wear, cheap and secure. These requirementsled to the design of comparatively large modules so as to limit pipingcosts.

5.5.3.2 Fibre and Bundle GeometriesParallel bundling was chosen, and a computerised bundling machine waspurpose built to carry it out very early in the project. Alternativetechniques were eliminated early on as shell side head losses were too highand the methods were over complex. A potting resin was chosen early onand by the middle of the project 100-mm diameter modules were beingproduced routinely and the first 300-mm units were also being produced.

5.5.3.3 Fouling Prevention: Backwash and RegenerationMembrane fouling research was carried out on several fronts:

a hydrodynamic modelling approach based on particle trajectories;data processing analogous to determining the fouling index forreverse osmosis was used to characterise the resources to be treated;analysis of the nature and amount of fouling material deposited atthe interface between membrane and water, as well as in the wateritself;accelerated fouling experiments involving specific substances of thesame chemical family as foulants identified in the resources;a statistical analysis of the results taking into account water qualityand process parameters.

The first two approaches were abandoned as being too elaborate andtime-consuming to calibrate.

The analysis and accelerated fouling experiments generated the richestbody of data and suggested technical methods to reduce and controlfouling problems in the final process used today. It was found that specificcompounds such as polyphenols, polysaccharides, proteins and carboxylicacids tend to accumulate at the membrane surface, binding together theparticles and contributing to the cohesiveness of the filtration cake. Thesesubstances are found in natural waters where they constitute the organicmatrix (Mallevialle et al., 1987). It was also found that specific compondsadsorb to the membrane surface contributing to the irreversible fouling of


the membrane. The severity of the fouling was dependent on the nature ofthe polymer used for the membrane and led to the discovery of a polymerwhich showed the least irreversible adsorption as well as the leastirreversible fouling, (Fig. 5.13).

These results were used as one of t.he guidelines used for choosing themembrane material which included susceptibility to adsorption and easeof cleaning by hydraulic means.

The statistical analysis was especially successful for waters characterisedby low turbidities and low levels of organics. In order to quantify the dataon flux reduction a generalised exponential law was used and the evolution of the parameters used in the law were quantified with respect to rawwater quality parameters and process operating conditions. It was foundthat in general 8-day runs were required to determine the stable values ofthe exponential law parameters.

When determining the equilibrium flux to be used as the design flux forthe plants it was found that a spherical regression routine generated a 14%average discrepancy when compared to actual values. The highest discrepancies (56%) were found with high turbidity, high organic content waters.The statistical model was not considered reliable for these waters due tothe insufficiency of data on such waters.

This approach was then used to define seven water classes fromtap water to tertiary effluents which were related to filtration process parameters and performance using the Factorial Analysis of Correspondence.

5.5.3.4 Pilot Scale Validation: The Long Term TestThe aim of the pilot studies was to validate the choices made in theprevious parts of the work as well as to point out the further problems tobe solved and prepare for the implementation of membrane filtration ofraw waters as an industrial technique. The pilot plant experiments werealso used to yield the initial data for technico-economic evaluation of theprocess.

5.5.3.4(a) GROUND WATERS

Pilot studies were conducted on ground waters from the early stages of theproject, first to assist in the choice of membrane material and then todetermine the optimal choice of process parameters (operating pressure,tangential velocity, backwash frequency and run duration). These experiments were performed primarily on ground waters as it was decided thatultrafiltration could solve the existing treatment problems associated withthis type of resource (occasional turbidity giving rise to unsteady treatedwater quality).

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5.5.3.4(b) SURFACE WATERS

Surface waters were also treated using ultrafiltration membranes fromdifferent sources including those developed by this project. It was foundthat the latter membranes were less susceptible to fouling than othercommercially available ultrafiltration membranes. It was necessary to useeither a higher tangential flow velocity or a lower permeation rate forthese waters than for ground waters in order to achieve a suitable processoperation.

As reported in the section on fouling, organic materials are a determining factor in the fouling of membranes. Since surface watersgenerally contain more of these compounds than ground waters it wasdecided to add powdered activated carbon (PAC) to the raw surfacewater prior to ultrafiltration. The influence of the PAC on thehydraulic behaviour of the process was assessed and found to be negligible. It was found that the use of PAC improved the quality ofthe treated water as predicted from its adsorption properties (Anselmeand Charles, 1990; Laine et al., 1990; Anselme et al., 1991). Longterm effects could not be assessed and therefore a demonstration plantwas designed and built at Suresnes (Hauts de Seine), a facility treatingwater from the River Seine downstream of Paris (Anselme and Charles,1990).

5.5.3.4(c) WASTE WATERS AND BIOLOGICAL PROCESSES

In this section two cases are addressed where the raw water IS verydifferent.

a ground water contammg very high levels of ammonium forwhich a biological process is preferable to the addition ofchlorine;a tertiary effluent which contains high levels of organic compoundsand has a high microbiological count.

These 2 cases have in common the presence of or use of bacteria leading tospecific problems related to the filtration of biomass and the potentialbiodegradation of the membrane material.

In both cases it was found that while the process was technicallyfeasible the fluxes were too low for the process to be economically viable.This type of experiment showed that in certain cases bacteria athigh concentration can be more resistant to variations in their habitat,including nutrient shock loads and the transient presence oftoxins.

190

5.5.4 Step 3: The First Plants

J. A. Howell

5.5.4.1 Their Size, Performances and LimitationsAt the end of 1990 the following plants were in operation:

Site Nominal throughput(m 3 h- 1 )

Amoncourt IODouchy 50Le Baizil 5Gracay 30Blomac (Sirroc'eau) 10Suresnes 8

The water sources on which these plants are operating are in most caseswell waters in karstic regions.

The targeted pollutants in these sources are suspended solids whoseconcentration is very variable as the sources are affected by rain run-off.This causes turbidity spikes reaching 350 NTU for Amoncourt.

The case of Suresnes is peculiar as it uses PAC addition allowing thetreatment of organics as well as solids.

5.5.4.2 The Price of Water Quality InsuranceIn this part of the report only operating costs will be addressed. Theseinclude reagents, energy, labour and membrane replacement costs. Theyare, wherever possible, related to local market conditions.

5.5.4.2(a) REAGENTS

Chlorine. The only reagent used on a permanent basis is chlorine used asa final disinfectant and also a disinfectant for the membrane in thebackwash sequence. At Douchy the extra chlorine demand as a result ofmembrane disinfection is 0·1-0·3 g . m - 3 depending on the backwashfrequency. This compares to the treated water demand of O'3 g' m - 3.

Regeneration requirement. The membrane regeneration frequency depends on the resource quality. At Amoncourt the membranes have beenregenerated only three times since start-up. Le Baizil has been regeneratedonce and Douchy not at all at the time of writing. Based on experience ofthe above plants it is estimated each square metre of membrane requires70 g of regenerant and this is required after producing approximately 200600 m21m3 depending on the quality of the water. No price is yet available


0,5

0,0

for the regenerant as it is not yet commercially available although this isplanned for the near future.

Energy. The quality of the energy consumption data varies with the sizeof the plant. No data are available for Ie Baizil but all energy needs of theplant at Amoncourt were recorded. These are shown in Fig. 5.14. Theconsumption averages 1·75 kWh/m 3 for the entire period January '89 toJanuary '91. No details on the nature of the energy needs are available.

Energy (kWhlm3)

3,0

2,5

2,0

1,5

1,0

~~bMM~~JunJul~I~~Nov~j~M~A~~Jun~I~~~~~

Time (since Jan. 1989)

Fig. 5.14. Amoncourt overall energy consumption as a function of time (monthly averages).

The most interesting case is that of the Douchy plant where energyconsumption was recorded for the different needs including pumping ofthe feed, recirculation, backwashing, pumping into the distribution network and others. The maximum overall need when the plant is in therecirculation mode is 1·6 kWhim 3 which is consistent with the Amoncourtdata. This was expected as the two sites have similar configurations of thedistribution network, and the sources are similar. Figure 5.15 shows theenergy consumption distributed according to use. This shows that themajor element of the consumption is the recycle (0,6 kWh/m 3

) includingbackwash, pump losses and purges and compares with the theoretical(tube pressure drop only) energy needs of 0·172 kWh/m 3

.

Labour. In the Lyonnaise des Eaux-Dumez company it is standardpolicy to visit each plant once a week. During this visit the operatorchecks water meters, free chlorine in the distributed water and the generaloperating condition of the plant. These visits require at least 30 min on siteand constitute the irreducible man-power requirement for a plant.

192 J. A. Howell

Summer Prolile

• Inlel pump • OUIlel pump • Olher

Wimer Prolile

1,5

1,0

0,5

0,0

Energy (kWh/m3)

2,0

Fig. 5.15, Seasonal energy partition diagram at Douchy.

Table 5.8Man Power Required for 1 Year of Operation of Ultrafiltration

(Minimum Required Man Power = 52 h'year - 1)

Amoncourt Douchy

Routine control } 98 h'year- 1

72 h'year- t

Electrician 24 h'year- I

Produced water (m l) 27660 115000

Table 5.8 shows that actual man-power used on the Douchy andAmoncourt plants is seen to be little higher than the minimum.

Membrane replacement. Laboratory experiments aimed at an assessment ofthe membrane life expectancy show that it is reasonable to assume theirreplacement on a 5-year cycle. The anticipated production will be 3650 m3/m2

•

Since the first plant was installed in November 1988, Lyonaise des Eauxhas been involved in the running of six ultrafiltration plants, five of themin a rural environment. The experience gathered shows that treated waterquality is very reliably high. Production problems are not significantlydifferent from those at conventional plants. The quality of the waterproduced is far better using ultrafiltration and the plants are more reliablethan conventional treatments such as deep bed filtration.

As far as the production cost is concerned it was found to be stronglyinfluenced by local market conditions and amortisement policies.

5.5.4.2(b) THE NEXT CHALLENGE

As far as the major water distribution companies are concerned R&D iscurrently underway to tackle the problems of surface water treatment. The


main contaminant to be removed is algae. Work is undertaken to treatsurface water in a more complete way by integrating other treatmentprocesses within the ultrafiltration system.

5.5.4.2(c) THE FUTURE

The possibilities of membranes as highly reliable separators is veryattractive. Laboratory experiments are underway aimed at the use ofmembranes for the removal of specific pollutants such as dissolved iron,manganese, nitrate, sulphate, pesticides. No results have been published sofar on these experiments. There is no doubt that removing any pollutantfrom water is feasible using a pressure driven membrane process. The costfactors, both capital and operating must be weighed against product qualitywhen considering the adoption of any of these processes in the future.

5.6 A CASE STUDY IN THE DEVELOPMENT OF A DESIGNFOR CROSS FILTRAnON OF MYCELIAL CELLSt

This is taken from an example from industry in which a design study wascarried out in order to develop the choice of a microfiltration system for a400-m2 ceramic microfiltration plant. The ceramic filters are chosen becauseof their long life, high flux and good chemical, heat and solvent resistance.This makes them a good choice for biotechnological applications.

For the purposes of the case study we will assume that the choice hasbeen reduced to that of which tubular ceramic element is most suitable forthe purpose, and what operating conditions should be used. The optionsavailable for the tube are O'2-llm, O'45-llm and 50-kDa pore sizes in tubesof either 4 or 6 mm in internal diameter.

The operating conditions which must be selected are the pressure, thecross-flow velocity, the amount of concentration before diafiltration isintroduced and the degree of diafiltration used. It is assumed that thetemperature is set by the process requirements.

The choices are made by carrying out a series of pilot experiments todetermine the way in which performance changes with the variousvariables used. In this example we shall consider the selection of themajority of the above factors.

The number of potential experiments is large, and if one is consideringseveral different manufacturers products, extremely large. It is thus advisable to restrict consideration of further options as quickly as possiblebased on the results of early experiments.

t This section was contributed by P. Crocker.

194 J. A. Howell

The goal of the experimental programme is to get the best combinationof capital cost, operating cost, product recovery and product concentration. The capital cost is influenced by the overall system size which needs adetermination of flux, operating time and module configuration (series orparallel). The operating cost is influenced by the cross-flow velocity, thetransmembrane pressure, the membrane life, water use for cleaning anddiafiltration and the simplicity of the control system. Product recovery isinfluenced by the product transmission through the membrane and thedegree of diafiltration used. The last two factors also influence the finalproduct concentration.

5.6.1 Pore Size

The effect of pore size is to increase or decrease the degree of transmission of the desired permeate product and also to ensure the near totalretention of the desired retentate solids. It is found that the degree ofretention is affected by transmembrane pressure and cross-flow velocity.A series of experiments were carried out to measure transmission ofproduct as a function of operating condition and pore size. As Fig. 5.16shows the transmission varied across the whole range of conditions withone set of conditions showing a significant improvement over the others.The choice of a low transmembrane pressure (1 bar) and a O'2-~m poresize could then be made on the grounds of product quality. The transmission seemed to be better if it were low. No attempt is made to further

'lbge transmission

100

80

60

40

20

0-"'------,------'------,------"2 m/s 6m/s

0.45 um DUF

Fig. 5.16. Transmission of protein at different flow rates, transmembrane pressure andpore sizes.


quantify or refine these results but the choice of a O'2-llm pore size andthe low transmembrane pressure was made from these results. Thereare of course some anomalies in the results, especially odd is the observation that there was more transmission with the smaller pore sizedmembranes with the sole exception of the 85% transmission at thelowest pressure and cross-flow velocity for the middle pore sizemembrane. Under all other conditions the ultrafiltration 50-kDa cutoff membrane was the best. Such a result bears further investigation andprobably relates to the nature of the fouling of the two types ofmembrane with the tighter membrane retaining the cell cake on its outersurface preventing the build-up within the membrane pores of a rejecting layer. In any case the differences are quite small between thedesigns and will be outweighed by economic considerations of othersorts. Any lack of transmission can be countered by more diafiltration.The key point is that there is no obvious advantage in terms of productretention for the expensive options of high pressures and high cross-flowvelocity.

5.6.2 Time

Figure 5.17 shows the fouling rate with time at two different cross-flowvelocities. There is a dramatic difference between the two cross-flows ofalmost fourfold increase in flux. The results were quantified in each case byfitting a crude but effective time decay model to the flux decline curve. Thismodel was then available to simulate performance over the time course ofany concentration process.

J = 1121 ·0_093----,.,- -:-=..-----=---=------=----=====----=----:::..::..'-"~-=J----70

100.---------------------,

90 -~~,"'------ ----- ------------------- --------- -

80 --

40 -----------------------.-.------ ------ --- - .. ----_.---- -------

30 + ----- --- ----- ------ ----------..----- ..-----

~:='---c~_+~_.~~~-=~=--=~-L,=--~~~~4---EJ·~

50 100 150 200 250 300 350 400Time mn

Fig. 5.17. Flux versus time for two different cross-flow velocities on a Q'2-llm membrane.

196

5.6.3 Pressure

J. A. Howell

Figure 5.18 shows the effects of concentration and pressure on the flux.The familiar limiting flux behaviour is observed and suggests that there islittle advantage to be gained from operation at higher pressures than 2bar.

100,,.----------------------,

90 --...--------.---..-.----

80 .------..--..-.---------------------------.-.

70 ------.------.--------.-.

&: 60.5l. 50 -- --..----.--.-.-.-- fermenter'broth-----------

... 40 - .. -'-' ----------..-----.----.-.--- -------------.--.----

30 -------- ----.-

20 ----'-------.--- -.---------.--broth concentrated by 2.5 x

10 - ... -.-.::::;:::~c::-.- C'7_~_~"-~- moL n ...

...... - ."

O+----,-----,---r-----.---r---~-~-___l

o 100 200 300 400 500 600 700 800TMP kPs

Fig. 5.18. The variation of flux with transmembrane pressure at different concentrationfactors of the original mycelial broth. Cross flow 4 m/s.

5.6.4 Concentration

A more careful approach to determining the effect of concentration isshown then for two separate tube diameters in Figs 5.19 and 5.20. The fluxis also shown as a function of cross-flow velocity and in each case the data

5

&: 4.5

I 4

o 3.5

i 3u 2.5:g 2ui. 1.5

'8 1U 0.5

o

~

'/~ ~ ~

--------_..__.... _.. -_.,,--- .. - ..- ..._. --

f----Depreciation •

-----, - .-- --....... -- - - ------ _n~ IEnergy l

-,-----" --~ ---------- IUtilities I-

2 4 6 8 IMembrane Replacement ICross Flow mi.

Fig. 5.19. Flux versus the log of concentration for a O'2-Jlm membrane with 4-mm tubediameter at different cross-flows.

IDepreciation


2.5~---------------------,

'0

i 1.5

u2iB . ----

i __ ._______- EnergyUSo.5t--~;::=;=::~=====~r=5..::::><:: Utilities

o12---:4~-==:6===~e=~,r:;:M;:em::;:br::an=e~R~ep~,a~c=em=e~n~t

197

Cross Flow m/_

Fig. 5.20. Flux versus the log of concentration for a Q'2-llm membrane with 6-mm tubediameter at different cross-flows.

has been fitted by an equation which takes into account concentration andalso cross-flow velocity. These equations are typical of those one mightexpect for ultrafiltration and are less usual for microfiltration of cells inprecisely the form shown here. The actual data have been suppressed andit may be surmised that the equation is used to approximate the dataobscuring the usual plateau effect that is seen at intermediate concentrations for microfiltration. For both cases the dependence on cross-flowvelocity is higher than might be anticipated for a mass transfer coefficientdependent process. This favours higher cross-flow velocities more thanwould have been expected for a simple model and thus suggests that thepenalty of the excess energy required to send flow at a higher velocity mightwell be counteracted by the benefits of higher fluxes. It is also interesting thatthe larger diameter gives a higher flux (since the Reynolds number hasincreased) to an extent greater than might have been expected from knowncorrelations. Nevertheless the data as obtained is important and once it hasbeen quantified in equation form it becomes possible to perform an economic analysis for the choices of tube diameter and also cross-flow velocity.

The results of these calculations are shown in Figs 5.21 and 5.22 for allof the major costs which have been computed using the models developedin the study. These show a clear optimum cost at a flow velocity of 6 mlsand a tube diameter of 6 mm.

The economic factors included in these calculations are commerciallyconfidential but clearly require a knowledge of utility costs, membranecosts, value of lost product, and capital system cost.

The final design chosen was for 6-mm tubes with a cross-flow velocity of6 m . s- 1, a transmembrane pressure of 1 bar, a concentration before

198 J. A. Howell

----".......---"---------_._---

1000

-----=----------_.• --2 m/s

4 m/s --------..._-----1,

+-_.o..- ----j

+-------'~-------------_._-

14.-- --"--'6'-'m~s _

100

90

80

70

~ 60j.. 50:::Iu:: 40 -

30

20

10

0100

Concentration gIL

Fig. 5.21. The optimum recirculation velocity as determined by overall economics using4-mm tube diameter.

200..-------------------,180+--------------------1160+:--------------------1-",-140 ,

~ 120 -~-------- --- ------- ----------- -'-

~ 100 ".f 80~ -"",_ 6 m/s

60 ~ "'-4m/s~ "_

40 ....1-__ 2m/s ~"---...

100 1000Concentration giL

Fig. 5.22. The optimum recirculation velocity as determined by overall economics using6-mm tube diameter.

diafiltration of 2 X and a diafiltration dilution of 2·5 x. This achieved a90% product recovery at an average flux of 50 I· m - 2 h - I. It would beexpected that more rigid particles would use a lower cross-flow velocityand require a regular backpulse for cleaning of the cake.

How was the decision about diafiltration made? How were the calculations made to predict the overall performance?

The basic equations which are used for such a determination are acombination of normal mass balance equations for the system as havebeen discussed previously and also the equations which have been determined as a result of the experiments.

In this case we have several equations. A summary of the equationswhich quantify the flux gives the following.


For time dependence

where

Jo=66'3, k t = -0'093, u=6'7m's-1

For flow dependence

199

Together

J = kaukutk' In [~c]

Using the above expression to calculate the flux we can substitute thevalues into the expression for the rates of accumulation of the concentrations of the individual species.

Writing a mass balance for the overall volume, V, of liquid remaining ina batch system with a membrane area A;

dV-=-JAdt

t=O, V=Vo

The mass balance for the total antibiotic in the batch tank is:

d(Va)(it= -JA ap = -JA a(l-Robs )

Robs the rejection is a function of the flux J, so that the observed rejectionis unreliable and the true rejection R.

ap = l-Raw

where aw is the concentration of antibiotic at the membrane surface. Nowsince the ratio of the pseudo-limiting concentration of microorganisms kc

to the bulk concentration c is given by;

kc =c eXP(:m)and a local balance on antibiotic across the membrane gives

aw-ap ( J )---=exp -a-ap K m

zoo J. A. Howell

substituting for ap and using the previous equation it is possible to showthat

akca ------w- eR+kc(l-R)

The above can now be substituted into the mass balance for antibiotic andthe d V /dt term substituted from the first equation to give

da 1 JARea

dt VeR+(l-R)kc

Finally one has the equation for the rate of increase of cell concentrationwhich is:

d(eV)= -JAR edt c

where Rc is the rejection of cells Rc = 1Thus again substituting for d V/dt we have

de 1-=-JAedt V

This gives a monotonically increasing value for e. As it increasesthe volume in the batch tank decreases, but so does the flux. Therecomes a point where, as the antibiotic concentration is increasing slowlydue to the partial rejection, the system must be diafiltered to recoverretained antibiotic. A long optimisation is required owing to the numerical and non-linear nature of the model. There is no analytic solution.The higher the concentration at which diafiltration is initiated the smaller the volume of added water which has then to be removed and thehigher the final concentration of antibiotic in the permeate. On the otherhand, the lower the flux at which that added volume is removed. Fullimmediate dilution allows the concentration of cells to be immediatelyreduced and the flux to increase once more. Under a normal plateaucurve for flux versus cell concentration the natural point for diafiltrationis just before the plateau ends. Enough dilution is then allowed toachieve the required recovery of the initial antibiotic present. Althoughthe concentration may have increased slightly, most is removed with thepermeate. High recoveries coupled with the limited size of the batch tankmight require multiple diafiltration dilutions. Figure 5.23 shows how adouble diafiltration allows recovery of nearly 95% of the antibiotic inthe feed whilst maintaining the flux at moderately high levels. In thiscase the batch was concentrated 2 x before diafiltration thus the total

liquid added in the two diafiltration dilutions was equal to the originalfeed volume. The average flux during the run was approximately241 . m - 2 h - 1.

160

140

120

100 :c-80

,§.x;j

60 u::40

___ 20.... -.....:..

................-" -..

"-<' ••

.'........---.

i 100~------------------~c:2. 90

807060

5040

302010

O--l-O---1~00---20~0---30~0---40'--0--5"""0'-0:::::::=6=l-08

Time (min)Fig. 5.23. Flux versus time and the antibiotic concentration versus time in the retentateduring a double diafiltration run lasting 10 h. Cross-flow was 6 mls in a 6-mm diameter

tube.

NOMENCLATURE

For symbols not defined in text:

A Constantai Osmotic coefficientCb Bulk concentration (gil)Cp Solute concentration in permeate flux (gil)Cm Concentration at solution-membrane interface (gil)D Diffusion coefficient of bulk solution (m/s)H Height of channel (m)J local permeate flux (micron/s)J Average flux over the entrance length (lIm Ih)k Mass transfer coefficient or viscosity coefficient (l/g)L. Entrance length of concentration boundary layer (em)P Transmembrane pressure (Pa)Q Flow rate (ml/mn)R Membrane hydraulic resistance (Pa.s.m - t)x Distance from inlet of a channel (em)W Width of a channel (m)

202 J. A. Howell

Greek Symbolsb Thickness of concentration boundary layer (m)j1. Viscosity of bulk solution (Pa.s)1t Osmotic pressure (Pa)

REFERENCES

Anselme, C. & Charles, P. (1990). Chemviron Award.Anselme, c., Bersillon, 1. L. & Mallevialle, 1. (1991). The use of powdered

activated carbon for the removal of specific pollutants in ultrafiltration processes. Presented at Membrane Technologies in the Water Industry; AmericanWater Works Association of Membrane Processes Conference; March 10--13,1991, Orlando, Florida.

Barker, P. E., Poland, K., Till, A. & Alsop, R. M., (1989). The development of adiafiltration cascade system for the fractionation of a dextran hydrolysate.Chern. Eng. Res. Des., 67, 262-6.

Bersillon, 1. L. (1989). Fouling analysis and control. In Future Industrial Prospectsin Membrane Processes, ed. L. Cecille & J. C. Toussaint, Elsevier Science,Amsterdam.

Bourdon, F., Bourbigot, M. M. & Faivre, M. (1988). Microfiltration Tangentielledes Eaux d'Origine Karstique. L'Eau, l'Industrie, les Nuisances, 121, 35.

Clifton, M. J., Abidine, P., Aptel, P. & Sanchez, V. (1984). J. Membr. Sci., 21,233-46.

Da Costa, A. R., Fane, A. G., Fell, C. 1. D. & Franken, A. C. M. (1991). Optimalchannel spacer design for ultrafiltration. J. Membr. Sci., 62(3) 275-91.

Fiessinger, F., Mallevialle, 1., Leprince, A. & Weisner, M. (1986). Megatrends inwater treatment technologies. Water Res. Q., Jan.

Lahoussine-Turcaud, V, Wiesner, M. R., Bottero, 1. Y. & Mallevialle, 1. (1990).Coagulation pretreatment for ultrafiltration. 1. A WWA, 82 (12), 76.

Laine, 1. M., Clark, M. M. & Mallevialle, J. (1990). Ultrafiltration of lake water:effect of pretreatment on the partitioning of organics, THMFP and flux. J.AWWA, 82 (12),82.

Mallevialle, 1., Anselme, C. & Marsigny, O. (1987). Effect of Humic Substances onMembrane Processes. Proc. ACS Congress, Denver, Colo.

Olivieri, V. P., Willingham, G. A., Vickers, 1. c., McGahey, c., Kolega, M., Day,A., Johnson, W., Kopp, C. & Grohmann, G. S. (1991). Continuous microfiltration for the production of high quality watewater effluent, IWEM Symposiumon Advanced Sewage Treatment, London, November 1991.

Pritchard, M. (1990). The influence of rheology upon mass transfer in cross-flowmembrane filtration, Ph.D. Thesis, University of Bath.

Taddei, C. & Howell, 1. A. (1989). On the effect of membrane conditioning in cellharvesting using microfiltration. Biotech. Tech., 3, 155-60.

Chapter 6

FOULING PHENOMENA

1. A. HOWELL


& M. NVSTR6M

Department of Chemical Technology, Lappeenranta University of Technology,PB20, 43821, Lappeenranta, Finland

6.1 INTRODUCTION

The decline in permeate flux over a time period of minutes throughto days, often accompanied by an increase in solute rejection, is attributable to a variety of mechanisms known collectively as fouling. Fluxreduction due to fouling is distinguished from that due solely to concentration polarisation by its irreversibility: material accumulated at themembrane undergoes physico-chemical interactions with the membraneand with itself and is thus rendered immune to the mediating effects ofdiffusive mass transfer or particle back-transport. The definition of whatconstitutes an irreversible attachment is a relative one and is made withrespect to some specific removal force which is a function of suchcharacteristics as a fluid's shear rate, ionic strength and surface activity.The first part of this chapter discusses fouling phenomena in qualitativeterms whilst the second part discusses the mechanism in quantitativeterms.

There are a variety of fouling mechanisms which mayor may notbe significant in anyone situation depending upon the combinedcharacteristics of the membrane, feed stream and operating conditions.This chapter predominantly examines fouling by feedstreams containingprotein and cells but with reference made where appropriate to polysaccharides, colloidal salts and synthetic polymers.

203

204 J. A. Howell & M. Nystrom

6.1.1 Fouling Mechanisms

A clear discussion of the various mechanisms which cause fouling phenomena is frustrated by the lack of universally accepted and unambiguous labelswith which to describe them. Terms used in the literature overlap dependingon the background of the authors and some have been used in a collectivesense which is different to their more precise definition in chemistry. For thepurposes of this review, a broad categorisation is made under the termsadsorption and aggregation. Adsorption is used here to mean an interactionbetween solute and membrane. For protein solutions its effect upon fluxreaches a plateau at interface concentrations of below 1 gjl thus itsoccurrence could be considered as inevitable merely by bringing the feedstream into contact with the membrane. The term aggregation is used torepresent a variety of solute/solute interactions which are given such labelsas gelation, polymerisation, flocculation, adhesion or coagulation. Theseverity of these cake-forming mechanisms is dependent upon the localsolute concentration and thus upon the degree of polarization.

An experiment performed by Lopez-Leiva and Matthiasson (1981) willserve to demonstrate the distinction between adsorption, aggregation andpolarisation. A rotary filtration module was used in which the fluid shearstress was supplied by the rotation of a cylindrical membrane inside astationary housing providing Couette flow and thus avoiding the linkagebetween cross-flow rate and pressure-driving force. The results for BSAultrafiltration are shown in Fig. 6.1.

Upon commencement of the run adsorption effects were held to causean immediate flux decline of some 20% from the pure water flux (PWF).The centrifugal force was sufficient to prevent any build-up of a polarised

500 1000 1500 2000 2500 3000 3500 4000 4500Membrane rotation rpm.

+------.,.,..L~:L_--+------------~~

-------------------------------

+---------------- -------

100

90

.c~ 80 --><~ 70•1;• 60 f---E!. 50 1-------;

40

300

Fig. 6.1. Permeate flux as a function of membrane rotational velocity (adapted fromLopez-Leiva & Matthiasson, 1981).

Fouling Phenomena 205

concentration boundary layer until the membrane rotational speed fellbelow 2400 rpm. The subsequent flux decline ascribed to polarisation wascompletely reversible at about 1000 rpm where some hysteresis wasobserved upon increasing the shear stress again. This irreversible loss of fluxwas attributed to mechanisms described in this review as aggregation.

6.1.2 Interactions with the Environment

Adsorption and aggregation mechanisms arise from physical forces actingbetween solute molecules and with the membrane. If surfaces are broughttogether the sum of these forces determines whether an attachment is formed,be it a protein molecule adsorbing to a membrane, cells adhering to each otheror the precipitation of colloidal salts. Chemical bonding also occurs in specificcases, for example in aggregation between protein molecules, but not usuallywith adsorption of molecules to the relatively inert modern membranes.

6.1.2.1 Interfacial forces

6.1.2.1.1 ELECTROSTATIC FORCES

Most substances acquire a surface electric charge when brought into contactwith a polar medium originating from the ionisation of polar groups or bythe adsorption of ions. Most particles are negatively charged because anionsare preferentially adsorbed. The acquisition of a surface charge affects thedistribution of ions in solution such that a layer of counter ions closelysurrounds the surface with a diffuse layer of co-ions further out whichtogether constitute the electrical double layer. When two charged speciesapproach each other the double layers interact usually resulting in repulsion,most surfaces being negatively charged.

6.1.2.1.2 VAN DER WAALS FORCES

Molecules in close proximity induce charge polarization in each other due toelectromagnetic fluctuations. These potentially strong attractive forces canonly take effect when the surfaces are in close proximity. The superimposingof the above two forces in determining the strength of an interaction istermed DLVO theory after its original proponents.

6.1.2.1.3 SOLVATION FORCES

Water molecules form hydrogen bonds with hydrophilic surfaces and thusthe disruption of this ordered structure by the approach of another surface isenergetically unfavourable. The dehydration of hydrophobic surfaces, however, represents a gain in entropy giving rise to strongly attractive hydrophobic interactions.


6.1.2.1.4 STERIC FORCES

Polymeric material attached to the surfaces of particles can interactsterically at greater distances than can some of the above forces thusoverriding them. In some cases stability against adhesion is promoted dueto the unfavourable free energy associated with the overlapping of polymer segments through an osmotic-type mechanism whilst in others precipitation of the polymers may lead to an adhesive bridging effect.

6.1.2.2 Effect of pH and Ionic StrengthThe tertiary structure and stability of macromolecules and colloidal salts isinfluenced by the pH and ionic strength of the surrounding solutionthrough the interaction of the above forces. How the four main aspectswhich collectively determine the nature of protein fouling are modified bythe solution environment as summarised below. These principles form thebasis of many of the pretreatment techniques used to reduce fouling whichare discussed in more detail in Chapter 7.

6.1.2.2.1 MOLECULAR SIZE

Proteins are at their most compact at their isoelectric point, pI, due to aminimum of intramolecular electrostatic repulsions. Thus flux is lower atthis pH, for a given amount of deposition, due to low cake permeabilityand increased chance of pore blockage by the smaller particles. Lowerconcentrations of ions counteract this through allowing increased doublelayers and hence increased effective particle size.

6.1.2.2.2 INTER-MOLECULAR AFFINITY

Interparticle repulsion due to double-layer interactions is at a minimum atthe pI again leading to a lower cake permeability whilst away from the pI,repulsion is counteracted at high ionic strength again through chargeshielding. A moderate ionic concentration favours the dispersion ofproteins by increasing their solubility (salting-in) whilst at high protein orionic concentrations, salting-out can lead to an increase in flux becauseaggregated proteins form a more porous cake and are less likely to blockpores. It should be noted that certain salts will form complexes withprotein molecules leading to precipitation and loss of diffusivity.

6.1.2.2.3 MOLECULAR AFFINITY FOR THE MEMBRANE

As the pH falls below the pI, proteins become positively charged and thus anincrease in deposition is usually observ~d with hydrophilic membraneswhich are mostly negatively charged. This effect is noted primarily in lowfouling systems where the fouling layer consists mainly of a monolayer. Inmicroporous membranes, rejection will be high away from the pI as either


like-charged protein-membrane combinations will deter solute from entering the pores or oppositely charged ones will lead to internal deposition thusreducing the effective pore size. Low rejection by the pores at the pI may becounteracted by increased rejection due to greater surface deposition.

Hydrophobic protein residues can form strong attachments to hydrophobic membranes thus the latter are normally modified chemically by themembrane manufacturer or treated by the user to make them hydrophilic.Zeman (1983) observed increasing resistance of a hydrophobic membraneas the hydrophobicity of the membrane permeable solute increased.

6.1.2.2.4 MOLECULAR SHAPE AND INTEGRITY

Macromolecules alter in flexibility with pH as protons or hydroxyl ionsshield charged groups. This alters their susceptibility to pore blocking,particularly for linear polymers as shown by Choe et al. (1986b). Where thepresence of salts induces aggregation then rigid molecules will tend to formcrystalline precipitates whilst those which are flexible can intermingleforming an amorphous coagulum (Fig. 6.2).

@

1~~

~~

Prec ipitation

/~

_pH

Fig. 6.2. Conformational changes in a linear polymer with varying cation concentration(Choe et aI., 1986).

As proteins become denatured at extremes of pH or temperature orshear they expose internal hydrophobic and hydrophilic groups whichinteract with each other and the membrane.

6.1.3 Adsorption

Proteins in general have a high affinity for solid interfaces. This stemsfrom their relatively large size making multiple binding possible and the


heterogeneity of the amino acid residues comprising the protein allow it toform a wide variety of interfacial bonds: hydrophobic, van der Waals andpolar interactions. Desorption is unlikely as this would have to occur simultaneously at all adsorption sites although some exchange may take place.

With non-globular proteins like gelatin and with other flexible polymerssuch as the polysaccharides, dextran and pectin, the conformation of anadsorbed molecule is as pictured in Fig. 6.3 with many protruding trainsavailable for hydrophobic interactions or for the blockage of pores.Globular proteins such as enzymes are thought to retain their compactstructure upon adsorption, but some loss of activity has been found.

Fig. 6.3. Conformation of an adsorbed linear polymer molecule (Matthiasson, 1983).

Adsorption from only 0·01 g/I BSA solutions can result in a 25% loss offlux whilst accumulating only 0'2-10 mg/m 2 of protein. This correspondsto a full monolayer of protein on the surfaces. At concentrations above1 gil, Brash (1985) found that no more protein was deposited with celluloseacetate membranes whilst a spectrum of deposition levels was observedwith the more hydrophobic polysulphone and polyamide membranes.

6.1.3.1 Pore BlockageThe primary influence exerted by adsorbed macromolecules is by thosesituated in the vicinity of the membrane pores whereby the whole or partof the molecule can obstruct the passage of solvent and membranepermeable solute. The various permutations of pore blocking are afunction of the molecular size and shape in relation to the membrane poresize and space distribution:

complete pore blocking: the pore entrance is sealed;pore bridging: partial obstruction of the entrance;internal pore blinding: material not rejected by the pore entrance isadsorbed or trapped on the pore wall or the membrane support


The occurrence of pore blocking is usually assumed to be irreversibledue to the irreversibility of adsorption. Le and Howell (1984) proposed adynamic process whereby the loops and trains of a molecule which are notadsorbed are able to reversibly block the pores in a cyclic fashion. Thisconcept has been supported by Weldring and van't Riet (1988) whomeasured the hydraulic resistance of adsorbed methyl cellulose after theremoval of the polarisation layer. They observed a limiting flux withincreasing transmembrane pressure which they attributed to increasedpore blockage as the ratio of normal convection (permeate flux) to lateralconvection (cross-flow) increased. This phenomenon was reversible up to acritical pressure which was a function of shear, above which hysteresis wasobserved and the pore blockage became irreversible.

Le and Howell (1984) proposed a pore bridging model to explain thelack of a truly pressure-independent flux with colloidal suspensions. Onthe basis of the assumption that at least in some regions a monolayer ofparticles adjacent to the membrane does not fully block every pore andthose that are unblocked at anyone time will pass the full, pressuredependent solvent flux. Devereux and Hoare (1986a), working with precipitated soya protein, used a similar argument to explain how theobserved flux was linearly pressure dependent over the range of conditionsused, yet it varied inversely with mean particle size. Although the CarmanKozeny equation suggests that a cake of precipitated protein particles inthe size range of 5-9 ~m would be too porous to create an hydraulicresistance of the magnitude observed, deformation of the particles orpartial blinding of some pores together with bridging of the rest couldaccount for low permeabilities. For a coherent monolayer, the number ofpores obstructed decreases with increasing particle diameter because thedistance between adjacent particles increases. Degree of rejection ofsoluble protein present in the feed stream was also found to correlate withthe aCtive membrane resistance.

Fane et ai. (1981) indicated that the distribution of pore sizes has considerable influence on the extent of pore blocking. Assuming the applicability of the Hagen-Poiseuille equation, eqn (6.1), for flow through capillaries,they demonstrated that the majority of solvent flux in a clean membranepasses through a small proportion of pores (Figs 6.4a,b). These large poresare particularly vulnerable to blocking because the high local flux will lead toa correspondingly high solute concentration due to polarisation (assumingthat they are still small enough to reject solute molecules). This blockage,partial or complete, will lead to a dramatic decrease in flux and an increase inrejection. Used-but-clean membranes were found to have a higher rejectionfor protein than virgin membranes, indicating that some pore blockages donot respond to cleaning with O'IM NaOH.

35301510 20 25Pore diameter (nm)

Fig. 6.4a. Distribution of pore size and solvent flow for typical UF membranes.


100 100

90 90

80 80

c: 70 70 I• 8.=J

60 60 .c:ell

50 / 50:::I

I / e40 / 40 =8. / !/

~ 30 / 30/ ~

20 XM100A /.- XM300

20/

10 / 10/

"

30 30/

/

.a 25 25

~ ,/,/

!I 20 ,/ 206:,/ E'S ,/ :;.

I/

//1 >C15 15 i

c: /'

10 ]I /'

10..,

.., ..,• ...- ..,'0Q. 5 5

012 14 16 18 20 22 24 26 28 30 3lPore diameter (nm)

Fig.6.4b. Polarisation modulus and local flux versus pore diameter (Fane & Fell, 1987).

Le and Howell (1984) showed that under unstirred conditions whererejecting pores remained permanently blocked, pores which are too largeto be blocked become responsible for all permeation and the soluterejection eventually falls to zero. Reinhanian et al. (1983) observed adecrease in rejection with increasing transmembrane pressure for unstirredBSA ultrafiltration. This phenomenon was explained in terms of a weakpore bridging of large pores which collapsed at high pressures.

Internal pore blocking is a particularly serious fouling mechanismbecause it is exempt from the mediating effects of cross-flow and even asmall amount of adsorption can lead to a considerable change in themembrane's rejection characteristics. Isotropic microporous membraneswhich function as a hybrid of membrane filter and depth filter have a considerable internal surface area available for permeable solute adsorption.


With anisotropic microporous membranes macromolecules with molecular mass greater than the cut-off have been observed to coat internal poresin the support structure.

There is some debate over the exact relationship between flux and porediameter. Ultrafiltration pores can be modelled as straight cylindricalcapillaries using the Hagen-Poiseuille equation

Nnd~r !J.PJ = 128/l/ (6.1)

where N = No. of pores per unit area/= pore length

dpr = pore diameter

/l = fluid viscosity!J.P = transmembrane pressure

J = flux

(6.2)

or in view of the open network arrangement, often seen in membranesunder microscopic examination, they can be modelled as orifices, andmicroscopic examination of the membrane shows that for some polymericmembranes the physical configuration is closer to a network of orificesthan tubular pores.

Ndpr 3 !J.PJ = 24/l

Adsorption of permeable solute to the pore walls has the effect oftightening the pore size distribution. Zeman (1983) proposed the followingrelationship between the decrease in pore radius due to adsorption, !J.r,and the resulting decrease in water flux on the basis of the HagenPoseuille equation

!J.r = 1_[l-Joo

25

r J m

where !J.r = decrease in radius

6.1.4 Aggregation

(6.3)

6.1.4.1 ProteinsThe aggregation of protein molecules to form entities of a higher molecular weight is considered to be a two-step process involving denaturationand subsequent aggregation. Denaturation is taken here in a general senseas a change in the three dimensional structure of the protein from itsnative form, excluding the rupture of peptide bonds, and could arise outof the action of adsorption, shear, temperature or extremes of pH andionic strength. This alters the balance between solute-solvent and solutesolute interactions making the protein more vulnerable to aggregation


through such forces as hydrophobic and van der Waals forces or throughdisulphide bonding.

The task of designing a strategy which minimises fouling is complicatedby the numerous physico-chemical interactions that occur in complexfeedstreams. Listed below are examples of those which occur in theaggregation of milk proteins.

Complexation. Casein micelles are stabilised by the presence of calciumthus a change in the calcium concentration can alter this structuralequilibrium leading to micellar aggregation.

Association. Dimerisation and octamerisation of f3-lactoglobulin atneutral pH causes the formation of gelatinous material which when viewedwith scanning electron microscopy gives large sheets and globules of protein which form a dense cake. Flexible linear polymers can intermingle toform an amorphous coagulum under conditions which promote aggregation.

Coagulation. Hydrogen bonding between carboxyl groups and disulphide linkages are thought to be involved with coagulation reactions. Bytreating whey with chemicals that block the formation of these bonds,particularly the disulphide ones, fouling can be reduced. Coagulationresulting from pretreatment by heat denaturation is beneficial, formingporous, non-fouling cakes involving calcium in a complex with casein andf3-lactoglobulin (Hayes et al., 1974).

6.1.4.1(a) STRUCTURE OF THE FOULING LAYER

Several studies have been made of the structure of the whole fouling layerthrough electron microscopy, chemical analysis of material deposited onthe membrane and through inference from experimental studies and theory.

The foulant layer from the reverse osmosis of milk has been observed tohave three identifiable zones: two thin layers, each some lOnm thick,adjacent to the membrane, which appeared soon after the start ofoperation, covered by a layer of 30 flm in thickness which consisted oflarge granules. This layer was uniform in packing density except for thefirst 1 flm in thickness which was compacted possibly from high initialpermeation rates.

Two layers may sometimes be seen deposited on the membrane afterdraining: a thin gel-like deposit which resists removal by fluid shear belowa viscous layer which is easily removable, both layers consisting predominantly of casein. In the clarification of secondary sewage effluent toremove inorganic suspended solids, when only the base thin layer waspresent, little flux is observed yet rejection increases with time.

The non-homogeneity of fouling layers results in a cake resistanceproportional to mass to a power less than unity. Deposited layers are


compressible. The effect of transmembrane pressure on the specific cakeresistance, iX, is quantified by an exponential dependence

(6.4)

where b values range from 0·25 for latex (Doshi & Trettin, 1981) to 0·5 foradsorbed BSA (Chudacek & Fane, 1984).

The hydraulic resistance of macromolecular aggregates is lowered bythe presence of particulates in mixed feedstreams. Doshi and Trettin (1981)found an augmentation of flux for unstirred ultrafiltration of a starchsolution by the addition of titanium dioxide particles. They contended thatthe particles interfered with the formation of a coherent gel structure. Thestarch effluent studies of Harris (1986) found that high disulphide bondcontent feeds had a greater flux despite their higher viscosity, presumablydue to the more porous cake formed.

6.1.4.2 Inorganic PrecipitatesColloidal salts can form precipitates which seriously foul reverse osmosismembranes in particular. Neutralised whey permeate forms a gelatinousprecipitate which is an hydrated complex of calcium phosphate and citrate,known as apatite. In isolation, the precipitate formed is too porous to bedeleterious except when the pH adjustment occurs during filtration, e.g.during cleaning, where the precipitation occurs within the membrane pores.

6.1.4.3 Cells and other ParticulatesObservations of the fouling of membranes by cells suggest that thedynamics of flux decline is related to the degree of cake build-up on thesurface of the membrane (Fig. 6.5).

""

1.---------------------,0.9

0.8

0.7

~ 0.6+lC 0.5

i 0.4li-_===!2::::::======:......~_~0.3

0.2

0.1

5 10 15 20 25 30 35 40 45 50BSAg/100ml

Fig. 6.5. Flux decline and cake deposition with bacteria cells (Reismeier et al., 1987).(0, Polysulphone; +, polyamide; X, cellulose acetate).


It has also been shown by Taddei and Howell (1989) that the foulingbehaviour of cells is highy dependent on the culture conditions, themake up of the medium, and their treatment subsequent to fermentation. Sometimes even simple storage changes the filtration behaviour ascells may lyse, or become non-viable and their surface properties thuschange. It is difficult to re-entrain cells from a fully adhered conditionalthough under cross-flow conditions oscillations in flux have been observed suggesting periodic shedding of the cake. Attempts to induceshedding by altering cross-flow velocity have met with mixed successbut with a hydrophilic PVDF microporous membrane almost completeflux restoration was achieved by Gatenholm et al. (1988). Kroner et al.(1984 a) found that bacterial cake deposited at high bulk concentrations was irreversibly deposited and would not disperse with increased cross-flow or suspension dilution. Other methods of cleaningcell fouled membranes have been found to be effective and are discussedin Chapter 7.

Operation over long periods without cleaning can result in progressive fouling below an apparent steady-state level. Fane et al. (1982)found that this can be due to growth of cells in the fouling layer andslime formation may occur with deleterious effects on the membrane.It is suggested that regular cleaning of membranes exposed to cellsuspensions is initiated to avoid progressive fouling by growing adheredcells.

6.2 QUANTIFICATION OF SURFACE PHENOMENA

In MF, UF and RO the interaction between the surface properties of themembranes and the properties of the molecules in solution determine theamount of fouling and the flux through the membrane. If the macromolecules in solution are big enough to be totally rejected by themembrane, only the surface properties and not the properties of the poresdetermine fouling tendency, and the properties of the pores only determinethe flow-through of solvent. If solute molecules get partly stuck in thepores, fouling of pores and the retarded movement of the solute containingsolvent in the pores, determine the final flux result.

A totally perfect membrane surface for any possible process cannot befound. Rather it could be stated that every solution to be filtered shouldneed its own 'tailor made' surface. Modifications of the membranes can bemade to achieve this.

When the interaction between the molecules in solution and themembrane surface is such that adsorption takes place, the nature of


the bonds formed between surface and solute determine if the adsorption is reversible or irreversible. When it is irreversible fouling is theresult. This study deals mostly with macromolecules, which adsorb onthe surface with many segments or not at all, as it is statisticallyimprobable that all the adsorbed segments could be released at the sametime. This interaction depends partly on the electrochemical propertiesof the membranes and the solutes, partly on their hydrophilicity and ontheir conformational changes when interacting. Also physical propertiesof the membrane, such as smoothness, porosity and pore size influencefouling.

6.2.1 Electrochemical Properties of Membranes

6.2.1.1 Theory of Membrane-Solute InteractionsThe macromolecules of interest in a discussion of membrane/soluteinteractions are almost exclusively polyelectrolytes, and in aqueous solution the membrane surface is also mostly charged. As a first approximation, it may therefore be assumed that the static long-range forcesbetween the macromolecules and the membrane can be described by theDLVO theory (Derjaguin-Landau-Verwey-Overbeek) of colloidal stability. According to this theory the electrostatic effects are governed by theinteractions between the diffuse ion atmosphere outside the chargedsurfaces. For an infinitely thick flat surface (the membrane) and a sphere(the macromolecule) the electrostatic interaction is approximately givenNorde (1981) by eqn (6.5).

where Br is the dielectric constant of the medium, eo is the permittivity ofvacuum, R is the radius of the spheric particle, H is the distance betweenparticle and surface (R~H), ¢1 and ¢z are the potentials at the boundarybetween surface or particle, respectively, and the diffuse layer of ions in thesolvent. Localised adsorption of ions may occur inside this boundary. K isthe reciprocal Debye length, which depends on the ionic strength of themedium according to

(6.6)

where e is the elementary charge, k is the Boltzmann constant, T is theabsolute temperature, Ci is the concentration of ion i and Zi its valency.


Note that this interaction may be repulsive or attractive depending on thesign of the potentials.

The contribution of van der Waals forces to the interaction energy isapproximately given by

= _ ~ [2R(H +R) -I (H +2R)JVa 6 H(H+2R) n H

(6.7)

where A is the effective Hamaker coefficient of the system. A describes thenet van der Waals interactions between the particle, surface and thesolvent. On the molecular level the interactions are usually divided intodipolar forces, hydrogen bonds and dispersion forces. Provided only thedispersion forces are of importance A may be roughly approximated fromthe Hamaker coefficients of the individual materials involved according to

(6.8)

In eqn (6.8) subscript 3 refers to the solvent. Note that although the vander Waals forces between similar molecules are always positive (AI, A l ,

A 3 > 0), eqn (6.8) predicts that their contribution in a mixed system may bevery small or even negative.

The sum of the terms Vr and Va determines if repulsion or attraction(= resulting in adsorption) takes place. In the case of attraction the sign ofthe sum is negative. At low ionic strength the electrostatic forces arestronger and in the case of repulsion the total energy is more oftenpositive. At high ionic strength the electrostatic forces are shielded and thetotal energy is mostly negative. Also in the case of electrostatic attraction ahigh ionic strength reduces the total net negative energy. The effect of thetotal energy can be tested by adsorption experiments.

The adsorption isotherms, which often correlate with flux reduction(Nystrom et ai., 1990; Aimar et ai., 1986), have different forms if the surfaceand particles have the same or different charge signs at different ionicstrengths. At low ionic strength, the state of repulsion dominates when thesurface and the particle have the same charge sign, and the adsorptioncurve rises slowly. At high ionic strength it rises very abruptly. Also in thecase of opposite charge signs differences exist between low and high ionicstrengths. In this case the ionic strength rather determines the finalamount of coverage, which is influenced by the lateral interactions of theparticles at the surface.

In the dynamic state of filtration, when the concentration of solute nearthe membrane is determined by the concentration polarisation layer,which is not the same as in the bulk, the concentration on the membranecan be estimated according to different theories (Chapter 3) but also here it


is important to include an electrostatic term, depending on the charge ofthe particles in solution which describes the state of backdiffusion of thesolutes into the solution, when charges are involved. This procedure givesbetter estimates of the flux and the true membrane concentration at least inUF of charged particles (McDonogh et al., 1989; McDonogh et al., 1984).

6.2.1.2 Methods to Measure Surface Charges of MembranesIn order to estimate the effect of repulsion or attraction, the charges of themembranes and the molecules have to be determined, and preferably asfunctions of pH. Many types of membranes contain dissociated chargedgroups, the charges of which depend on their dissociation constants andthus on the solution pH. The charge density on the membrane isdetermined by the amount of dissociable groups. As the membranes cancarry both positively and negatively charged groups, the charges of whichdepend on pH, many charged membranes show an isoelectric point (pI),where the sum of the charges (measured electrophoretically) is zero just inthe same way as, e.g. for proteins. Some membranes can also be chargedbecause they adsorb ions from solution. The charge densities of themembranes can be calculated from different measurable quantities such aszeta potentials, streaming potentials, and titrated charged groups.

Zeta potentials (::::; c/> 1 in eqn (6.5)) of MF alumina membranes have beenmeasured electrophoretically after grinding the membrane material(Shimizu et al., 1989). The pI of the membrane was determined to bebetween 5·5 and 6·0. At pH 2-5 the membranes had a zeta potential ofabout +20 mV and from 7 to 11 about - 40 mV. This electrophoreticalgrinding method is applicable if the membrane material is homogeneousas the alumina membrane, but it is not applicable to an asymmetricmembrane from which the surface layer cannot be removed selectively.

Streaming potentials (~Es) of membranes can be measured and used toapproximate the zeta potential or the surface charge density of themembrane. Mostly the streaming potential is measured over the pores ofthe membrane. If only the surface of the membrane is modified to someextent or fouled, the streaming potential of the modified surface onlycomposes a very small part of the pore and thus only influences the totalstreaming potential in relation to its thickness compared to the length ofthe pore. From the streaming potentials zeta potentials «() can be calculated according to the Smoluchowski equation

,= ~Es "11 (6.9)~p ereo

where ~Es is the developed streaming potential difference correspondingto the applied pressure difference ~p over the membrane. 11 is the viscosity


and K the conductivity of the solution. The equation does well toapproximate the zeta potentials for MF membranes, but not for UFmembranes, where the pores are too small to have a free passage withoutoverlapping double-layers. This is a fact even for larger pores especially atlow ionic strength, as the double-layer thickness can reach values close to100 nm, and eqn (6.9) assumes laminar flow past a non-conducting flatsurface.

Streaming potentials have been measured, e.g. for

- polysulphone and sulphonated polysulphone UF membranes (Nys-trom et aI., 1989);

- membranes fouled with ovalbumin at different pH (Nystrom, 1989);- modified membranes (Nystrom et aI., 1989);- differently treated and charged poly(acrylo nitrile) (PAN) mem-

branes (Congjie et aI., 1987).- polycarbonate microfiltration membranes (Martinez et aI., 1989).

The measurements have been made with various electrolytes at differentconcentrations. Figure 6.6 shows results of zeta potentials calculated fromstreaming potentials for some types of membranes and the dependence ofthe zeta potential on pH.

From Fig. 6.6 it can be seen, that the Smoluchowski equation approximates the zeta potentials better for MF than for UF membranes, as seenfrom the too small values for the UF membranes (Nystrom et al., 1989).This can be understood knowing that the pK of the acidic groups in thepolycarbonate membrane is 192, which means that it should have a zetapotential less negative than the sulphonated polysulphone membrane,which is more strongly acidic.

The zeta potentials of MF membranes have been determined by Bowenet al. (1988) and Bowen and Clark (1984) using an electro-osmotic method.This method can be applied both to clean membranes and to membranescovered with deposited layers. Also by this method the zeta potentials canbe determined as functions of pH. The potential determined by electroosmosis is also that of the pores of the membrane as with the streamingpotential method. The electro-osmotic method is actually an inversemethod to the streaming potential method. In the first an electric current isapplied and the induced electro-osmotic flow of electrolyte is measuredand in the second one a pressure difference is applied and the generatedpotential difference is measured.

The charge densities of microfiltration membranes can be determined bypotentiometric titrations (Bowen et al., 1988). The pH meter has to be veryaccurate as the surface of the membrane contains only small amounts oftitratable groups. Figure 6.7 shows results from titration of a 0·21lm


rmV 3 4 5 6 7

pH

-5-.-,., ..

+ " -'-,+,.- + + + + +,-1--·--, ! _+ +

-10

GR 61 A-A

FS61 .---.GS61 +-...

-15

-3 f-20

>E Polycorbonote'-" Ns = 1.2 (1016) m-2

-10 pKs =3_92

[K ell = 10-3 N

02 3 4 5 6 7 8 9 10 II

pH

Fig. 6.6. Zeta potentials calculated from the equation of Smoluchowski from streaming potentials for polysulphone (GR), hydrophilized poly(vinyliden fluoride) (FS)and sulphonated polysulphone (GS) UF membranes with the same cut-off (Nystromet al., 1989) and a polycarbonate Nuclepore MF membrane (Keesom et al., 1988)

as functions of pH.

Anotec alumina membrane. In order to get a stronger signal manymembranes were applied in a stack (Bowen et al., 1988). A titrationmethod is a good and more sensitive method to changes in pH than, e.g.the electrophoretic method. The potentiometric titration gives the totalcharge of the membrane and the point of zero charge (pzc), while the zetapotential gives the pI of the membrane. Only in the absence of specificadsorption pI = pzc.

220

100'".5

u 80::1-::;:.,0\'- 60'".cu."

.2! 40'".t:i=

20

J. A. Howell & M. Nystrom

ol-_..L-_-L_-..l._--'l-----=~_..:...._ ___J

3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0

pH

Fig. 6.7. Net titrated charge in the pH range 1~3 for a 0'2-~m Anotec membrane. 0·01 M

NaCI (Bowen et aI., 1988).

From measured membrane and diffusion potentials charge densities ofMF membranes like polycarbonate nuclepore membranes can be calculated and studied as functions of the ionic strength (Hernandez et aI.,1985). The obtained values correlate with values obtained by Meares &Page (1972) from electro-osmotic measurements. This means that themethods are comparable.

It has to be understood, that in many cases, different methods do notgive the same values for the charge densities, but relative values can oftenbe obtained using the same method for different membranes. The discrepancy arises as the different methods measure different types of potentials.For example the zeta potential is measured at the edge of the non-movingion layer and it includes specific adsorption, which depends on themembrane surface and the molecules in solution. Titration results, on theother hand, emanate from charge properties at the actual surface of themembrane.

6.2.1.3 Influence of Charge on FoulingThe importance of the effect of electrostatic interaction between membrane and solutes in different kinds of membrane processes has beenrealised and the phenomenon has been utilised in some membraneapplications. It has been shown that negatively charged electrophoreticpaints are easier to remove by UF than positively charged paints withnegatively charged membranes. The positively charged paints adsorb onthe membrane due to electrostatic attractive forces and therefore thepermeate flux decreases with time. Consequently, e.g. non-ionic poly(vinylidene fluoride) (PVDF) membranes can be treated with positively


charged polyelectrolyte poly(ethylene imine) (PEl) and as found by Mir(1983) the flux remains good for long times with the positively charged paints.

An increase in flux and retention can be attained when electrostaticrepulsion is achieved with polyelectrolytes. Nystrom and Lindstrom (1988)showed this from the UF of chlorolignin, which is a polyelectrolyticdegradation product from lignin extracted from the alkaline bleachingstage of pulp. A high pH stabilises both the charge of the membrane andthe solute. The chlorolignin is negatively charged and completely dissociated at pH 10. Also the membrane is negatively charged, which results in agood flux, good retention and very little adsorption and fouling. As shownin Fig. 6.8 the opposite is true at low pH values, where electrostaticrepulsion is not effective.

u.

:lil-~ux reduction

:lil-~:lil-__ u ....•

R

....

"'7

1.'

pH

*-.......... Ad.orptlon

~*I-----*-• 7 • ----".--~ 05

*

"'-.",.".'t.....•• Zeta potential~. I..~ .. ......-

FR0.'

0.•

*U ./0.2 *8.1

3 •0r

mY -1

-2

-3

-.Fig.6.8. Factors influencing the result in ultrafiltration of chlorolignin with a polysulphonemembrane (GR 61) as functions of pH. Flux reduction (FR) and retention (R) measured atp= 5 bar and CCL=O·3 wt% and v=2·5 m/s. Adsorption (Ads.) measured in arbitrary unitsfrom oscillation frequency change of a quartz crystal at adsorption from a 1000 ppm aqueouschlorolignin solution. The degree of dissociation (a) of chlorolignin measured frompotentiometric titration experiments. Zeta potential of the polysulphone membrane cal-

culated from streaming potential measurements (Nystrom & Lindstrom, 1988).


Very small ions can be retained with tight UF membranes if electrostaticrepulsion is established. Eriksson (1988) called this technique nanofiltrationin order to point out that particles in the nanometer class are retained. Themembranes are also called loose reverse osmosis membranes. Smallunivalent ions like chloride ions pass through the membranes but multivalentions do not, if they carry the same charge as the membrane. Thus,for example Kimura and Tamano (1984) found that negatively chargedsulphonated polysulphone membranes with a cut-off value of 10000 retaindifferent amino acids with molar masses smaller than 100 g/mol at pHvalues, when they are negatively charged.

Much interest has been paid to the adsorption and ultrafiltrationproperties of proteins, especially to bovine serum albumin (BSA), usingdifferent kinds of membranes. Adsorption has been measured, e.g. byMatthiasson (1983) using 14C-marked BSA or by Aimar et al. (1986) witha 125I-labelled BSA, by Fane et al. (1983) quantifying the removedadsorbed BSA by the modified Lowry method and by Nystrom et al.(1991) by microweighing on a quartz crystal. BSA has also been ultrafiltered at different pH values and at different concentrations of salt andresults from adsorption and UF have been compared. Most experimentsshow that adsorption is at its highest and flux at its lowest at the pI of theprotein, where its net charge is zero. At pH values above the pI the proteinis negatively charged and with negatively charged membranes the proteinadsorption is small and the flux is good. However, the optimal conditionsare actually reached when pH is really high and the protein does notcontain any positively charged groups. When the pH value is nearer the pIof the protein, and the protein, although carrying a net negative chargealso contains positively charged groups, adsorption can take place andincrease fouling whatsoever the charge of the membrane. This is veryprobably due to the heterogeneous nature of the protein molecule, so thatalthough there is a net negative charge, positively charged domains of theprotein may be preferentially oriented and adsorbed to the membrane.Below the pI of the protein its net charge is positive and in combinationwith a positively charged membrane, flux is enhanced. Figure 6.9 showsresults by Wahlgren et al. (1990) from flux reduction caused by theadsorption of BSA at different pH values on some differently chargedmembranes treated with dextrans.

When salt is added the electrostatic effects are shielded, as predicted byeqn (6.5) and the result is more adsorption and fouling accompanied by aflux decrease. Some results (Hiemenz, 1977) can also be contradictory tothis shielding theory. Perhaps in these cases the shielding effect is counterbalanced by the effect that the protein prefers to be in a solution of highbut not too high ionic strength. Lee and Ruckenstein (1988) found that the

Fouling Phenomena

80

50

40

~ 30

Ita: 20

10

O2 3 4 5 6 7 8

pH

223

Fig. 6.9. Relative reduction of pure water flux (RFR) due to static adsorption of 2 wt%BSA solution as function of pH for neutral Dextran (0), positively charged DEAE Dextran(0), and negatively charged Dextran (.) modified polysulphone membranes (GR 61) and for

the unmodified GR 61 membrane (e) according to Matthiasson (1983).

salt increases adsorption almost linearly up to about 0'15M on a flatsurface and after that the increase levels off.

The effect of enhanced electrostatic repulsion can be used for theseparation of proteins with different pI as has been shown by Nakao et ai.(1988) for myoglobin and cytochrome C. Polysulphone was modified bysulphonation to have negative charge on the membrane. Also positivelycharged membranes were prepared to contain quaternary ammoniumgroups. The membranes were cast from the modified polysulphones sothat the pores became very much larger than the proteins to be separated.In the separation of myoglobin from cytochrome C negatively chargedmembranes were used at pH 9·2 near the pI of cytochrome C. Myoglobin(pI = 7'09) was rejected due to electrostatic repulsion and cytochrome Cpassed through the membrane pores. The reverse (cytochrome C wasrejected and myoglobin passed through the pores) was observed at pH 5·5with the positively charged membranes, as this pH was nearer the pI ofmyoglobin than cytochrome C.

As can be seen from the examples above the positive effect of electrostatic repulsion can often be observed to influence the filtration results.Non-protein polyelectrolytes mostly act according to the theory of electrostatic repulsion (Masse et ai., 1988), but it also applies to proteins tosome extent, when their conformational changes are not too complicated.

6.2.2 Hydrophilicity or Hydrophobicity of Membranes

As noted in Chapter 2 the hydrophilicity of the membrane seems to beimportant in filtration of water solutions, as a more hydrophilic membranecauses decreased adsorption and less fouling. Macromolecules, like proteins, which contain hydrophobic parts adsorb easily on hydrophobic


membranes. The adsorption layer is also more difficult to wash away froma hydrophobic surface than from a hydrophilic one. The adsorbed layer ona hydrophobic membrane surface mostly also has a higher resistance thanon a hydrophilic surface, which can be noticed as a decrease in flux.

When proteins adsorb on hydrophobic surfaces they usually have amore compact form than when they adsorb on hydrophilic surfaces, whichmakes the adsorption layer denser and less permeable to the solvent. Beingcompact molecules, the proteins also block the pores more easily. Theprocesses involved in adsorption on surfaces of varying hydrophilicity isfar from clear. Lundstrom (1983) has stated that in water solutionsadsorption involves the removal of water from the surface if strong bondsare to be formed between the surface and the solute. The molecules alsotend to change their conformation, turning their hydrophobic patchesagainst the surface, when adsorbing on a hydrophobic surface. Oftenadsorption is entropically driven (Norde, 1981), which means that theadsorbed molecules get a more favourable conformation after adsorption.When the sorbent has a large dielectric constant there has to be aredistribution of charge in the molecules at adsorption.

6.2.2.1 Methods to Measure Hydrophilicity and Wettability of MembranesThe hydrophilicity or wettability of a membrane can be determined withdifferent methods. One method is to determine the contact angle (0)between the membrane (S) and e.g. water (L). The angle according to eqn(6.10) depends on the interfacial tensions (y) of the interfaces involved (Fig.6.10). V= vapour phase.

YSV=YSL +YLv cos 0 (6.10)

The thermodynamic contact angle in eqn (6.10) often differs from theobserved contact angle as the surface is seldom an extremely well-defined,

Se..ne drop C.ptl". bubble Wilhelmy m.

S SV

d' L CY V

•S

'YSl 'YSV L

Fig. 6.10. Sessile, drop, captive bubble and Wilhelmy method for contact angle determination.


homogeneous surface. The discrepancy can arise from chemical heterogeneity of the surface, surface roughness or porosity and swelling ofthe surface with the wetting liquid. All effects may give rise to contactangle hysteresis and sometimes to slow attainment of equilibrium. Dealingwith membranes all these matters probably influence the results. When 0 issmall (the liquid phase = water), the surface is more hydrophilic and ismore easily wetted by water. The greatest difficulty when measuringcontact angles of membranes is the roughness of the surface and theporosity. Nystrom et al. (1992) have found that the contact angle for aporous membrane is often smaller than for a non-porous surface of thesame material. Whether it correlates with porosity or pore size still has tobe determined.

Contact angles can be determined by, e.g. the sessile drop, the captivebubble or the Wilhelmy method (Fig. 6.10). Further information can befound in Chapter 2, in Zhang (1989) and Nystrom et al. (1992). Theaccuracy of the measured values is very low for all three methods onporous surfaces. In order to be able to study hysteresis effects in contactangle measurements both advancing and receding contact angles aredetermined. The advancing angle is the one that develops when liquid isadded to the drop on the plane in the sessile drop method. The recedingangle is developed when liquid is withdrawn from the drop. With membranes the hysteresis effect is very large. Often there is a difference of30-40° between the advancing (Oa) and receding (Or) angles. The advancingangle seems to be the more reliable when comparing different materials.

The difference between the advancing and receding contact angles ispartly due to the heterogeneity of the surface, partly to the roughness andthe pores of the membranes. The larger advancing angles measure thehydrophobic parts of the surface and the smaller receding contact anglesthe hydrophilic parts. Thus changes in hydrophobicity can be observed aschanges in the advancing angles and vice versa. Some data on contactangle measurements are given in Table 6.1 both for membranes and somemembrane materials.

A method to measure hydrophobicities of membranes, the stickingbubble technique, has recently been developed by Keurentjes et al. (1989).In this method the contact angle is assumed not to be influenced by thepresence of pores. The membrane is submerged in liquids of differentsurface tensions. Air bubbles are attached to the membrane, and thereference surface tension for the membrane is the one at which the airbubble detaches from the membrane with 50% probability. The lower thisreference surface tension value the more hydrophobic is the membrane.

A measure of the attractive term Va of the membrane in interaction withthe testing substance can be made by calculating the Hamaker constant for

Table 6.1Contact Angles in Degrees for Membranes and MembraneMaterials as Reported by A: Zhang (1989); B: Nystrom et al.

(1992) and C: Jonsson et al. (1989)

Membrane ( A) 8. 8,

Polysulphone, GR 90 70 40Polysulphone, GR 61 72 42Sulphonated polysulphone, GS 61 54 16Cellulose acetate, DDS 600 60 47Polyacrylonitrile, Daicel DUY M 53 34Polyolefine, NTU 3150 83 54Polysulphone, GR 81 (Wilhelmy) (B) 77 20Polysulphone, GR 61 (Wilhelmy) (B) 68 12

Membrane material (A)

Polyolefine 83 54Cellulose acetate 60 47Polyacrylonitrile 53 34Polysulphone (GR, Wilhelmy) (B) 90 68

Membrane material (C) Equilibrium contact angle, 8

Poly(ethylene) (PE) 87Poly(methyl methacrylate) (PMMA) 62Poly(vinyl chloride) (PVC) 60Polyamide 6,6 (PA) 32Polycarbonate (PC) 88Poly(vinylidene fluoride) (PVDF) 90

this interaction according to eqn (6.8) (Lee & Ruckenstein, 1988). Anincreasing value for the Hamaker constant correlates with increasedattraction. This can be interpreted to mean that the attractive term Va (eqn6.7) actually describes all but electrostatic interaction. The Hamakerconstant for every phase is proportional to the dispersive part of its surfacetension (Hiemenz, 1977), and it can therefore be calculated from contactangle measurements.

6.2.2.2 Influence of Hydrophilicity on Fouling as Calculated fromAdsorption, Flux and RetentionFrom the work of Fane and Kim (1988) there seems to be a correlationbetween increase of contact angle and decrease of flux. This mostly is thecase, when (} < 90°. Many times both in adsorption experiments onnon-porous surfaces, which can serve as models for membranes, as in realfiltration experiments the hydrophobicity has not been quantified andcorrelated to the results, however.

Some experiments have been made, where the hydrophilicities ofsurfaces have been related to their adsorption tendency and/or filtration properties. In the work of Fane and Kim (1988) and Lee and

Ruckenstein (1988) contact angles have usually been the measure ofhydrophilicity.

From adsorption experiments on polymer materials with 8:::;; 90° Golander and Kiss (1988) have shown that a protein (IgG) adsorbs in differentamounts on surfaces of different hydrophilicity. As test surfaces servedpoly(vinylchloride) (PVC, most hydrophobic), a copolymer of poly(methacrylic acid) and polymethacrylate (PMA, intermediate hydrophobic) andpoly(ethylene oxide) (PEO, very hydrophilic). On PEO adsorption waspractically zero. On PMA the adsorbed protein formed a thinner layerthan on PVC, the thickness of the layer being about a monolayer with facedown for PMA and a layer with edge down for PVC.

Lee and Ruckenstein (1988) tested the adsorption of BSA at pH 7·4 onsurfaces of different hydrophilicities. The hydrophilicity of the surface wascharacterised by its contact angle against water (0° < 8 < 180°). Alsoadsorption at different pH values were tested. Poly(methyl methacrylate)(PMMA) with a contact angle about 90° (about the same as for polysulphone) seemed to give the highest adsorption even if it was classified as anintermediately hydrophobic surface. After desorption in buffer the layerthickness was some 2,5-3,0 monolayers. For the more hydrophilic surfacesonly one monolayer or 1-1'5 f.lg/cm 2 remained. The adsorption decreasedwith increasing 8 for the membranes with 8>90°, which was contradictoryto their theoretical expectations. For the more hydrophilic surfaces thecorrelation with contact angle was poor but going in the right direction,and at least adsorption was less on them. Correlation was also poor withadsorption and the values of the Hamaker constants. No correlationseems to exist between hydrophobicity increase and adsorption for BSA at8>90°. The interpretation may be that the BSA solution does not wet thesurface at very high 8 and therefore adsorption is inverse to 8.

Since hydrophilic polymers prevent adsorption, hydrophobic membranes have been grafted with hydrophilic polymers to prevent fouling inthe filtration of protein solutions (see Chapter 7). Mostly PEO has beenused giving very good results on fouling prevention and flux increase. Insome cases PEO has enhanced flux many times. In these experiments ithas also been shown by Osada et al. (1986) that PEO gives better resultsthan poly(methacrylic acid) (PMAA), which is consistent with the adsorption experiments above.

Matthiasson (1983) tested adsorption and flux reduction after adsorption of 14C-Iabelled BSA on membranes made of different materials andwith different cut-off values. The experiments were made at different pHvalues, and at varying salt and BSA concentration. Adsorption wassmaller on the more hydrophilic cellulose acetate membrane than on themore hydrophobic polysulphone membrane, and adsorption did not


depend on pore size. For the polysulphone membranes adsorption andflux reduction increased very much when the pores were large. The relativeresistance of the membranes versus the amount of BSA adsorbed showedlinearity up to monolayer thickness and then a new type of linearity tookplace. The conclusion of this would be that the first layer is more firmlyadsorbed on the hydrophobic polysulphone surface and that it has adifferent conformation than the second and the following ones.

In the ultrafiltration of /3-lactoglobulin, Hanemaaijer et al. (1989) haveshown that there is no flux decrease or fouling when UF is performed witha very hydrophilic membrane (regenerated cellulose) assuming the poresize of the membrane is smaller than the protein molecule. When ahydrophobic polysulphone membrane is used at the same conditions, fouling and flux decrease result. This can be seen in Fig. 6.11, where foulingcan be observed as an increase in retention after protein adsorption.

retention (-.1

70 CLEAN MEMBRANES

RC· regenerated cellulose60 PSp. polysulfone RC5

50

40

30

20~.!Sp6

10 ~P8p:0--~RC3O

MEM BRANES afteradsorption of13-lactoglobu lin(at pH 5)

RC~

PSp6PSp20

1 2 3saccharide hydrodynamic diameter (nm)

Fig. 6.11. The effect of protein adsorption in the retention of oligosaccharides by severalhydrophobic polysulphone (PSP) and hydrophilic regenerated cellulose (RC) UF mem

branes (Hanemaaijer, et al., 1989).

The fouling induced by hydrophobic membranes seems to be a problemmostly with proteins, as they contain hydrophobic domains. The proteinsalso take new conformations when adsorbing and Sakurai et al. (1980)have found that they differ from a.hydrophobic to a hydrophilic surface.As protein solutions also mostly contain electrolyte, which seems topromote their hydrophobic properties due to the screening of electrostaticeffects, hydrophobic interactions are enhanced (Lesins and Ruckenstein,1989). The hydrophobic attraction force seems to be stronger and acts onlonger distances than expected, on the basis of the DVLO theory as has


been shown by Claesson et al. (1989) with the newly developed surfaceforce apparatus. This new method to measure interaction can also registerhow protein conformation and charges change during adsorption andafter adsorption. These results can probably also, in the future, becorrelated to filtration results and fouling.

6.2.3 Steric Effects

Iwata and Matsuda (1988) have shown that if the membrane materialcontains protruding mobile groups, either naturally or applied by grafting,these groups can form a steric hindrance over the surface and the pores.When the solvent conditions are favourable for the groups to entangle intosolution the hindrance is effective, which means that only solvent molecules pass the pores but macromolecules are retained. If solvent conditions change to a poor solvent the grafts take a more compact conformation, which allows the pores to be free for passage of the macromoleculesresulting in a possible blocking and fouling. If the grafts are ionic in naturethey can also repel each other and in this way open the pores, whichmakes it possible for small or uncharged molecules to pass. But moleculescarrying the same charge as the graft are naturally retained. (This isdiscussed further in Chapter 7, Part 2).

6.2.4 Porosity, Pore Size and Surface Roughness

Apart from the more chemical properties of the membrane, the physicalstructure also plays an important role in the fouling of membranes. Thesize of the pores compared to the size of the molecules to be retained canbe crucial. As most membranes do not have homogeneous pore sizes (see,for example, Nilsson (1989», there are almost always pores that are largerthan the molecules to be filtered, and thus the molecules can enter thepores, get stuck and block the flow of solvent. As most molecules are notrigid spheres they can also enter and pass or block pores with a smallerdiameter than their own. Some of the molecules blocking the pores can ofcourse get loose with time.

6.2.4.1 Measurement MethodsThe pore size of a membrane is actually not an absolute units measurable quantity as the membrane material is not rigid. Also the conformational state of the membrane polymer depends on the solutionconditions, and consequently so does the size of the pores. For instance,if the membrane material adsorbs solvent the pore can decrease due tothe swelling of the polymer material. On the other hand, the pores can


be enlarged if the solvent (e.g. at suitable pH) causes internal repulsion between the lingering molecular chains attached to the porewalls.

Because of these effects it can be expected that different measurementmethods of pore size give different results depending on the nature of theexperimental conditions. Therefore the results from methods not made insimilar conditions as the filtrations are rather unreliable as they do notmeasure the true conditions.

With electron microscopy only larger pores can be seen (MF membranesand UF macropores). EM demands a dry membrane and vacuum sodeformations of the surface can be expected. With Hg-intrusion methodsvery high pressures are involved and the mercury-membrane interactions do not resemble the normal solvent-membrane interactions.Similar criticisms can be made with respect to other methods, whereeither gas or hydrophobic solvent are forced through the pores in orderto measure the pore sizes, as with different kinds of bubble-point techniquesand capillary condensation techniques. Naturally, these methods giveat least some kind of relative values. Combined bubble pressure andsolvent permeability methods seem to give the best results since themembrane is tested in the wet state and the liquids involved can beoptimally chosen.

For hydrophilic conditions values closest to the true pore sizes andpore size distributions of membranes (MF and UF) can be estimatedby measuring cut-off curves for model substances of different molarmasses. As model substances neutral dextrans and poly(ethylene glycols)have been used by a number of workers (for example, Johansen et al.(1989), Jonsson (1985), Schock et al. (1989) and Nobrega et al. (1989)).The advantage of this method is that as the pores are not circularcapillaries, and most molecules are not rigid spheres, deformable hydrophilic molecules as the dextrans and the poly(ethylene glycols) resemblemany of the solute molecules to be filtered. This method is not perfecteither as most molecules differ from each other in terms of rigidity anddeformability.

Surface roughness can be measured with photogrammetry, which is ameasurement of the surface topography from stereo-micrographs. Faneand Kim (1988) have found that this method yields information about theroughness on the nano scale. Some information can also be obtained fromgood scanning electron microscopy pictures.

Surface roughness can also, in principle, be measured from contact anglehysteresis, but as the measurement of contact angles of membranes alreadyis very complicated, it seems to be rather impossible today to get reliableresults with this method.


6.2.4.2 Influence of Pore Size on FoulingOne way to test if flux loss comes from real adsorption phenomena orfrom pore plugging is to do the filtration experiment both with positiveflux, zero flux and negative flux. This method has been used by Johansenet al. (1989). The desired flux conditions can be achieved by using anapparatus, where also the permeate side can be pressurised. At zero ornegative flux, fouling has to come from pure adsorption. For BSA with apolysulphone membrane (GR 51, cut-off 50 000) the effect of pore blockingseems to be small. Most of the fouling comes from adsorption and fromthe first contact of BSA with the membrane and is not appreciablyincreased by changing the solute concentration at the membrane solutioninterface.

Using radioactive adsorption methods Robertson & Zydney (1990)found that BSA is adsorbed both on the skin and in the matrix of the testpolyethersulphone membrane, and more in the skin than in the matrix.Protein molecules even entered pores, where the diameters were smallerthan half the diameter of the protein. In large pores the protein formeda monolayer, but in small pores the pores were plugged and flux hadto take place through the open pores. From Table 6.2 it can be seen thatflux reduction was smaller in the experiments, where the pores weresmaller than the BSA molecules. Consequently also in these experimentsit was shown that adsorption on the pore walls actually reduces fluxmost. The amounts of BSA adsorbed were independent of bulk proteinconcentration.

Table 6.2Effect of Protein (BSA) Adsorption on the Hydraulic Permeability (Lp) of the Skin and the Corresponding Reduction in Effective Pore Radius (R) for Polyethersulphone Membranes withDifferent Cut-off Values (from Robertson and Zydney (1990»

Membrane Rp,dean Lp,adsorbedlL p,c1ean Rcut-off [,4] [,4]

50000 37 0·68 ±0'14 3±2100000 50 0·54 ±O'll 7±2300000 80 0·2 ±0·3 30±20

1000000 125 0·057 ± 0'027 64±8

Analogous results to the ones above were also achieved by Hanemaaijeret al. (1989) in UF of p-Iactoglobulin at different pH values with hydrophobic polysulphone and hydrophilic regenerated cellulose membraneswith different pore sizes. With the hydrophilic membranes a reduction inpore size was noticed at the pI of the protein with a membrane having alarger pore size than the size of the protein. This most probably is caused


(6.11)

by plugging of pores as there seemed to be no reduction of pore size at allwith membranes having a smaller pore size than the size of the protein. Atall pH values studied a reduction in pore size was the case with thehydrophobic polysulphone membranes. The reduction of pore size wasmore prominent with the membranes with larger pore sizes even thoughthe resulting increase in resistance of the membrane and in retention waslarger with the membranes with small pores.

As a conclusion it can be said that it seems that if the molecules canenter the pores, due to the extremely strong tendency of the proteins toadsorb, a monolayer is formed more or less independent of the bulkconcentration. The pores are thus constricted or blocked. The pores thatremain open are those that are too small for the passage of solute or thosethat are so big that a total monolayer adsorption in the pores still leaves afree passage for permeate to be formed.

6.2.4.3 Influence of Surface Roughness on FoulingThe influence of surface roughness on flux and fouling has been investigated by Fane and Kim (1988). They showed that the flux loss increaseswith increase in surface roughness. The membranes tested by Fane andKim (1988) were of different kinds of materials. Kim et at. (1989) have alsofound that the smoothing of the surface by application of LangmuirBlodgett layers also decreased flux loss and fouling.

6.2.5 Conclusions

The properties of membranes that mostly influence fouling probablydepend to a certain degree on what process is involved (MF, UF or RO)and what types of solutions are filtered. The discussion above mostlyapplies to MF and UF membranes and water solutions. At these conditions the best membrane should be a hydrophilic membrane with a chargeof the same sign as the solute to be filtered. The porosity should be as largeas possible, and the pore sizes so small that the solutes cannot enter them.The pore size distribution should be as narrow as possible and themembrane surface as smooth as possible.

6.3 FOULING MODELS

By analogy to the standard Darcy's-Iaw filtration model, flux can beconsidered to be controlled by several resistances in series

J= ~pJ1(R m +Rbi +Rf )


where the R;'s are respectively the resistance of the membrane, boundarylayer and fouling layer.

In experimental terms, Rbi represents the increase in flux observedwhen the feed stream is replaced by pure solvent, supposedly leavingthe fouling layer intact. Whether the physical nature of Rbi is hydraulicor osmotic is not considered here. This section will focus on how Rris described in relation to concentration and operating conditions andits dynamic behaviour as a function of convection, reaction kineticsand re-entrainment. It will consider only macromolecular solutions. Ingeneral, the models proposed were not intended to be predictive orcomprehensive but rather as a quantitative vehicle for illustratingvarious aspects of observed fouling phenomena. A comparison of thesemodels has been made by Aimar et al. (1988) for cheese whey ultrafiltration.

6.3.1 Unstirred Cake Filtration Model

Reinhanian et al. (1983) described the initial stages of protein ultrafiltration under unstirred conditions as cake deposition rather than as adiffusion-polarisation process. They showed that by neglecting RbI in eqn(6.11) and by using eqn (6.12) below for Rr, a plot of tjV versus V (volumepermeated) yields a straight line whose slope is indicative of the specificcake resistance, rx. The value of rx was a function of pH and ionic strength.

VRr=rxC-

A(6.12)

where V = volume of filtrate passed.It was suggested that this procedure could be used to evaluate rx from

experimental data. Values obtained were compared to those predicted bythe Carman-Kozeny equation for packed beds of rigid particles. On thebasis that a globular protein can be approximated to a sphere, rx is givenby

(6.13)

where e= porosity or void fraction = O· 36 for random-packed spheres.Experimental and predicted values of rx for BSA all fell within the range

of 1015_10 16 mjkg. The value of rx is unfortunately highly sensitive to the(unmeasurable) value of the porosity which is used.

If one now considers the behaviour of cells in microfiltration using thesame Carman-Kozeny equation and uses a rigid sphere assumption it is


found that a cake of 1~m diameter particles should have a permeabilitysome 104-105 times greater than that of a typical bacterial cell deposit.Experimental evidence suggests that 10-~m thick cakes of red blood cellscan provide significant pressure drops (Stepner, 1985). Even in cross-flowthe cake model has been found to be reasonable as a representation offouling layer resistance. Reismeier et al. (1987) found that the dynamics offlux decline in bacterial cross-flow filtration corresponded to the build-upof deposited material (Fig. 6.12).

l00:r------------------,

1i"O---:50.----1""TOO-:----

150...---2QO-,-----l250

Time (min)

Fig. 6.12. Flux decline and cake deposition with bacterial cells (Reismeier et al., 1987).

Estimates of ex for bacterial cells have been made by Resmeier et al.(1987) using eqn (6.11) to determine the total cake resistance, combinedwith a retrospective measurement of cake mass, the latter being defined asthat material which remains adhered to the membrane on draining themodule. specific cake resistances of 1015 mjkg were obtained, compared to1012 mlkg predicted by the Carman-Kozeny equation. This suggests thatcompressibility of the cake might be very important in establishing thespecific resistance.

6.3.2 Standard Blocking Model

Furthermore pore blocking might be important. This can be investigatedby constructing a plot of tlV versus t where V is permeate volume collectedup to time t. If a straight line is obtained this is indicative of pore blocking.Such plots complement tlV versus V plots mentioned above. Some recentunpublished work with a cross-flow microfiltration module and baker'syeast suggests that one can expect pore blocking to dominate during the


period up to 10 minutes with a cake filtration model fitting the data forthe next 30 minutes. Although the first mentioned fouling mechanism isdominant for a shorter period, it can be equally important.

6.3.3 Physico-chemical Model

Aimar et al. (1986) observed analogous kinetic behaviour between thedeposition of protein and the increase in Rr (Fig. 6.13) and proposed aphysico-chemically limited fouling mechanism described by eqn (6.14). Asthe experiments were carried out under zero permeation conditions therewas no convective limitation.

400

350

300

- 250!~

=:'200Sii: 150

100

50

Rr= Rr{(I- p exp( -qcrt)}

---------\ ~~("--- +

IJ

7

6

(6.14)

00 10 20 30 40 50 60 70 80 900

Filtration time (min)

Fig. 6.13. Profile of fouling resistance with time as a function of protein concentration(Reproduced from Aimar et al. (1986) with permission from Elsevier Science Publishers.)

where Rf = long-term fouling resistance and p, q, and r = constants.The constant p was introduced to allow for the very rapid initial increase

in hydraulic resistance, possibly due to adsorption of protein to themembrane causing pore blocking. Rt was described either by a Langmuir orFreundlich type expression and was a function of bulk concentration andsolution pH. Matthiasson (1983 a) proposed a similar equation for zeropermeation deposition under unstirred conditions which included twodifferent rate constants, q, to describe behaviour up to 300 gil of BSA.

6.3.4 Re-entrainment Controlled Deposition

Suki et at. (1984) measured considerably less deposition and lower Rrvalues at increased cross-flow velocities (Fig. 6.14). They postulated that


16~----------------,

50

x10

0.1

lCo gil

16141210642 8t,h

Fig. 6.14. Deposition versus pH at different cross-flow velocities (Suki et al., 1986).

deposition ceases when the yield stress of the top-most layers of theaggregated solute is exceeded. The rate of deposition is thus governed by adeposition potential, i.e.

dmr (* )-oc mr -mrdt

(6.15)

where mt is the plateau deposition, thus

Rr = rxmt(l-e- Q') (6.16)

(6.17)

Equation (6.16) appears similar in form to eqn (6.14) but the parameter qis not as strongly dependent on C as the dependence found in eqn (6.15).However, the experimental evidence was based on measurements offouling with BSA over the range 0'1-2%. A similar model was proposedby Howell et al. (1981) for the first 10 min of ultrafiltration. Probstein et al.(1981) have shown that it is consistent with a mechanistic model whichassumes that deposition is independent of cake thicknesses, but removal islinearly dependent on such thickness. This was also evident from the dataof Suki et al., (1986) (Fig. 6.15).

The deposition rate was also dependent on pH but this was notquantified. A similar form of model was proposed by Wu et al. (1991).They showed that the flux decline during ultrafiltration of proteins wasproportional to the flux with an ageing proportionality constant. This canbe likened to a deposition rate which is proportional to flux with anadhesion rate which declines exponentially with time.

dJdt = -k1J exp(-k2 T)

where k 1 and k2 are constants.


200 10r---------~

~uCl:i

§ 100"~

",ji

&.~

o 2 4 6 8 10pH

8

2

0'=2.......-~----!:----!::o-~!,J

Fig. 6.15. Cake resistance versus pH at different cross-flow velocities and ionic strength(after Suki et al., 1986).

6.3.5 Reaction Model

Velicangil et at. (1981) modelled the accumulating fouling layer followingthe first 10 min of deposition as a second order reaction at the concentration at the membrane surface. The data for cheese whey fouling and BSAfouling gave good agreement with the model.

(6.18)

where kr is the rate constant.The process eventually reaches a pseudo-steady state as the surface

concentration declines rapidly with flux. Combining the eqns (6.11) and(6.18) with the concentration polarisation equation yields.

dt5 2 [ 2,1,P ]dt =krCb exp ( t5)

kp Rm +pg

6.3.6 Convection-Controlled Deposition

(6.19)

Kimura and Nakao (1975) proposed a similar convectively limited fluxmodel for the deposition of inorganic suspended solids in a reverseosmosis module used for effluent clarification. Deposition occurred whenthe rate of convection exceeded the rate of mass transfer. The modelincluded a correction for membrane compaction and assumed thatthe re-entrainment of the suspended solids was by a Fickian diffusion


mechanism. They noted that the experimentally determined cake resistance suggested increased cake compaction for higher initial fluxes.

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Golander, c.-A. & Kiss, E. (1988). Protein adsorption on functionalized andESCA-characterized polymer films studied by ellipsometry. J. Colloid InterfaceSci., 121, 240-253.

Hanemaaijer, J. H., Robbertsen, T., van den Boomgaard, Th. & Gunnink, J. W.(1989). Fouling of ultrafiltration membranes. The role of protein adsorptionand salt precipitation. J. Membr. Sci., 40, 199-217.

Harris, 1. L., (1986). Influence of gel layer rheology on UF flux of wheat starcheffluent. J. Membr. Sci., 29,97-109.

Hayes, J. F., Dunkerley, J. A., Muller, L. L. & Griffin, A. T. (1974). Studies onwhey processing by UFo 2 Improving permeation rates by preventing fouling.Aust. J. Dairy. Tech., 29, 132-140.

Hernandez, A., Ibanez, J. A. & Tejerina, A. F. (1985). True and adsorbed chargesin passive membranes. Surface charge density and ionic selectivity of severalmicroporous membranes. Sep. Sci. Techn., 20, 297-314.

Hiemenz, P. C. (1977). Principles ofColloid and Surface Chemistry, Marcel Dekker,Inc., New York.

Iwata, H. & Matsuda, T. (1988). Preparation and properties of novel environment-sensitive membranes prepared by graft polymerization onto a porousmembrane. J. Membr. Sci., 38, 185-199.

Johansen, P. L., Jonsson, G. & Hernandez, A. (1989). Transport and fouling properties of commercial ultrafiltration membranes, Poster no. 17, 6th InternationalSymposium on Synthetic Membranes in Science and Industry. Tiibingen 4-8 Sept.

Jonsson, G. (1985). Molecular weight cut-off curves for ultrafiltration membranesof varying pore sizes. Desalination, 53, 3-10.

Jonsson, S., Golander, C. G., Biverstedt, A., Gothe, S. & Stenius, P., Adhesion ofphotocurable acrylates to solid polymer substrates. J. Appl. Polym. Sci., 38,2037-2055.

Keesom, W. H., Zelenka, R. L. & Radke, C. J. (1988). A zeta-potential model forionic surfactant adsorption on an ionogenic hydrophobic surface. J. ColloidInterface Sci., 125, 575-585.

Keurentjes, 1. T. F., Harbrecht, 1. G., Brinkman, D., Hanemaaijer, 1. H., CohenStuart, M. A. & van't Riet, K. (1989). Hydrophobicity measurements ofmicrofiltration and ultrafiltration membranes. J. Membr. Sci., 47, 333-344.

Kim, K. 1., Fane, A. G. & Fell, C. J. D. (1989). The effect of Langmuir-Blodgettlayer pretreatment on the performance of ultrafiltration membranes. J. Membr.Sci., 43, 187-204.

Kimura, S. & Nakao, S. (1975). Fouling of cellulose acetate tubular reverseosmosis modules treating the industrial water in Tokyo. Desai., 17, 267-88.

Kimura, S. & Tamano, A. (1984) Separation of amino acids by charged ultrafiltration membranes, ed. E. Drioli & M. Nakagaki, Membr. Membr. Processes,(Proc. Eur.-Jpn. Congr. Membr. Membr. Processes), pp. 191-197.

Kujawski, W., Adamczak, P. & Narebska, A. (1989). A fully automated system forthe determination of pore size distribution in microfiltration and ultrafiltrationmembranes. Sep. Sci. Techn., 24 (7 & 8), 495-506.

Le, M. S. & Howell, J. A. (1984). Alternative model for UFo Chem. Eng. Res. Des.,62,373-80.


Lee, S. H. & Ruckenstein, E. (1988). Adsorption of proteins onto polymericsurfaces of different hydrophilicities-A case study with bovine serum albumin.J. Colloid Interface Sci., 125, 365-379.

Lesins, V. & Ruckenstein, E. (1989). Chromatographic probing of protein-sorbentinteractions. J. Colloid Interface Sci., 132, 566-577.

Lim, T. H., Dunkley, W. L., & Merson, R. L., (1971). J. Dairy Sc., 54(3), 306-11.Lopez-Leiva, M. & Matthiason, E., (1981). In Fundamentals & Applications of

Surface Phenomena Associated with Fouling & Cleaning in Food Processing, ed.Hallstrom, Lund, Tragaardh, Sweden, pp. 209-308.

Lundstrom, I. (1983). Surface physics and biological phenomena. Phys. Scr., T4,5-13.

McDonogh, R. M., Fell, C. J. D. & Fane, A. G. (1984). Surface charge andpermeability in the ultrafiltration of non-flocculating colloids. J. Membr. Sci.,21, 285-294.

McDonogh, R. M., Fane, A. G. and Fell, C. J. D. (1989). Charge effects inthe cross-flow filtration of colloids and particulates. J. Membr. Sci., 43,69-85.

Martinez, D. L., Martinez, V. F., Hernandez, G. A. & Tejerina, G. F. (1989).Streaming potential of some polycarbonate microporous membranes whenbathed by lithium chloride, sodium chloride, magnesium chloride, and calciumchloride aqueous solutions. J. Colloid Interface Sci., 132, 27-33.

Masse, P., Martinez, P., Verdier, A. & Choe, T. B. (1988). Fouling in ultrafiltrationof macromolecular solutions. The role of ionic environment. Studies in Environmental Science, 34 (Chem. Prot. Environ. 1987) 235-244.

Matthiasson, E. (1983). The role of macromolecular adsorption in fouling ofultrafiltration membranes. J. Membr. Sci., 16, 23-36.

Meares, P. & Page, K. R. (1972). Rapid force flux transitions in highly porousmembranes, Phi/os. Trans. R. Soc., 272, 1-46.

Mir, L. (1983). Positively charged ultrafiltration membranes and their manufacture for the separation of cathodic electrodeposition paint compositions, US4,849,106 (Cl. 210.490; BOID13/00), 18 July 1989, US Appl. 501,438, 06 Jun1983; 4 pp.

Munari, S., Bottino, A., Moretti, P., Capannelli, G. & Becchi, I. (1989).Permoporometric study on ultrafiltration membranes. J. Membr. Sci., 41,69-86.

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Nobrega, R., de Balmann, H., Aimar, P. & Sanchez, V. (1989). Transfer of dextranthrough ultrafiltration membranes: A study of rejection data analysed by gelpermeation chromatography. J. Membr. Sci., 45, 17-36.

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Nystrom, M. & Lindstrom, M. (1988). Optimal removal of chlorolignin byultrafiltration achieved by pH control. Desalination, 70, 145-156.

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237-58.Reismeier, B., Kroner, K. H. & Kula, M. R. (1987). J. Membr. Sci., 34, 245-66.Robertson, B. C. & Zydney, A. L. (1990). Protein adsorption in asymmetric

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Schock, G., Miquel, A. & Birkenberger, R. (1989). Characterization of ultrafiltration membranes: cut-off determination by gel permeation chromatography. J.Membr. Sci., 41, 55-67.

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the N. Y. Acad. Sci., 369, 355.Wahlgren, M. c., Sivik, B. & Nystrom, M. (1990). Dextran modifications of

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tion membranes with regard to fouling, Lie. thesis, Dept. of Food Engineering,University of Lund, Lund.

Chapter 7

FLUX ENHANCEMENT

M. NYSTROM

Department of Chemical Technology, Lappeenranta University of Technology,PB20, 43821, Lappeenranta, Finland

& J. A. HOWELL

School of Chemical Engineering, University of Bath,Claverton Down, Bath, UK. BA2 7A Y

Many different approaches have been taken to combat fouling and concentration polarisation. These involve either modifying the hydrodynamics abovethe membrane surface, the properties of the membrane surface itself or theelectrical forces acting between the solute and the membrane surface. Thischapter reviews the first two methods and shows how they are used inpractice. The first section considers the effects that hydrodynamic factorshave on the performance of membrane filtration systems.

7.1 IMPROVED HYDRODYNAMICS

7.1.1 Turbulent Flow

The hydrodynamic approach to improving the flux is either to reduce theconcentration polarisation by increasing the mass transfer away from themembrane or to reduce fouling based on increasing the wall shear rateand/or scouring the membrane surface. This is achieved most easily bysimply increasing the cross-flow rate either directly, so that the flow changesfrom laminar to turbulent, or indirectly, by modification of the channelgeometry. In all cases of interest here cross-flow is assumed. As Blatt et al.stated in 1970, owing to the extremely low diffusion coefficients ofmacromolecules and colloids in solution, the minimisation of polarisation(and realisation of high ultrafiltration rates) is far more critical for them than

243

244 M. Nystrom & J. A. Howell

for the case of microsolutes. For a given volumetric flow rate, the masstransfer coefficient can be maximised by maximising the shear rate: modulesoperating in turbulent flow achieve this by using large recirculation rateswhich involve high pressure drops and may cause damage to liquids thatare sensitive to temperature and mechanical treatment; with laminarflow modules, this can be achieved with little or no recirculation but byminimising channel depth. In each case pressure drop is increased.

Laminar flow systems can accept process streams which contain significant amounts of coarse suspended matter only if open-channel geometriesare used without obstructive turbulence promoters which can be blocked byparticles commonly produced during fermentation of micro-organisms.Some broths may be found to have larger particles originating with lowquality feed materials but such particles can be readily removed if so desiredat an earlier stage than membrane filtration. Such streams must either beprefiltered, settled or centrifuged to remove large particles prior to ultrafiltration or alternatively processed in wide conduit turbulent flow systems.

7.1.2 Turbulence/Convection Promoters

A variety of turbulence promoters are used in practice, especially in flatsheet and spirally wound systems. They have been criticised for contributing to pore blockages but so long as they are used with particle-freesolutions or fine suspensions they need not give rise to problems. Mostattention has been devoted to fixed or static turbulence promoters. Staticrods, wire spirals, plastic mesh and metal grills are examples of some of themany different types of turbulence promoters which have been tested.These alter the flow field in two ways: obstructing the flow increases theaverage flow velocity over that in an otherwise empty tube and the shearrate in the neighbourhood of the membrane wall is increased. At sufficiently high Re numbers, secondary flows and turbulent eddies may beestablished which enhance mixing at the membrane surface and thereforereduce concentration polarisation and/or fouling.

The design of commercial turbulence promoters has not been intensivelystudied until recently. Rather, materials readily available from plastic meshmanufacturers seem to have been used with little attempt to understand thedetailed principles behind their operation. More recently a study by DaCosta et ai. (1991) has reviewed the basis for use of these devices andevaluated a number ofcomparative designs. The most common designs tendto be woven and sintered open plastic mesh in a square or rhomboid meshpattern with the filaments placed obliquely to the flow. The mesh owing to itswoven pattern allows fluid to flow over it on both sides and is in sparsecontact with the membrane surfaces on either side of the channel. Usually

Flux Enhancement 245

the mesh separates two membrane surfaces maintaining a desired channelwidth, supporting the membranes and also providing turbulence promotiondue to flow over the filaments generating vortices behind them. Unfortunately, where the filaments contact the membrane surfaces there tends alsoto be a dead spot immediately downstream of the filament leading to astagnant region with a high propensity to foul.

The considerations which are taken into account in the rational design ofsuch meshes are firstly the pressure drop created in the channel by theaddition of the mesh and secondly the increased mass transfer coefficientcreated by the turbulence. Both of these quantities are a function of thecross-flow velocity and one seeks a design which provides a higher increasein mass transfer coefficients at as Iowan increase as possible in pressure drop.Da Costa et al. working with modified commercial spacers give an equationfor the mass transfer coefficient in terms of the Sherwood Number

Sh={kdh/D}

Sh = O·OO96Reo-S1 SC0 60

(7.1)

(7.2)

(7.3)

The relationship above is applicable to several but by no means all designsand is accurate to within ± 15%. The mass transfer coefficient, and hencethe flux, increase with the characteristic angle which is the angle throughwhich the flow is turned as it moves from cell to cell in the spacer. Withthese spacers there was little scale effect. It is interesting that even thoughthe flow over the spacers is turbulent, the insides in the above equationappear to be similar to those for laminar flow in an empty channel whilstfor turbulent flow a very different equation emerges. With an emptychannel there was a significant effect of scale and the above equation forthe Sherwood number had to be modified by a ratio of hydraulic channeldiameter to channel length to the 1/3rd power.

(d )0-33

Sh = 1'86Re°-43 SCO- 32 ~

The pressure drops which are the other important factor are given by arelationship for the friction factor, f.

(7.4)

For the spacers tested the value of m was close to 1·71 which is in the rangefor that for turbulent flow in an empty channel in contrast to 1 for laminarflow. The factor of proportionality varied over a factor of about 4 for thevarious spacers used.

Other approaches to creating turbulence include the use of a fluidisedbed. Van der Waal et al. (1977) describe how the irregular flow of liquid


around the particles and not the movement of the particles themselves isresponsible for the improved mass transfer. An erosive action whichremoves the gel or fouling layer may also occur due to the impulse of theparticles. However, the final selection of fluidised bed particles must be acompromise as larger and heavier particles cause a greater enhancement ofthe mass transfer but also increase the susceptibility of damage to themembrane. Some have noted that membrane damage may be reduced byappropriate start-up procedure and the nature of the fouling layer itselfwhich may provide a protective effect.

Some general conclusions concerning the use of turbulence promoterscan be drawn:

(a) the maximum increase in the rate of forced convection and thedegree of flux enhancement is dependent upon Re. This dependencyon Re is system and/or feed specific (Thomas and Watson, 1968;Copas and Middleman, 1974; Hiddink et al. 1980).

(b) optimum spacing between promoters and optimum distance fromthe transfer surface depends on the particular flow configuration(Thomas and Watson, 1968).

(c) most of the convection promoters occupy a sizeable volume fraction(typically 20-50%). This increases the frictional pressure drop byfactors as large as several hundred, resulting in reduced volumetricthroughput rates. Turbulence promoters generally produce thesame flux as empty units at a much lower cross-flow velocity whichmeans that the frictional pressure drop will be similar to or evensmaller than with empty systems. Certainly the power consumptionwhich is the product of the two will usually be less.

7.1.3 Rotating Membranes

A rotating module design represents another approach of minimising theconcentration polarisation problem. These devices contain concentriccylinders of which the inner is rotated causing flow instability in theannulus. Instability first occurs in the form of doughnut shaped counterrotating concentric Taylor vortices which can move along the annulus inideal plug flow. Long term tests have shown that fouling is retarded,transmission enhanced and fluxes are high, especially when operatedwhere laminar vortices are present. The major advantage of a rotating unitis that the permeate flux becomes independent of the circulation flow, asthe shear rate at the membrane surface is controlled by the rotationalvelocity. This means higher viscosity or concentrated feeds can be treatedin single pass flow, reducing circulation pumping costs. Hallstrom and


Lopez-Leiva (1978) used a rotary module consisting of an external fixedpressure shell and an internal rotary perforated stainless steel tube whichacts as the support for a semipermeable membrane. Between the externalshell and the inner rotating tube a narrow slit is formed-this 0·7 mm wideannular space forms the hold-up volume for the feed/concentrate. Thiswidth is typical of such devices and means scale-up to industrial filtrationmay be difficult. For the ultrafiltration of skim milk significant fluximprovements occurred as rotational speed increased. No limiting fluxbehaviour was observed within the experimental range of velocity gradients (up to 8000 Is - 1). With this device, membranes may be located onboth the outer stationary cylinder as well as the inner rotating drum. Therotating filter can be used for clarification, ultrafiltration and microfiltration purposes and also in thickening operations.

7.1.4 Backflushing

When hollow fibres are used with feed on either the lumen or shell sideback flushing can be used to flush the membrane pores and the operatingsurface. The shell and fibre must be designed to withstand the backflushing operation but there are increasing numbers of installations incommercial use in biotechnology which claim to use this technique.

Backflushing serves to clean the membrane surface by forcing permeateor other fluid such as air back through the fibre which loosens and lifts offthe cake accumulated on the inside of the fibre. A reservoir is required toaccumulate the filtrate and the backwash fluid should contain no suspended matter which might foul the outer sponge-like structure of thefibre. Typically flushing periods of a few seconds every few minutes arefound to be most effective with a trade off between the down time and lossof permeate (if used for flushing) against increased flux.

Recycling, achieved by closing off the permeate ports, allows the feedstream to circulate throughout the fibres. The permeate that is continuallyproduced results in a pressure build up in the cartridge shell until an equilibrium pressure is reached which is very close to the average of the inlet andoutlet pressures of the feed stream. This means that inside the first half of thefibre the pressure is greater than in the shell while the converse is true forthe second half. For full effect it is necessary to operate with flow in alternatedirections over the flushing period. The reverse backflushing action iscoupled with a high shear rate of fluid across the inside of the fibre wall, effectively removing material loosely adhering to the membrane surface. Bothnormal ultrafiltration and backwashing occur but at greatly reduced ratesdue to the reduced transmembrane pressure. Both backflushing and recycling are often more effective if carried out in conjunction with cleaning agents.


A novel approach to backwashing is discussed by Fane and Fell (1987).The Memtec system is only feasible for hollow fibre membranes with arelatively low bubble point. The feed suspension is pumped across theoutside of the fibre and the filtrate passes out through the lumen. The fluxdeclines as colloids deposit on and within the membrane. This effect isreversed by pulsing the lumen with gas (air, nitrogen, etc) and backwashing with a gas/permeate mixture. The gas pulse expands the fibre andopens the pores allowing fouling material to be flushed out. This is claimedto be more effective in controlling fouling than a liquid backwash forparticulate systems (Olivieri et ai., 1991).

Periodic flow reversal is also used to reduce fouling. Goel andMcCutchan (1976) used this method in a tubular reverse osmosis systemwith Colorado river water as feed material. The average fluxes attainedwere 10-15% greater and the flux decline decreased between cleaningruns. These improvements were attributed to added turbulence due to flowreversal, movement of the high salt concentration region from one end ofthe flow path to the other at short intervals and precipitating gypsumcrystals being denied time for growth.

7.1.5 Pulsed Flow

Lowe and Durkee (1971) took a slightly different approach for reverseosmosis of orange juice concentrate which involved pulsing of the concentrate along with plastic spheres from one end of the feed channel to theother. This provided a threefold improvement in flux and significant fluxdeterioration was not observed.

Edwards and Wilkinson (1971) have found that pulsed flow in pipeswill:

(a) enhance mass and heat transfer;(b) modify the laminar/turbulent transition;(c) heighten the migration of solid particles away from the wall;(d) shift the maximum 'velocity under laminar flow conditions towards

the wall region.

Flux increases of up to 70% have been found with pulsing frequenciesup to 1 Hz in reverse osmosis of a 10 wt% sucrose solution in theturbulent or laminar-turbulent transition regimes.

Milisic and Bersillon (1986) investigated the use of pulsed flow as ananti-fouling technique in cross-flow filtration of a 0,1-1,0 g 1- 1 bentonitesolution in a rectangular channel. Pulsations were produced by anair-driven valve located upstream from the filtration cell, fully automatedfor this purpose. Unlike backflushing, neither filtrate nor much energy is

Flux Enhancemenl 249

required for this system to be operated. The flux was increased by as muchas five times compared with the flux in a standard run and there is anoptimum range of values for the frequency and pulse duration; higherfluxes being favoured by higher frequency and shorter pulse duration.Pulsed flow does not appear to solve the important problem of membraneclogging by colloids or macromolecular material likely to occur in naturalwater.

Bauser et al. (1982) showed that pulsed flow may be used to improvemembrane performance under experimental conditions where a non-linearrelationship between flux and wall shear rate exists. They applied aperiodic sequence of pumping pulses keeping the mean flow constant bysimultaneous adjustment of the frequency and amplitude. Results for themicrofiltration of whey under conditions of constant transmembranepressure showed 25% improvements in flux after 1 hand 38% after 2-3 h.Similar results have been obtained for blood serum filtration, the maximum gain in this case being about 30%.

Subsequently, Bauser et at. (1986) took a different approach, applying apulsatile negative pressure to the filtrate side of the test module. Gains ofabout 50% were achieved with feasible pressure amplitudes and frequencies for the ultrafiltration of whey. Long-term tests over several daysdetected no membrane damage due to pulsed flow.

Pulsed flow may be induced by other means such as vibration of aporous plate above the membrane surface, pump vibration or ultrasound.The use of pulsed electrical fields is discussed in Chapter 8.

7.1.6 Dimpled/Furrowed Membranes

Bellhouse et at. (1973) rejected pulsed flow by itself as a means ofimproved mass transfer and developed dimpled membrane 'lungs' foroxygen and carbon dioxide transfer between air and blood. These membranes consist of a large number of small, partly spherical dimplesconcave to the fluid channel (Dorrington et at., 1986). When pulsedflow is used in this system, significant improvements in gas permeationrates were observed. Sobey (1980) analysed mixing in the Bellhousemembrane oxygenator device using CFD and showed that its dimensionswere nearly optimal in terms of mixing performance. It appears thatin steady flow vortices form in the furrows, but remain trapped there,and little or no fluid exchange occurs between the vortices and themainstream. For vortex mixing to be effective, the flow must be pulsatileand reversing. On flow reversal, these vortices are ejected from thefurrows and immediately replaced by a set of counter-rotating vortices.It is this combination of vortex motion in the hollows and vortex


ejection which was thought to eliminate fluid boundary layers andaugment mass transfer.

In a practical mass transfer device there will be a mean flow superimposed on the oscillatory flow. Sobey (1980) also investigated the influenceof the ratio of net forward to maximum flow, NFR, on the flow patterns.When this ratio is small the basic mixing mechanism remains unaltered.Alternatively if this ratio is large, then the flow becomes unidirectional andno vortex ejection occurs. When both flow components are of the sameorder of magnitude, (NFR =0·4-{)·6), the flow patterns become complicated and it is impossible to decide a priori whether high or low convectivemixing would be obtained. These results were verified by Stephanoff et ai.(1980) using flow visualisation.

Wyatt et ai. (1987) successfully applied this technique to the harvestingof microorganisms using E. coli and a 0·2 ~m polysuiphone membrane.Volumetric fluxes of the order of 3~OO I m - 2 h - 1 were achieved with nopressure applied to the system. The application of low pressures to theretentate line also increased fluxes. An increase in pressure from 0 to56 mmHg increased the percentage of permeate obtained from 49 to 94%using repeated single pass filtration. Optimal permeate flux was achievedwith a dimpled membrane with pulsed flow. Fluxes increased withincreasing frequency over the range 2-5 Hz. With both flat and dimpledmembranes, water fluxes after each experiment were the same, equallingabout 25% of the initial clean water flux for no pulsing; with pulsing, thecorresponding values were 51 and 75%, respectively. They described anumber of other potential applications: removal of cell debris; the harvesting of shear sensitive cells; prefiltration of water and media; ultrafiltration(e.g. to separate enzymes); and the clarification of solvents.

7.1.7 Application of Pulsatile Flow with Baffles

Finnigan and Howell (1989) have used a tubular membrane system withgeometrical inserts of doughnut or disc shape to create a periodicallygrooved channel. A significant improvement in flux was observed with thebaffled systems under both steady and pulsed flow conditions. The relativeimprovement reached a maximum in the Re range 750-2200 and 350-1550at Cb = 10 and 25 g 1- 1, respectively. At a higher Reynolds number of 6450,fluxes were greater than or equal in magnitude to fluxes corresponding tofully turbulent flow conditions (Re = 16000-50000) in a conventionalsystem. In pulsed flow, comparative fluxes could be obtained at relativelylow net cross-flow velocities when the pulsed flow Reynolds number,Rep = 6450, where Rep is calculated from the maximum velocity in pulsedflow. At F 1m = 4 bar, fluxes varied from 60-70 I m - 2 h - 1 for a conventional


system at Re=16QOO-50000 to 75-95Im- 2 h- 1 for the different discbaffled systems. The 'decoupling' of flux from net cross-flow velocity offersthe opportunity for use of this system in a single pass, continuous mode ofoperation for thickening purposes or to avoid the pumping costs associated with recirculation.

Flow visualisation was used to study the flow patterns in the conventional and baffled systems under pulsed and steady flow conditions. Insteady flow, baffles increased local mass transfer rates by promotingturbulence and interrupting development of the boundary layer. Vortexmixing occurred with pulsed flow in the baffled systems enhancing masstransfer and preventing the development of velocity and concentrationboundary layers.

The frequency and amplitude needed to be above certain minimumvalues for an optimum improvement in flux to be observed. At the sameRep value, it was more effective to improve fluxes using short strokesrather than long strokes, as the frequency was higher in the formersituation. In general, a greater improvement in mass transfer, mixing andflux was observed with 'short, fast' strokes rather than 'long, slow' strokes.Further improvements in flux were obtained by increasing Rep (higherfrequencies and/or amplitudes (lower St)) until the onset of pressuredependent behaviour.

Colman and Mitchell (1990) investigated vortex mixing generated bypulsed flow to enhance membrane performance. A system was designed inwhich 3-mm high baffles were spaced away from the surface of a flat sheetmembrane in a 6-mm high rectangular channel. An interbaffle spacing of12 mm was found to be optimal for mass transfer. The flow structureassociated with pulsed flow in this baffled system shows the same sequenceof vortex creation, expansion and ejection each cycle, as described bySobey (1980) and Mackley (1987). As frequency is increased the flowbecomes chaotic but this basic vortex mixing mechanism remains unchanged. The RTD was shown to exhibit plug flow characteristics withlow axial dispersion. A mass transfer coefficient, measured at zero flux,equivalent to steady flow at Re> 10000 in an empty tube was achieved byusing pulsed flow in baffled channels when the net cross-flow rate isRe= 100-200. Thus, the mass transfer coefficient can be made independentof the net cross-flow velocity and is relatively constant, provided flowreversal occurs. When there is no flow reversal, the effect of the superimposed oscillations diminishes and the mass transfer becomes mean flowdominated.

A flux, equivalent to that from turbulent cross-flow was achieved usingthis technique with pervaporation membranes. This technique was alsoapplied to the ultrafiltration of a 1 wt% solution of Dextran T500 (mol. wt


(MW)=5OO000) using DDS GR40 PP membranes (MWCO= 100000).Dextran is a low fouling solute and no permanent fouling of the membranewas observed. Fluxes were enhanced by a factor of three when pulsed flowat a pulsed Reynolds number, Rep, of 800, is superimposed on a low netcross-flow (Re = 200) in a baffled channel relative to the flux in anunbaffled channel with steady flow (Re = 200). The pulsed flow flux isequivalent to the flux for steady flow in the baffled channel at Re = 1000and greater than the flux in the unbaffled channel at the maximumcross-flow velocity attainable in the test rig (Re = 3000). Limiting fluxbehaviour is demonstrated by each system and is reached at approximately 0·5 and 1·0 bar for the unbaffled and baffled systems respectively. Byincorporating this technique into membrane module design, it will bepossible to control mass transfer to the membrane surface independentlyof the net cross-flow and permeate driving force. No assessment of thepower requirement was made.

7.1.8 Conclusions

The vortex mixing technique in baffled systems shows considerable potential for application to membrane filtration systems:

(a) good radial mixing is achieved with the radial and axial velocitycomponents being of similar magnitude;

(b) near plug flow characteristics can be obtained with low axialdispersion thus maintaining axial concentration gradients along thelength of the module;

(c) the mixing effect, mass transfer and flux can be decoupled from thenet cross-flow rate;

(d) energy consumption within this system is expected to be small;(e) fluxes in pulsed flow in the baffled system are similar in magnitude

to steady flow turbulent fluxes in an unbaffled tube.

7.2 FLUX ENHANCEMENT-SURFACE MODIFICAnONS

As has been discussed briefly in Chapter 2 enhancement can be achievedby changing the properties of the membrane surface so that the solventeasily penetrates the membrane pores and the molecules in the retentatedo not adsorb on the membrane surface or in the pores of the membrane.One way to change the membrane properties is to modify the membranebefore filtration either permanently or dynamically, i.e. in a reversible way.Another way is to change the solution conditions in such a direction, that


the membrane properties match the solution to be filtered so that foulingis not favoured. With modifications membranes can be partly 'tailor made'for an individual process. It is often theoretically possible to predict or atleast guess what kind of modification would be suitable for a specificfiltration process in order to achieve optimal performance.

Different aspects of modification have to be taken into account, whenmodification results are evaluated. Mostly flux enhancement is a goal, as itmeans improvement of the process economy. On the other hand, the profitfrom flux enhancement is often counterbalanced by an undesired decreasein retention. Prevention of permanent fouling of the membrane is also agoal.

The hydrophobicity of membrane surfaces seems to be one cause offouling and flux decrease, especially when protein solutions are filtered.The proteins adsorb more or less irreversibly on the hydrophobic surfaceor in the hydrophobic pores. Hence, it is believed that if more hydrophilicgroups are introduced in the polymer backbone, a flux increase and lessfouling can be expected. If the modification also introduces groups thatprevent the solute from entering the pores either by electrostatic or stericrepulsion or by the formation of a secondary membrane, also retentioncan be increased or at least not decreased. A coarse surface is often moreapt to foul, and therefore smoothening the surface with a secondary layercan decrease fouling and improve flux.

Modification methods for membranes have been investigated duringthe last 10 years, as the importance of the membrane surface properties for flux have been realised. Today it is one central field of interestin membrane technology. In the following paragraphs some methodsof modification for flux enhancement are described. The modifications can be carried out either before or after membrane preparationand with varying durability, and the methods are classified according tothat.

7.2.1 Permanent Modification of the Membrane Surface

7.2.1.1 Modification of the Membrane Polymer before Membrane CastingIf the membrane polymer is modified before the membrane is castone has the advantage of being able to control the pore size in thecasting procedure. This kind of modification could be classified as producing new membrane materials, but it has been discussed in this section,in those cases, where the intention of the modification is to changean already existing membrane material in a more favourable directionfor a certain process. When the membrane material is modified beforecasting the modification is homogeneous, which means that the pores,


the membrane surface and the inside of the membrane are modifiedto an equal extent.

Hydrophilic monomers can be grafted into a hydrophobic polymerbackbone, e.g. by y-radiation or by chemical methods. Thus an increase inpermeate flux and in rejection of hydrophilic neutral substances has beenachieved. The flux increase has been up to tenfold and the rejectionincrease threefold as shown by Vigo and Uliana (1987, 1988, 1989). Theyprepared UF membranes by grafting hydrophobic poly(vinyl chloride)(PVC) with less hydrophobic monomers of vinyl acetate (VAc), hydroxyethyl methacrylate (HEMA) and acrylonitrile (AN). They tried outtheir membranes with dextran solutions and found out that there was anoptimal percentage of grafted material, which gave a maximum in flux andretention of dextran (Fig. 7.1). In this way they combined the good castingproperties of a hydrophobic membrane with the increase in water affinityachieved by the introduction of hydrophilic groups. When the PVCmembrane material was modified with AN (which was polymerised topoly(acrylonitrile) segments), Vigo and Uliana (1988) found that themacropores of the membrane changed from narrow finger-like tubularpores to larger cavities. Increase in pore size was also noticed by Miyamaet al. (1988), when they introduced hydrophilic poly(vinyl alcohol) (PVA)groups in a more hydrophobic polymer material during casting.

100

IIII

Eii:'

10GRAFTING 0'0

20

•

10GRAFTING 0'0

20

Fig. 7.1. Permeate flux (F) and rejection to Dextran 110,000 vs. grafting %. (Vigo andUliana, 1989.)

An increase in the hydrophilicity of the membrane can also make itperform better in the fractionation of proteins. This has been shown byHashimoto and Sumimoto (1987). They introduced by mixing morepoly(oxyethylene glycol) (POE-OH) in a copolymer of polyamide (PA)and polyoxyethylene (POE) during the preparation of ultrafiltration


membranes. This modification method also improved water flux in densemembranes.

In all the examples above a better flux in the filtration of hydrophilicsubstances in water solutions has been achieved with an increase in themembrane hydrophilicity. Retention decrease has not been observed evenif the macro pores of the membranes have been enlarged according toelectron microscopy. Probably the grafted hydrophilic material forms aprotective coating at the entrances of the pores, which allows the permeation of water but not of the macromolecules in solution.

7.2.1.2 Permanent Modification of the Membrane after CastingWhen membranes are modified after casting, only the membrane surfaceor sometimes also the pores are modified. As described by a number ofworkers (for example Vigo et al. (1988), Wolff et al. (1988) and Lai andChao (1988)) the modification process can be carried out by plasmatreatment of the membrane surface in an inert atmosphere like argon ornitrogen, if oxidation of the surface is not desired. One advantage ofplasma treatment is that it easily modifies the membrane surface withoutaffecting the bulk properties of the membrane. The treatment is made inoxygen plasma if oxidised groups should be formed in the membranematerial. If some kind of monomer is introduced in the gaseous atmosphere it can be grafted onto the membrane surface. The plasma treatmentis mostly a rather rough method and has to be carried out only forseconds, so that the membrane surface is not destroyed. The method canbe modified so that the membranes can be treated for longer periods.Plasma treatment gives the best results when performed with dry membranes, and is thus not suitable for all kinds of membranes.

As described by Van et al. (1988) the grafting of the membranes can alsobe carried out with UV-irradiation in an atmosphere containing thegrafting substance. If milder conditions are desired the modification can bemade in solution, where the modification agent is present (Nystrom, 1990).In this way longer modification times can be used and the experiments areeasier to repeat.

Always when some kind of irradiation or glow discharge is used formodification the membrane surface is destroyed to some extent, whichdepends on the time of exposure. Following the work of Vigo et al. (1988),Nystrom (1990), Zeni et al. (1988) and Shimomura (1984) the degradationcan be seen as an increase in flux combined with a decrease in retention.Shimomura et al. (1984) showed, as illustrated in Fig. 7.2, that in thebeginning of plasma treatment flux is enhanced and rejection increased.Spectral analysis supported the hypothesis that the reason was theformation of hydrophilic groups in the membrane. Later, when deeper


90

70

80'

REGION 2

REGION 1,:PI..ASI"A COND ITI OMS,I HE, 0.1 TORR, 0.35 kv

R£J (II

r-x-=::::::;:::==o==:=::::::::---:----, 100-60

20

FLUX (UlHI

o"-_....L.__"--_-'-__"""-_--"__......._-.J

o 2 lj 6 8 10 12

PLASM TREATPlENT rtllE ("INI

Fig. 7.2. Change of water flux and salt rejection as a function of plasma treatment time(RO operating conditions; 0·5% NaCI, 25°C, 50 kg/em) (Shimomura el at., 1984).

levels of the membrane are reached with the treatment, there is no furtherincrease in hydrophilicity and flux decreases due to an increase ofcross-linked layers. Finally the deterioration of the surface increases andrejection starts to decrease and flux increases.

When oxygen is present during the treatment the effect of pore enlargement is more pronounced. This can be due either to the etching effect ofoxygen or to the repulsion of the formed charged groups in the membranepores. Plasma or UV treatment has been carried out both with RO by Laiand Chao (1988) and Yan et ai. (1988) and UF membranes by Vigo et ai.(1988), Wolff et ai. (1988), Nystrom (1990) and Zeni et ai. (1988). When thetreatment introduces charged groups in the membrane material, retentionof similarly charged substances is increased due to electrostatic repulsionat the entrance of the pores. Also electroviscous effects cause decreasedmobility of the substances inside the pores, and hence salts are betterretained by, e.g. surface-treated tight UF membranes. These treatmenteffects can also result in a lower flux.

Membranes can also be permanently modified by purely chemicalmethods. With these methods that have been used by Wahlgren et ai.(1990), Yokota and Kawasaki (1987) and Higuchi et ai. (1988) the porescan also be modified. The membranes usually lose some water flux, but iffouling is decreased the total permeate flux in the process can still beenhanced even if the improvement is not very outstanding.

When membranes are permanently modified, some kind of functionalisation of the membrane can be the goal. As an example can be mentioned


experiments carried out by Wolff et ai. (1988), where commercial polysulphone UF membranes were plasma-treated in NH3 atmosphere andamine groups were created on the membrane skin. These groups wereconverted with acylating agents. The pretreatment of the membranesincreased the permeate flux and increased retention even of small organicsubstances but not of salts. Also the compaction properties of themembranes were improved. In this case the improvement of rejection oflow molar mass « 1000 g/mol) compounds was achieved, because thegroups grafted on the membrane induced association of the organicmolecules on the membrane, and this layer formed a secondary membranein filtration.

7.2.2 Dynamic Modification of Membrane Surfaces

7.2.2.1 Modification with PolymersMembranes can be non-permanently pretreated with different kinds ofadsorbing polymers either by passive adsorption of the polymer from asolution onto the membrane surface or by convective adsorption duringfiltration of the adsorbent. This type of modification layer can often bewashed away, especially if it has been made by passive adsorption of smallmolecules and not of polyelectrolytes. As convective adsorption meansthat the modification agent is applied onto the membrane from a solutionwhich is ultrafiltered through the membrane with applied pressure, acertain amount of pore adsorption results. As a result the pores areblocked to some extent and flux decreases. Because of this, also adsorptionof high molar mass polymers gives better flux results as they do not blockthe pores. Kim et ai. (1988) tried out ionic and non-ionic polymers, and asmall non-ionic surfactant and found out that the non-ionic surfactantseemed to be the best modification agent. In earlier work Fane et al. (1985)found that the initial UF flux was typically 20-30% higher after modification and the rate of fouling some 10-20% lower than for the untreatedmembrane. The modified membranes were tested with BSA at pH 5. Themodification could be repeated after washing and it even improved withtime, probably because of favourable interaction of the modification agentwith the alkaline sodium hydroxide used in the washing solution.

The modifications mentioned above are usually made on hydrophobicmembranes, like polysulphone membranes, to make them more hydrophilic. If the adsorbing substance is a surfactant or a polymer withboth hydrophobic and hydrophilic parts, the hydrophobic parts adsorb bymeans of hydrophobic interaction on the membrane while the hydrophilicparts protrude out in the solution and in this way form a secondaryhydrophilic layer which prevents fouling and flux decrease. This type of


modification was used by Nystrom (1990) on a polysulphone UF membrane with an AB block copolymer of POE and PVAc and it gave goodresults with different kinds of protein solutions especially near the isoelectric points of the proteins.

Flux enhancement has mostly been achieved in the filtration of proteinsolutions when hydrophobic membranes have been modified with hydrophilic non-ionic polymers. In the work by Michaels et al. (1987) no fluxenhancement or decrease of fouling was noticed in some cases whennaturally hydrophilic membranes were treated or if hydrophobic membranes were treated with anionic polymers. The result for ionic polymers issurprising but the optimal conditions for electrostatic repulsion might nothave been achieved in the experiments. Contradictory results were obtained when polysulphone UF membranes were treated with positivelycharged polyelectrolytes. An increase in flux and a decrease in fouling wereachieved at pH 6 in UF of positively charged lysozyme by Nystrom et al.(1990). The importance of charged modified membranes was also shown inRO and UF by Linder and Shavit (1988) for maintaining high fluxes athigh concentrations by eliminating build-up of high osmotic pressuresemanating from adsorption.

The adsorbed modifying layer can be further treated and functionalisedfor some special kind of separation problem. This was done with hollowfiber polysulphone MF membranes, which were modified with a cellulosicpolymer surfactant to make the surface more hydrophilic. Then in thework by Tripodi et al. (1988) the membranes were functionalised withgrafted sulphopropyl groups to introduce charged groups for ion exchange. The antigen IgG was purified by this method because beingpositively charged it adhered to the negatively charged membrane. Therest of the molecules in solution were negatively charged at the solutionpH and therefore they were electrostatically repelled, which resulted inreduced fouling and thus increased flux. When all the sites in themembrane were occupied by IgG molecules the pH was changed and theantigen molecules were concentrated.

Kimura et al. (1985) have found that dynamic macromolecular membranes can also be formed on a porous ceramic tube surface by buildingthem up during filtration of the macromolecular solution. Particularlygood flux and retention results were obtained with ovalbumin as aself-rejecting membrane.

7.2.2.2 Modification with Inorganic CompoundsA currently commercial method to make modifications of membranes is tomodify an open pore filtration membrane with some kind of salt, usuallyan oxide. Often zirconia or alumina is used. This type of modification has


developed into the manufacture of so called mineral membranes. Originally dynamically modified types of membranes were developed formicrofiltration or ultrafiltration. With these types of modifications hydrophilic membranes are formed, the charges of which depend strongly onpH (Neytzell-de Wilde et aI., (1988)). A dual layer can be formed by furthertreatment with poly(acrylic acid). Flux and retention of the dual membrane can be further increased by pretreatment of the support with fumedsilica.

7.2.2.3 Modification with Langmuir-Blodgett LayersThe pretreatment of the membrane surface can also be carried out bymodifying the membrane with a Langmuir-Blodgett layer. This is amonomolecular layer, which can be formed on the surface of a non-solventin a Langmuir film balance and then transferred from the liquid-airinterface onto the membrane. This type of modification was carried out byKim et al. (1989). Different kinds of surfactants were used and compared tostearic acid. The layer thickness varied from one to ten monolayers. Theinitial water flux through the membrances decreased with increasingnumber of surfactant layers due to the increased resistance of the membranes. During UF of 0·1 % BSA the results were as good with stearic acidas with surfactants with their hydrophilic parts turned away from themembrane. The final flux after 3 h of UF was higher with the modifiedmembranes than with those without modification. The membranes coatedwith stearic acid surprisingly showed less flux reduction than those coatedwith surfactant. The results were explained by a smoothening of themembrane surface, which reduced BSA deposition, and the hypothesis wasconfirmed by measurements of BSA adsorption.

7.2.3 Surface Effects Depending on Solution Conditions

As both the membranes and the molecules in the solution to be filtered canbe charged, also the solution conditions influence the surface effects. Mostmembranes carry some kind of charge either because of ionic groups orbecause of adsorption of ions from the solution (see Chapter 6). The ionicgroups have their specific pK values and the charge therefore depends onthe pH of the solution. If electrostatic repulsion between the membranesurface and the solutes is achieved, fouling is decreased and retention isincreased. It has been shown by Nystrom and Lindstrom (1988) that smallmolecules with a molar mass of about 1000 g/mol can be retained by a20000 cut-off membrane at the right pH and when the pH is changedunfavourably the result is the opposite. Also for protein solutions fromboth the same laboratory Nystrom et al. (1989) and that of Nakao et al.


(1988) have found that flux and retention are increased at pH-values faraway from their isoelectric points, if their charges have the same signs asthe membranes. By performing ultrafiltration at different pH, separation ofproteins can be achieved.

The effect of surface charge has been noticed for the separation of smallcharged molecules and salt and the method is called nanofiltration. In thistype of filtration Cadotte et ai. (1988) have shown that the good retentionof an RO membrane is combined with the enhanced flux of a UFmembrane. The processes have to be carried out at such a pH that the signof the charged molecules is the same as that of the membrane. Theelectrostatic effects are diminished by neutral salts as the charges areshielded.

The effect of a good or a poor solvent was shown by Iwata and Matsuda(1988) for poly(vinylidene fluoride) microfiltration membranes graftedwith poly(acrylamide) or poly(acrylic acid). The membranes show sensitivity to solution conditions in the filtration of BSA or dextran. At low pH orat an increased content of methanol the flux increases and retentiondecreases. The effect is explained by the assumption that for the hydrophilic graft polymer the good solvent conditions let the grafted chainsentangle from the surface into solution. Thus the membrane changes froma microfiltration membrane to an ultrafiltration membrane with lower fluxbut good retention. In a poor solvent the chains lay down on the surfaceand the opposite condition is the case. The same effect was also shown byOsada et ai. (1986) for PVA membranes grafted with poly(methyacrylicacid). At low pH the conformation of the grafted chains is compact and themembrane shows high water permeability. At high pH again the graftedchains expand and water flux is decreased but retention increased (Fig.7.3). The grafts also react to changes in salinity or complexing agent. Forinstance, if the grafted membranes are treated with PEG, so that the ratioof oxyethylene units to the carboxyls in the graft is equilibrated, a maximalincrease in water flux is achieved.

7.2.4 Conclusions

In many cases flux enhancement can be achieved by making the membrane surface more hydrophilic, as less solute is adsorbed at theseconditions. The hydrophilic groups on the surface form a barrier forsolutes to pass the pores, but make it possible for water to enter the poreswith a resulting flux increase. If the membrane material and/or the solutesare ionic in nature this effect can be magnified by choosing a pH at whichelectrostatic repulsion prevails between membrane and solute molecules.Due to electrostatic repulsive forces also the membrane pores are enlarged

B


c

A

~'P1CX~o

+&iM~TM~M

Fig. 7.3. Schematic illustration of the change in permeability of mechanochemical membranes with grafted polymers. A: medium of low pH or high ion concentration. B: mediumof high pH or low ion concentration. C: polymer-polymer complexation. 0: polymer-

metal complexation (Reproduced from Osada et al., 1986).

at these optimal conditions. In hydrophobic solvents flux enhancementhas to be achieved by modifying the membrane in a way favourable for ahydrophobic solvent.

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Bauser, H., Chmiel, H., Stroh, N. & Walitza, E. (1986). Control of concentrationpolarization and fouling in medical, food and biotechnical applications. J.M embr. Sci., 27, 195-202.

Bellhouse, B. J., Bellhouse, F. H., Curl, C. M., MacMillan, T. I., Gunning, A. 1.,Spratt, E. H., MacMurray, S. B. & Nelems, J. M. (1973). A high efficiencymembrane oxygenator and pulsatile pumping system, and its application toanimal trials. Trans. Am. Soc. Artif. Intern. Organs, 19, 72-9.


Blatt, W. F., Dravid, A., Michaels, A S. & Nelsen, L. (1970). Solute polarizationand cake formation in membrane ultrafiltration: causes, consequences andcontrol techniques. In: Membrane Science and Technology, ed. J. E. Flinn,Plenum Press, New York, pp. 47-97.

Cadotte, 1., Forester, R., Kim, M., Petersen, R. & Stocker, T. (1988). Nanofiltration membranes broaden the use of membrane separation technology. Desalination, 70, 77-88.

Colman, D. A. & Mitchell, W. S. (1990). Enhanced mass transfer for membraneprocesses. I. Chem. E. Symp. Ser., 118,87-103.

Copas, A. L. & Middleman, S. (1974). Use of convection promotion in theultrafiltration of a gel-forming solute. Ind. Eng. Chem. Process Des. Dev., 13(2),143-5.

Da Costa, A. R., Fane, A. G., Fell, C. J. D. & Franken, A C. M. (1991). Optimalchannel spacer design for ultrafiltration. J. Membr. Sci., 62(3) 275-91.

Dorrington, K. L., Ralph, M. E., Bellhouse, B. J., Gardez, 1. P. & Sykes, M. K.(1985). Oxygen and CO 2 transfer of a polypropylene dimpled membrane lungwith variable secondary flows. J. Biomed. Eng., 7, 89-99.

Edwards, M. F. & Wilkinson, W. L. (1971). Review of potential applications ofpulsating flow in pipes. Trans. Inst. Chem. Eng., 49, 85-93.

Fane, A G. & Fell, C. J. D. (1987). A review of fouling and fouling control inultrafiltration. Desalination, 62, 117-36.

Fane, A. G., Fell, C. 1. D. & Kim, K. 1. (1985). The effect of surfactantpretreatment on the ultrafiltration of proteins. Desalination, 53, 37-55.

Finnigan, S. M. & Howell, J. A. (1989). The effect of pulsatile flow on ultrafiltration fluxes in a baffled tubular membrane system. Chem. Eng. Res. Des., 67(3),278-82.

Goel, V. & McCutchan, 1. W. (1976). Colorado River desalting by reverse osmosis.Proceedings. 5th Int. Symp. Fresh Water from the Sea, Alghero, May 16-20, 4,143-56.

Hallstrom, B. & Lopez-Leiva, M. (1978). Description of a rotating ultrafiltrationmodule. Desalination, 24, 273-9.

Hashimoto, K. & Sumimoto, H. (1987). Condensation of aqueous solutions ofproteins by their accelerated permeation through the new porous hydrophilic block copolymer membrane. Proceedings of the 1987 InternationalCongress on Membranes and Membrane Processes, Tokyo, Japan, June 8-12,pp.253-4.

Hiddink, 1., Kloosterboer, D. & Bruin, S. (1980). Evaluation of static mixers asconvection promoters in the ultrafiltration of dairy liquids. Desalination, 35,149-67.

Higuchi, A, Iwata, N., Tsubaki, M. & Nakagawa, T. (1988). Surface-modifiedpolysulfone hollow fibers. J. Appl. Polym. Sci., 36, 1753-67.

Iwata, H. & Matsuda, T. (1988). Preparation and properties of novel environment-sensitive membranes prepared by graft polymerization onto a porousmembrane. J. Membr. Sci., 38, 185-99.

Kim, K. 1., Fane, A. G. & Fell, C. 1. D. (1988). The performance of ultrafiltrationmembranes pretreated by polymers. Desalination, 70, 229-49.

Kim, K. 1., Fane, A. G. & Fell, C. J. D. (1989). The effect of Langmuir-Blodgettlayer pretreatment on the performance of ultrafiltration membranes. 1. Membr.Sci., 43, 187-204.


Kimura, S., Ohtani, T. & Watanabe, A. (1985). Nature of dynamically formedultrafiltration membranes, In: Reverse osmosis and ultrafiltration, ed. S.Sourirajan and T. Matsuura, ACS Symp. Ser. 281, American Chemical Society,Washington, D.C., pp. 35-46.

Lai, 1. Y. & Chao, Y. C. (1988). Plasma treated nylon 4 membranes for reverseosmosis desalination, Proceedings 1M T EC'88 International Membrane Technology Conference, 15-17 November, 1988, Sydney, J44-J47.

Linder, C. & Shavit, R. (1988). Robust industrial intermediate ROjUF membranesfor the concentration and desalting of low molecular weight organic solutions.Proceedings IMTEC'88 International Membrane Technology Conference, 15-17November, Sydney, B49.

Lowe, E. & Durkee, E. L. (1971). Dynamic turbulence promotion in reverseosmosis processing of liquid foods. J. Food Sci., 36, 31-2.

Mackley, M. (1987). Using oscillatory flows to improve performance. The Chern.Eng., 43, 18-20.

Michaels, A. S., Robertson, C. R. & Reihanian, H. (1987). Mitigation of proteinfouling of lipophilic ultrafiltration membranes by presorption of hydrophilicpolymers. Proceedings of the 1987 International Congress on Membranes andMembrane Processes, Tokyo, Japan, June 8-12, pp. 17-19.

Milisic, V. & Bersillon, 1. L. (1986), Anti-fouling techniques in cross flowmicrofiltration. 4th World Filtration Congress, Ostend, April, 11.19-11.23.

Miyama, H., Tanaka, K., Nosaka, Y., Fujii, N., Tanzawa, H. & Nagaoka, S.(1988). Charged ultrafiltration membrane for permeation of proteins. J. Appl.Polym. Sci., 36, 925-33.

Nakao, S., Osada, H., Kurata, H., Tsuru, T & Kimura, S. (1988). Separation ofproteins by charged ultrafiltration membranes. Desalination, 70, 191-205.

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Nystrom, M. (1990). Prevention of fouling by modification of UF membranes,Proceedings ICOM '90, Vol. 1, Chicago, pp. 90-2.

Nystrom, M. & Lindstrom, M. (1988). Optimal removal of chlorolignin byultrafiltration achieved by pH control. Desalination, 70, 145-56.

Nystrom, M., Lindstrom, M. & Matthiasson, E. (1989) Streaming potential as atool in the characterization of ultrafilration membranes. Colloids Surf, 36,297-312.

Nystrom, M., Laatikainen, M., Turku, K. & Jarvinen, P. (1990). Resistance tofouling accomplished by modification of ultrafiltration membranes. Progr.Colloid Polym. Sci., 82, 321-9.

Olivieri, V. P., Willingham, G. A., Vickers, 1. c., McGahey, c., Kolega, M., Day,A., Johnson, W., Kopp, C. & Grohmann, G. S. (1991). Continuous microfiltration for the production of high quality wastewater effluent. IW EM Symposiumon Advanced Sewage Treatment, London November.

Osada, Y., Honda, K. & Ohta, M. (1986). Control of water permeability bymechanochemical contraction of poly(methacrylic acid)-grafted membranes. J.Membr. Sci., 27, 327-38.

Shimomura, T, Hirakawa, M., Murase, I., Sasaki, M. & Sano, T (1984).Preparation of polyacrylonitrile reverse osmosis membrane by plasma treatment. J. Appl. Polym. Sci.: Appl. Polym. Symp., 38, 173-83.


Sobey, I. 1. (1980). On flow through furrowed channels. Part 1. Calculated flowpatterns. J. Fluid. Mech., 96(1), 1-26.

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Thomas, D. G. & Watson, J. S. (1968). Reduction of concentration polarization ofdynamically formed hyperfiltration membranes by detached turbulence promoters. Ind. Eng. Chem. Process Des. Dev., 7(3), 397-401.

Tripodi, M. K., Hassett, R. 1., Shaffer, A. F., Stimpson, D. I., Burke, 1. J.,Stedronsky, E. R. & Henis, J. M. (1988). Applications of surface modifiedmembranes for protein purification. Proceedings IMTEC'88 InternationalMembrane Technology Conference, 15-17 November, Sydney, A7-AtO.

Van der Waal, M. 1., van der Velden, P. M., Koning, J., Smolders, C. A. & vanSwaay, W. P. M. (1977). Use of fluidized beds as turbulence promoters intubular membrane systems. Desalination, 22, 465-83.

Vigo, F. & Uliana, C. (1987). Ultrafiltration membranes obtained by grafting ofhydrophilic monomers onto polyvinylchloride. Proceedings of the 1987 International Congress on Membranes and Membrane Processes, Tokyo, Japan, June8-12, pp. 275-6.

Vigo, F. & Uliana, C. (1989). Ultrafiltration membranes obtained by graftinghydrophilic monomers onto poly(vinyl chloride). J. Appl. Polym. Sci., 38,1197-209.

Vigo, F., Nicchia, M. & Uliana, C. (1988). Poly(vinyl chloride) ultrafiltrationmembranes modified by high frequency discharge treatment. J. Membr. Sci., 36,187-99.

Vigo, F., Uliana, C. & Dondero, G. (1988). Ultrafiltration membranes obtained bypoly(acrylonitrile) grafted onto poly(vinylchloride). Desalination, 70, 277-92.

Wahlgren, M., Sivik, B. & Nystrom, M. (1990). Dextran modifications of polysulfone UF-membranes: Streaming potential and BSA fouling characteristics. ActaPolytech. Scand., Ch-series, 194, 1-18.

Wolff, 1., Steinhauser, H. & Ellinghorst, G. (1988). Tailoring of ultrafiltrationmembranes by plasma treatment and their application for the desalination andconcentration of water-soluble organic substances. J. Membr. Sci., 36, 207~14.

Wyatt, 1. M., Knowles, C. 1. & Bellhouse, B. J. (1987). A novel membrane modulefor use in biotechnology that has high transmembrane flux rates and lowfouling. Proceedings of International Conference on Bioreactors and Biotransformations, ed. G. W. Moody & P. B. Baker, Gleneagles, Scotland, pp. 166-172.

Yan, W., Yang, P. & Wang, Y. (1988). UV-radiation grafting of acrylamide ontocellulose acetate reverse osmosis membrane. Shuichuli Jishu, 14(4), 213-8.

Yokota, M. & Kawasaki, H. (1987). Hydrophilization of porous membranes byreactive sulfones, Ger. Offen. DE 3,835,612 (CI. C0817/12, 27 Apr 1989), JPAppl. 87/263,322, 19 Oct, to pp.

Zeni, M., Bellobono, I. R., Muffato, F., Polissi, A., Selli, E. & Rastelli, E. (1988).Photosynthetic membranes. VI. Characterization of ultrafiltration membranesprepared by photografting zeolite-epoxy-diacrylate resin composites onto cellu-lose. J. Membr. Sci., 36,277-95. .

Chapter 8

ELECTROCHEMICAL ASPECTS OF MICROFILTRATIONAND ULTRAFILTRATION

w. R. BOWEN

Biochemical Engineering Group, Department of Chemical Engineering,University College of Swansea, University of Wales, Swansea, UK, SA2 8PP

8.1 INTRODUCTION

The separation characteristics of microfiltration and ultrafiltration membranes depend on their physical properties such as their porosity, pore sizedistribution and pore structure. However, such membranes cannot beunderstood simply as sieves. Neither in this context can the materials to beseparated, particles, colloids, microbial cells or proteins, be sufficientlycharacterised in terms of size or molecular weight. In particular, theelectrochemical properties of the membrane surfaces and dispersed materials or solutes can have a significant influence on the nature andmagnitude of the interactions between the membrane and the substancesbeing processed. This chapter begins by describing the nature of theseelectrochemical properties and their influence on conventional pressuredriven membrane processes. It is then shown how the application of externalelectric fields can make use of these properties to substantially improve theperformance of membrane separations, giving a range of processes knowncollectively as electrofiltration or electrically enhanced membrane processes.

8.2 THE ELECTRICAL DOUBLE LAYER

Most substances acquire a surface electrical charge when brought intocontact with a polar (e.g. aqueous) medium. This may arise by iondissociation, ion adsorption or ion dissolution. In aqueous solutions,proton equilibria at the surface are especially important. For example,proteins bear a pH dependent charge due to the ionisation of acidic orbasic amino acid side chains. Microbial cells bear a net charge due to the

265

266 W. R. Bowen

Distance from surface

ionisation of groups in the outer part of the cell wall. For example, cells ofthe yeast Saccharomyces cerevisiae have a high negative charge undernormal fermentation conditions due to the high phosphomannan contentof the outer layer of the yeast cell wall.

Surface charge produces an ordering of the surrounding solution, inparticular, ions of opposite sign of charge are attracted toward the surface.When combined with the randomising effect of thermal motion, this leadsto the formation of an 'eletrical double layer' comprising the chargedsurface and the neutralising excess of counter ions (Fig. 8.1). The exactstructure of this double layer is a subject of considerable complexity(Hunter, 1981). However, the basis of most current theories is that thesolution part of the double layer may be divided into two regions:

(a) The compact or inner region very near to the solid surface in whichthe charge and potential distribution are determined mainly by thegeometrical restrictions of ion and molecular size and short rangeinteractions between ions, surface and adjoining dipoles.

(b) A diffuse layer further out from the wall where the PoissonBoltzmann equation will give a reasonable representation of thepotential distribution. In one dimension this may be written,

where ljJ is the potential at a distance x from the surface, £0 thepermittivity of a vacuum, D the dielectric constant of the medium,n? the bulk concentration of ions of charge Zi, e is the electronic unitof charge, kB is Boltzmann's constant and T the temperature.

II~+, @+

Charged : 'ttlsurface +

f+,

-.II+XH

Fig. 8.1. Schematic representation of the electrical double layer and potential distributionat a charged surface.

An important parameter in the quantitative description of electrochemicalinteractions is K, defined as,

(8.2)

Aspects of Microjiltration and Ultrajiltration 267

Increasing ionic strength causes an increase in K as a result of which thepotential falls off more rapidly with distance. This is referred to ascompression of the double layer. The distance 11K is referred to as the'thickness of the double layer', though the region of varying potentialextends to a distance of about 31K before the potential has decayed toabout 2% of its surface value.

8.3 ELECTROKINETIC EFFECTS

If an electric field is applied parallel to such a charged surface, forces areexerted on both the solution part of the double layer and the surface.These forces are opposite in direction, due to the separation of chargebetween the two phases. The mobile part of the double layer will moveunder the influence of the field, carrying solvent with it. If the chargedsurface is mobile it too will migrate, but in the opposite direction. Theseevents are conventionally divided into two limiting cases:

8.3.1 Electrophoresis

The transport of a charged surface relative to stationary liquid by anelectric field, for example, the movement of ions or particles betweenelectrodes (Fig. 8.2a). The velocity of movement will be determined bythe strength of the electric field and the electrophoretic mobility of theparticle,

(8.3)

where up is the particle velocity, up is the particle electrophoretic mobility,and E the mean electric field gradient. For cases in which the double layerthickness is small compared to the particle radius (Ka ~ 1, where a is theradius), then Smoluchowski's equation may be used to relate the electrophoretic mobility to the 'zeta-potential'.

(8.4)

where the zeta-potential (() is the electrical potential at the surface of shearbetween the mobile and immobile parts of the double layer and J1 is theelectrolyte viscosity. This condition often holds in the processing ofbiological materials such as, for example, microbial cells in fermentationbroths. If the condition is not met then up and ( are best related bynumerical methods (Hunter, 1981). It should be noted that as the doublelayer is compressed by increasing ionic strength, so the magnitude of ( andup will decrease if the position of the shear plane remains constant.

268 W. R. Bowen

+-- + +

Cathode +~ ++ +-:: Anode+-+ -~++.-±+ + +

+

la)

Electroosmotictransport ofElectrolyte

•.. /1-Pore :

Membrane

lb)Fig. 8.2. Schematic representations of: (a) electrophoretic transport of a negatively chargedparticle in an electric field; and (b) electro-osmotic transport through a single pore of a

negatively charged membrane.

8.3.2 Electro-osmosis

The transport of a liquid relative to an immobile charged surface by anelectric field, for example, the movement of water through a capillaryunder the influence of a potential gradient. In the present context,electro-osmosis could occur through the charged pores of a membrane(Fig. 8.2b) or through the charged porous matrix formed by a filter cake orgel layer deposited on the membrane surface. The velocity of movementwill be determined by the electric field gradient and what may be termedthe electro-osmotic mobility of the porous matrix,

(8.5)

where De is the electro-osmotic velocity and Ue the electro-osmotic mobility. If the radius of the pore is much larger than the double layer thickness(Kr ~ 1, where r is the pore radius), then as shown by Smoluchowski (1914)the electro-osmotic flow rate may be related to the zeta-potential of theporous medium by

(8.6)

Aspects of Microfiltration and Ultrafiltration 269

where V.O is the volume flow rate, ] is the current density and 20 isthe bulk electrolyte conductivity. This condition will usually hold formicrofiltration of biological process streams, but not for ultrafiltration.The equation shows that the rate of electro-osmosis is greatest for highzeta-potential in low conductivity solutions. If the restriction on Kr is notmet then electro-osmotic flow rates must be related to zeta-potential by

(8.7)

where F is a function of Kr and ( must be evaluated by numerical methods.See for example Levine et at. (1975) and James and Williams (1992).

8.4 MEASUREMENT OF ELECTROCHEMICAL PROPERTIES

Electrophoretic mobilities can be determined using a number of commercially available instruments. The simplest require direct visual observation of individual particles (e.g. microbial cells) migrating under a knownpotential gradient. The light scattered from the particles is observedthrough a microscope and the time taken to migrate a known distancerecorded. Such a system is effective but time consuming. Fully automatedinstruments make use of various optical principles. For example,measurement of quasi-electric light scattering and the resulting dopplerfrequency shifts due to particle motion can be used to calculate amobility distribution. This and simpler systems are limited to very dilutedispersions with dispersed materials of sizes greater than 20-50 nm.Measurements on more concentrated samples require gravimetric determination of electrophoretic transport. Measurements on macromoleculesin free solution are best carried out by the moving boundary method (seeShaw, 1969).

Equipment specifically designed for determination of the electro-osmotic mobility or zeta-potential of intact membranes is not readily availablecommercially. However, various types of equipment have been describedby Bowen and Clarke (1984) and Lee and Hong (1988). A simpleapparatus allowing such determination is shown in Fig. 8.3. Application ofa constant current between an electrode positioned behind a membraneand a counter electrode induces flow into a tube. A small peristaltic pumptransfers these extracts to an electronic balance. The electro-osmoticmobility is obtained directly, and the zeta-potential calculated from theratio V.o/] (electro-osmotic flow rate/current density). The same techniquehas been used by Bowen and Jacobs (1986) to determine the electroosmotic properties of layers deposited on membranes. As discussed and

270 W. R. Bowen

r Electro-osmotically transportedelectrolyte to pump and balance

Conductivity probe

f+--+-Electrode connection

,----d/_---- ....1

(

f--- Outer vessel wall+-- Water jacket at 25°C

j~II--r--lnner vessel wall

pH Probe

Level sensors

Capillary

Membrane(electrode

behind) J f:!I ~-:- Circular platinum

~==_=_-_-, ~~ '...../ electrode

I, I. 63mm J• 90mm .1

EEo~

Fig. 8.3. Equipment for the determination of the electrokinetic properties of membranes(after Bowen and Cooke (1991)).

demonstrated by Ibanez et al. (1988) and Nystrom et al. (1988), membranesmay also be electrochemically characterised by streaming potentialmeasurements, measurement of the potential generated when an electrolyte is flowed under pressure through the membrane. The nature andnumber of charged groups at membrane surfaces may be quantified bymeans of surface pH titration (Bowen & Hughes, 1991 ).

The surface electrochemical properties of membranes are determinedby the nature of the membrane materials, the manufacturing conditions and the environment in which they are used. There are differencesin zeta-potential even for membranes of the same material but different pore size due to the variation in manufacturing conditions whichdetermines the pore size (Bowen & Cooke, 1990, 1991). Surface electrochemical properties are sometimes chemically modified in order toachieve specific operating characteristics, for example, minimum membrane fouling.

Aspects of Microfiltration and Ultrafiltration

8.5 ELECTROCHEMICAL EFFECTS IN CONVENTIONALMEMBRANE PROCESSES

27\

As all membranes and most dispersed materials bear a surface charge, itmay be expected that electrochemical effects play a significant role inconventional ultrafiltration and microfiltration processes. This is indeed thecase. For example, careful control of pH is important in the membraneprocessing of protein solutions so as to prevent the precipitation of proteinon the membrane surface, which is most likely at the pI of the protein (thepH at which it has zero net charge). Also, when an electrolyte flows througha charged porous medium a streaming potential is established whichproduces a net backflow of liquid by the electro-osmotic effect. The net effectis a reduced flow in the forward direction, an example of an electroviscouseffect as described by Hunter (1981). The effect is quantifiable and readilymeasureable, being greatest at high zeta-potential and low ionic strength(Table 8.1) (Bowen & Goenaga, 1990). However, for most processes, andprobably all biotechnological processes, this reduction in permeation rate issmall compared with losses due to solute/membrane interactions.

Table 8.1Variation of Electrolyte Permeation Rate with Ionic Strengthat pH 8 for CapilIary Pore Microfiltration Membranes

(Anopore, 0·2 j.lm) (after Bowen and Goenaga (\990))

Ionic strength J (mh- / ) R m x /0-11 (m- I )

(M)

R.O \·926 2·9310- 4 \·937 2·9\10- 3 \·964 2'8610- 2 2·024 2·7910- 1 2·057 2·74

Note: Reverse osmosis water (R.O.) is pH 6·8.J corrected to !1p = \OOk N m - 2

Some important examples of interactions controlled by surface electrochemical properties areas are described in the following sections.

8.5.1 Electrocoat Paint Recovery

Electrocoat paint recovery was one of the first major uses of ultrafiltration and is still important (Cheryan, 1986). There are two types ofelectrocoating process: anodic deposition, where the item to be painted ispositively charged and the paint negatively charged, and cathodic deposition where the item to be painted is negatively charged and the paint

272 W. R. Bowen

positively charged. Ultrafiltration is used for the recovery and recycling ofundeposited paint which is essential to the economic operation of theprocess. Over a hundred such units are in use. Successful operation requirescareful selection of membrane and operating conditions. For paints used inanodic deposition it is best to use membranes that are negatively charged.However, paints used in cathodic deposition foul such membranes veryrapidly due to the charge-interaction between the positively charged paintand the membrane surface. In this case much better performance is obtainedwith positively charged membranes. Correct choice of membrane allows theprocess to operate at a constant permeation rate for many months.

8.5.2 Adsorption of Proteins

Adsorption of proteins on ultrafiltration membranes leads to a reductionin membrane permeation rate and modification of the rejection properties(see, for example, Matthiasson, 1983). The ionic environment in theprocess feed influences adsorption, pore blocking and deposition ofproteins and other macromolecules (Masse et al., 1988). From a technological point of view, adsorption of proteins at microfiltration membranescan be a more significant phenomenon than adsorption at ultrafiltrationmembranes as in the former case proteins are more often required to betransported through the membrane. The internal surface area of membranes is 2-3 orders of magnitude greater than their planar surface area. Anumber of factors are important in determining the amount of proteinadsorbed, including the magnitude and sign of charge of both protein andsurface and the degree of hydration of the protein. In some caseselectrostatic effects are dominant, the protein showing the greatest tendency to adsorb when it has a net charge of opposite sign to the surface. Inother cases the degree of hydration is most important. Maximum adsorption then occurs at the pI of the protein where the degree of hydration isminimum allowing short range attractive forces to come into play. This isanalogous to protein precipitation.

Figure 8Aa shows how the zeta-potential of an inorganic membranedepends on pH (Bowen & Hughes, 1991). The dependence on pH of theamount of the protein bovine serum albumin (BSA) adsorbed on such amembrane is shown in Fig. 8Ab (Bowen & Hughes, 1990). This is anexample of both electrostatic and hydration effects having a role to play.The isoelectric point of the protein is at pH 4·9. At pH 6·5 both membraneand protein bear a negative charge. The charge on the protein decreases asthe pH approaches its isoelectric point, and the amount of adsorbedprotein increases. Between pH 4·9 and 4·5 the protein has a net positivecharge and the membrane a net negative charge. However, there is no


80.---.-----,..----.--r----,--,-...,

> 40E"-1 0 I-----Q----------lc:~g, -40to4iN -80

3.0 4.0 5.0 6.0 7.0 80 9.0pH

273

(bl 3.0 4.0 5.0pH

6.0 7.0

Fig. 8.4. (a) The variation of zeta-potential with pH for a 0·2-~m capillary pore membrane(Anopore) in 1O- 2 MNaCI solution. (0) calculated using eqn (8.6); (0) numericallycalculated value (after Bowen and Hughes (1991)). (b) The variation with pH of the amountof BSA adsorbed at the same type of membrane. Initial solution protein concentration

0.1 gl-I (after Bowen and Hughes (1990)).

increase in protein adsorption, but rather a small decrease which mayreflect an increase in protein size due to increasing hydration. At pHvalues below pH 4·5 both protein and membrane are positively charged.Here the amount of protein adsorbed decreases rapidly as electrostaticrepulsion dominates.

8.5.3 Rejection at Ultrafiltration Membranes

Rejection at ultrafiltration membranes can also depend strongly on themembrane and solute electrochemical properties. The effects have beenbest studied with membranes of MWCO (molecular weight cut oft) atleast an order of magnitude greater than the molecular weights of thesolutes to be rejected. In such cases, rejection is low at the isoelectricpoint of the solute, and high at a pH at which the solute has the sameoverall sign of charge as the membrane. Fractionation of mixtures of theproteins myoglobin (mol. wt 175(0) and cytochrome C (mol. wt 12400)using charge modified polysulphone membranes is a well-studied case

274 W. R. Bowen

(Nakao et ai., 1988). At the isoelectric point of cytochrome C, myoglobinhas a net negative charge. Under such conditions, myoglobin was 80%rejected at a negatively charged membrane whilst cytochrome C permeated completely through the membrane. Conversely, at the isoelectricpoint of myoglobin, cytochrome C has a net positive charge and was 20%rejected at a positively charged membrane whilst the rejection of myoglobin was almost zero.

It is also possible to fractionate smaller molecules by using electrochemical effects. Studies of the rejection of amino acids (mol. wt 70-200)at negatively charged polysulphone membranes (MWCO 10 000) byKimura and Tamano (1986) have shown that, under comparable conditions, acidic amino acids were very well rejected, neutral amino acidspoorly rejected and basic acids about 50% rejected. The basic amino acidswere also adsorbed on the membrane giving reduced permeation rates.Hence, by manipulating pH it is possible to control rejection, which is lowfor the neutral form and increases on both sides of the isoelectric point.Such control allowed the fractionation of mixtures, for example, 85%rejection of i-aspartate (mol. wt 173) with only 15% rejection of iisoleucine (mol. wt 131).

8.5.4 Membrane Filtration of Colloidal Materials

The membrane filtration of colloidal materials is influenced by particleelectrochemical properties in a number of ways. The formation of layers ofparticulate materials on the membrane surface, 'filter cakes', can beimportant in microfiltration and also ultrafiltration. The specific resistanceof such cakes can be a function of the charge properties of the particles.Figure 8.5 shows the results of an analysis of data for the constantpressure, unstirred ultrafiltration of colloidal silica (r = 12.1 nm). Thedependence of the specific cake resistance (~) on particle zeta-potential

cB

so~ 40

.§ 30"~: 20

-;; 10

~O"----_L-------JL-------'_-----'_-----JL-------J20 40 60 80 100

Zeta potential/mY

Fig. 8.5. Effect of zeta-potential on the specific resistance of colloidal silica filter cakes(after McDonogh et al. (1984».

Aspects oj Microfiltration and Ultrafiltration 275

(varied by addition of salts and pH adjustment) shows three distinctregions. In region A, 0( increases with increasing zeta-potential due todeflocculation, and hence reduction in the effective size, of the particles inthe cake (0(=f(r 2 ». In region B, increasing zeta-potential gives areduction in 0( as the repulsive force between the deflocculated particlesincreases giving a more open cake. The solid lines in this region are amodel prediction (McDonogh et al., 1989). At the highest zeta-potentials,in region C, there is an increase in 0( with increasing zeta-potential due tothe effect of electro-osmotic counterflow. As can be seen from the Fig. 8.5,these effects can give rise to an order of magnitude variation in the specificcake resistance.

It has also been shown by McDonogh et al. (1989) that the factors whichcontrol concentration polarisation in cross-flow ultrafiltration may becharge dependent. In the conventional film theory the polarised layer isdescribed as arising due to the convective transport of particles to thesurface and their diffusive back-transport into the process stream. However, charged particles will experience an extra force, electrostatic repulsion, as they are brought closer together in the polarised layer. It has beenshown that the effect of the electrostatic force on a particle may bedescribed by an equation of the form

J = k In(Cm/Cb ) +k f: (PeAp/kB T) dx (8.8)

where k is the mass transfer coefficient, Cb the bulk particle concentration,Cn the particle concentration at the membrane surface, f> the thickness ofthe boundary film, P e the electrostatic pressure, A p the projected area of aparticle, kB the Boltzmann constant and T the temperature. The first termon the right hand side of the equation is the usual film-theory term. Thesecond term is a representation of the electrostatic enhancement inultrafiltration flux. This latter term is a function of particle zeta-potentialand ionic environment. Figure 8.6a shows theoretical predictions ofultrafiltration flux as a function of zeta-potential for small particles atthree ionic strengths. There are very substantial differences between thepredictions from the film theory and this electrostatic interaction model.Figure 8.6b shows comparative predictions of ultrafiltration flux as afunction of particle size. Flux augmentation due to electrostatic effects ispredicted to be very significant for a < 100 nm. For a > 10 Jlm the effect ispredicted to be negligible, although for such particles diffusion is unlikelyto be the dominant back-transport mechanism. Comparison with someexperimental fluxes is shown in Fig. 8.6c. Values predicted using theelectrostatic interaction model follow the trends of the experimental data,though with an underestimation of flux at low zeta-potentials and an

276 W. R. Bowen

- 400N~'f;-'~200:>

u::

(a)10 20 30 40

Zeta potential/mY50

:.c 10''e-'~ 10:>

u::

(b)

0.1 l..l.-__L-_-.J..-=-_--'-:-__~

10' 102 10'

Radius/nm

200

,NL:.

'e-'100"-><:>

u::

10 20 30Zeta potential/mY

Ie)Fig. 8.6. Comparison of electrostatic interaction model with conventional film theory.(after McDonogh et al. (1989)). (a) Comparison of conventional theory (0) with the addedeffect of electrostatic interaction (solid lines). a= 12·1 nm, Cb =0'3% (vjv). (b) Dependenceof predicted flux in cross-flow as a function of particle size. (A) conventional film theory;(6) including effect of electrostatic interaction. (c) Experimental cross-flow ultrafiltrationfluxes (dashed lines), «0) Re = 78; ( x ) Re = 140; (+) Re = 2(0) compared with theoreticalfluxes (full lines) at Re = 78 (0,.) and Re =200 (6, A) (conventional theory as open

symbols and electrostatic interaction theory as closed symbols).

overestimation at higher zeta-potentials. The conventional film modelunderpredicts at all zeta-potentials and is in error by a factor of seven atthe higher zeta-potentials. According to Bowen and Goenaga (1990) suchelectrostatic enhancement of backtransport may also explain why for thecross-flow microfiltration of larger polydisperse particles the specificresistance of the cakes formed shows that they contain fewer smaller (morehighly charged) particles as filtration progresses. Overall, this is a complextopic in need of further elucidation.

The main ways in which electrochemical properties can influenceconventional microfiltration and ultrafiltration are summarised in Table8.2.


Table 8.2Summary of Electrochemical Effects in Conventional Microfiltration and Ultrafiltration

Controlled by properties of dispersed materials in process feedDeposition at membrane surfaceHydrodynamic resistance of filter cakes or gelsElectrostatic flux enhancement

Controlled by membrane propertiesElectroviscous flux reduction

Controlled by interaction of membrane and dispersed materialsAdsorption of macromoleculesMembrane foulingMembrane rejection characteristics

8.6 THEORY OF CONVENTIONAL ELECTROFILTRATION

As surface electrochemical effects can have a substantial influence on theperformance of solely pressure driven membrane processes, it is a logicaldevelopment to consider the effect of the application of externally appliedelectric fields on membrane processes. In conventional electrofiltration acontinuous and constant electric field is applied across the membrane andthe process feed, usually by the incorporation of electrodes behind themembrane and on the opposite wall of the feed compartment of themembrane module.

For any filtration process, the filtration flux may generally be describedby an equation of the form

(8.9)

where i1p is the pressure driving force and R, is the sum of the resistancesto flow. For the case of cross-flow filtration, this total resistance may bewritten in the form,

(8.10)

where Rm is the membrane resistance and Rc the resistance of depositedlayers (cake or gel). Rr is the film resistance, which may be written

(8.11 )

where the first term in the denominator on the right hand side describesdiffusive back-transport and Dr is the particle radial migration velocity. Ineqn (8.10) the film resistance is multipled by the pressure driving force asin the case of film control the flux should be independent of the drivingforce.

278 W. R. Bowen

Cross-flow electrofiltration may be treated theoretically as cross-flowfiltration with superimposed electric fields. The electrical effects includeelectrophoresis of dispersed materials and electro-osmosis in the membrane and the filter cake. This leads to changes in the resistance terms ofegn (8.10). Thus, considering first electrophoretic transport of particles,egn (8.11) becomes

(8.12)

where egn (8.4) has been used. In the case of electrofiltration the membrane resistance includes both the effects of membrane permeability andelectro-osmosis, for the pore walls of almost all membranes are charged.Two membrane resistances may be specified,

and

J Om = /!ip/J1Rom (8.13)

(8.14)

where J Om is the flux through the membrane in the absence of an electricfield (with Rom the corresponding membrane resistance) and J m is the fluxin the presence of an electric field. If the contributions due to permeabilityand electro-osmotic effects are assumed to be additive

J m =JOm + uemE (8.15)

where egn (8.5) has been used and Uem is the electro-osmotic mobility ofthe membrane. Combining egns (8.13), (8.14) and (8.15) gives

(8.16)

If the resistance of any cake is assumed to be constant, then it is possible towrite an analogous expression for the effects of electro-osmosis on theresistance of the cake when an electric field is applied,

(8.17)

where Roc is the cake resistance in the absence of an electric field, Uee is theelectro-osmotic mobility of the cake and JOe is the flux through the cake inthe absence of an electric field.

These modified resistances may then be applied directly in egns (8.9) and(8.10) to give an overall expression for steady state electrofiltration. It isalso possible to develop descriptions of electrofiltration based on modifications of the osmotic pressure model of ultrafiltration described inChapter 3. This has been done by Vivoni-Assice (1989).

The concept of the critical voltage gradient, Ee , is important in understanding conventional electrofiltration. The critical voltage gradient is the

Aspects oj Microfiltration and Ultrafiltration 279

voltage gradient at which the net particle migration toward the membraneis zero. That is, at the critical voltage gradient there is a balance betweenthe convective transport of dispersed materials toward the membrane andthe electrical, diffusive and radial migration away from the membrane.Following Henry et al. (1977) and Henry (1984) three distinct regimes ofoperation may then be defined.

(a) The voltage gradient is less than the critical. There is still a netmigration of dispersed materials toward the membrane. A cake orgel layer is formed and increasing the cross-flow velocity increasesthe rate of filtration.

(b) The voltage gradient is equal to the critical voltage gradient. Herethere is no diffusive transport as there is no concentration gradient.

(c) The voltage gradient exceeds the critical voltage gradient. Theelectrophoretic migration velocity is greater than the convectiveflow. The concentration of dispersed materials is lowest next to themembrane. Increasing the cross-flow velocity will decrease the rateof filtration if the dispersed materials are small and diffusiveback-transport is important. When the dispersed materials are largeand radial back-transport is important, increasing the cross-flowvelocity will still increase the filtration rate.

An understanding of these regimes is important in the operation ofelectrofiltration processes. The use of electrofiltration in these differentregimes is also of value in fundamental studies as they provide a means ofseparately quantifying the effects of concentration polarisation and cake orgel formation in cross-flow filtration (Vivoni-Assice, 1989).

An analysis of particle trajectories during electrofiltration has also beencarried out by Wakeman and Tarleton (1987). This study assumed that flowwas fully developed and laminar, that the filtration rate was constant alongthe length of the membrane module and that the pressure gradient normal tothe porous surface was negligible. The Navier-Stokes equation was thenused to provide axial and radial fluid velocity profiles for tubular and flatsheet modules, and the Laplace equation was used to give the distribution ofelectrical potential. Calculations were then carried out on the trajectories ofparticles introduced at one end of the laminar space. The magnitude of thereduction in deposition on application of an electric field was quantified.

8.7 ELECTROFILTRATION MODULE DESIGN

Electrofiltration modules may be of tubular, flat sheet or spirally woundconfigurations. The essential features of conventional membrane modules

280 W. R. Bowen

are still required. In addition, electrodes and a means of connecting theelectrodes to a power supply have to be introduced. In many cases themembrane support may form one of the electrodes. This is often ofstainless steel, which is an excellent cathode material. The best anodematerials are titanium electrodes coated with a thin layer, just a fewmicrometers thick, of a noble metal such as platinum. Such electrodes arealready widely used in the chlor-alkali industry and for the protection ofoff-shore oil installations.

Electrolysis will take place at the electrodes when an electric field isapplied. The most likely cathode reaction is

2HzO+2e--+Hz+ 20H- (8.18)

Nobler metals such as Cu, Hg, Ag or Au may deposit on the cathode ifthey occur in significant concentrations, though this is rare. The mostlikely reaction at an electrochemically stable anode is

(8.19)

Electrolysis in feeds containing chloride may produce chlorine gas depending on the kinetics at the surface of the electrode. Provision should hencebe made for allowing the escape of gas at both the anode and the cathode.If the process feed or permeate are sensitive to pH changes or gasevolution it will be necessary to isolate the electrodes by means ofion-exchange membranes, as is the practice in the design of electrodialysisstacks.

The design of a simple flat sheet electrofiltration module suitable fortest-rig studies is shown in Fig. 8.7. The process feed compartment is 41 cmlong, 3.5 cm wide and 0.4 cm deep. Polymeric or inorganic membranes aresupported on a stainless steel mesh which also serves as an electrode. Themesh rests on a ring which runs along the outer wall of the permeatechamber. The counter electrode, a platinised titanium mesh, lies flush with

To permeateconnection

L--.,.L~..;!T,--,

\Stainless steel

connector(to contact ring)

Membrane

Stainless steel mesh

Gaskets

Titanium connector

~__~ ~_to_'l_e)__A__E+\'_tr_o_de -----,

Fig. 8.7. Design of a flat sheet electrofiltration module (after Bowen et al. (t989a».


the outer wall of the process feed compartment. Multiple membranechambers may be constructed between a single pair of electrodes by meansof a plate and frame arrangement (Visvanathan & Ben Aim, 1990).

8.8 APPLICAnONS OF ELECTROFILTRAnON

Three major goals in the development of pressure driven membraneprocesses are the reduction of concentration polarisation, the reduction ofthe effects of membrane fouling and the improvement of the selectivity ofthe processes. Progress toward these goals can be made by carefulselection of membranes, close attention to process operating conditionsand the use of hydrodynamic control effected by pulsated feed flows ornon-planar membrane surfaces. However, it is clear from the preceding analysis that the use of applied electric fields can also potentiallyfacilitate the achievement of these goals. This section considers somespecific examples, with attention being directed to applications in biotechnology.

8.8.1 Convention Electrofiltration

The formation of gel layers is one of the limiting factors in the ultrafiltration of biological materials. This is one of the reasons for studying theelectrofiltration of such materials. Such use of continuously appliedelectric fields was termed electro-ultrafiltration by Rios et al. (1988). Adetailed study has been made for the case of solutions of gelatin byYukawa et al. (1983) using a tubular electrofiltration mo)dule. The relationbetween the total filtration flux and the filtration time is shown in Fig. 8.8aat several electric field strengths. In all cases a steady state was reachedwith the filtration flux at the highest field strength used being three timesthat for conventional cross-flow filtration. It was considered that thefalling flux period corresponded to the gel forming period (Ee > E) and thatthe steady state corresponded to a period when the transport of gelatintoward the membrane due to convection became equal to the transport inthe reverse direction due to diffusion and electrophoresis (E e = E). Therelationship between filtration flux and electric field strength was linear(Fig. 8.8b). It was understood that the slopes of these straight linesrepresented the electrophoretic mobility of the gelatin (see eqns (8.9), (8.10)and (8.16)). It was thought that these slopes and the intercepts variedbecause both the mass transfer coefficient and the electrophoretic mobilityvaried with the filtration flux. Changes in pH or degree of proteinaggregation may have been responsible for the latter effect.

282 W. R. Bowen

20

- ~..'" 15 1:Si~'UI'i/lJlfJcrrf\11'i1m"WV,"","W""W,,",,'iIW"""iJ'i!'il'V'iIW

E 0:::::: 10 ~oooooooooooooooooooooooo

"' fj~MMMM"MMMMMl'.e 5 0 00000000000000000000000000x

~ 0 '------'--,-----'-:-_--'------".L---,J'-------'----'o 600 1200 1800 2400 3000 3600

(al tis

E (Vim)

o 0

336 (;553 0

910 'iI

30

E",'5. 2.0

ex~ 10

olbl

500 1000 1500E/(V m-1

)

[b Ikg/m3J

5.0 0

7.5 t:.10.0 0

15.0 'iI

Fig. 8.8. Ultrafiltration and electrofiltration of gelatin solutions (after Yukawa et al.(1983)). (a)Time dependence of the permeation rate. ~p=203kNm-2; Cb =7·5kgm- 3

;

cross-flow velocity =0'8 m s- I; T = 38°C. (b) Relationship between applied field strengthand permeation rate.

Pressure driven membrane processes are designed to separate in termsof the size of dispersed materials. However, due to mutual interactionsbetween materials in the process stream and between the dispersedmaterials and the membrane surface, effective fractionation often requiresan order of magnitude difference in size. Membrane fractionation ofbiological materials could be a very exciting commercial prospect. Aselectrofiltration manipulates materials in terms of electrophoretic mobilityin addition to size, attention has been directed toward the possibility ofachieving fractionation. For example, fractionation of the blood proteinsbovine serum albumin and y-globulin has been studied as a function of pHby Radovich and Sparks (1979) and Radovich et al. (1980). The magnitudeof the retention (R) of a charged macrosolute in a single solute solutionalways increased when an electric field of the appropriate polarity wasapplied (R=I-(Cu /Cr ) where Cu and Cr are the bulk concentrations ofthe ultrafiltrate and retentate). For mixtures, the membrane's ability todiscriminate between different solutes was defined in terms of a selectivityfactor (ex1 =(I-Rd/(I-Rz ), where R 1 and Rz are the retention factors ofeach solute). At a pH 8'2, where both proteins are negatively charged,application of an electric field improved the retention of both proteins


but did not change the selectivity factor. At a pH of 4'7, where the albuminis slightly positively charged and the globulin negatively charged, application of an electric field of 390 V m - I increased the retention of globulin(from 0·927 to 0'976), decreased the retention of albumin (from 0·641 to0'59), and hence increased the value of (XI from 4·9 to 17·1. This typeof separation is of great importance in the production of pure bloodproducts.

8.8.2 Pulsed Electrophoretic Cleaning

Although conventional electrofiltration can be a very successful means ofimproving the performance of membrane separations, it has severaldisadvantages. These include a relatively high energy requirement, possibly substantial heat production and changes in the process feed due toreactions at the electrodes. The establishment of electrically enhancedmembrane processes as acceptable unit operations will require the minimisaton of energy use and heat production. The latter is especiallyimportant in the processing of biological materials. The use of suchprocesses will also be facilitated if they can be carried out in modulesclosely comparable to those used conventionally for cross-flow microfiltration and ultrafiltration (as shown in Fig. 8.7, for example).

For these reasons, attention has been directed by Wakeman andTarleton (1987) and Bowen and Goenaga (1989) to the use of pulsedelectric fields. If relatively infrequent pulses are effective, then the maindrawbacks of continuous field application can be substantially diminished.In microfiltration, it is especially materials deposited on the membranesurface, filter cakes, that provide the main hydrodynamic resistance toflow. Such materials often retain a surface charge and hence an electrophoretic mobility. It is therefore possible to remove such materials by theperiodic application of electric field pulses. This process is termed pulsedelectrophoretic cleaning. Figure 8.9 shows a comparison of cross-flowmicrofiltration with and without such cleaning for the filtration of Baker'syeast dispersions. In the case of the pulsed electrophoretic cleaning, pulsesof 10 s, duration were applied periodically throughout the process, thoughthe electric field was only applied for 2% of the overall process time. Avery substantial improvement in the rate of filtration is apparent.

8.8.3 Electrolytic Membrane Cleaning

Electrolytic membrane cleaning is another process that makes use of pulsedelectric fields, though its primary mode of operation is quite distinct frompulsed electrophoretic cleaning. As reported by Bowen et ai. (1989b) it

284 W. R. Bowen

----------

o0 L-_----'__----'__----'__----'

L: 02E

"OJ

~r:::~ 0.1~

u:::

o 50 100 150 200

Time/min

Fig. 8.9. Pulsed electrophoretic cleaning during the filtration of Baker's yeast dispersions.(-- -) pulsed field; (-) no field. Yeast concentration 10 gl-l at pH 4·5 in 1O- 2 M KN0 3solution, cross-flow velocity 0·9 m s- 1, tip = l00kN m - 2 (after Bowen and Goenaga (1989)).

makes positive use of what in some circumstances is a disadvantage, gasevolution at the electrodes. In this case an electric field pulse is applieddirectly to an electrically conducting membrane, such as a stainless steelmicrofilter. This causes the formation of microbubbles at the membranesurface which push foulant material into the feed stream. The foulantmaterials are then carried along by the cross-flow and also electrophoretically transported away from the membrane surface by the applied electricfield. Microbubble cleaning of surfaces is very effective as the cleaningprocess is initiated at the interface between the surface and the foulantrather than at the interface between the foulant and the solution, the latterbeing the case with back flushing of chemical cleaning.

Data from a test-rig study of the cross-flow microfiltration of Baker'syeast dispersions is shown in Fig. 8.10. The upper curve (a) is for normalcross-flow filtration where no cleaning is applied during the experiment.The time to collect a given volume of permeate increases greatly during theexperiment. The lower curves show how in-situ membrane cleaning maycombat membrane fouling and maintain permeation rates. Thus, in curves(b), (c) and (d) the collection times have been maintained at nominally lessthan 200, 100 and 50 s, respectively, by the application of voltage pulses atthe peaks of the saw teeth. In all cases the pulses were of 0·92 kA m - 2 witha duration of 7·5 s. As a result, the average permeation rates for theduration of the test runs were, (a) 321m- 2 h- l , (b) 1841m- 2 h- l , (c)2661 m - 2 h - 1, (d) 300 1m - 2 h - I. Hence, a very substantial improvementin the filtration flux is achieved for a modest input of electrical energy.

The use of pulsed field techniques also has an important capitaladvantage. As the electric field is applied for only a small percentage of theoverall process, typically 2-10%, it is possible to clean modules sequentially so reducing the required power supply capacity. A related process,in-situ membrane restoration, can give very effective cleaning of filters after

600

500

400

300'""2 200co<lJ

~ 100a.-'E

C>

i:t~<lJE

~::~

285

1 2 3 4

Tot al permeate volume/L

Fig. 8.10. Application of electrolytic membrane cleaning in the filtration of Baker's yeastdispersions. (a) no cleaning, and cleaning pulses (0'92 kA m - 2 for 7·5 s) applied at nominalminimum permeation rates of (b) 50 ml/200 s, (c) 50 ml/100 s, (d) 50 mlj50 s. Yeast concentration 50gl- 1 in at pH 4·5 in 1O- 2 MKN03 solution, cross-flow velocity 1'43ms- 1

,

~p=67'5kN m- 2, (after Bowen et al. (1989b)).

use by the application of current pulses while circulating a clean electrolytesolution at neutral pH through the membrane module.

8.8.4 Electro-osmotic backwashing

It is well known that substantial improvements in membrane performancecan result from temporary reversal of mass flow through the membrane,backwashing. Mechanical reversal of flow can be complex, so the use ofelectric fields to produce such reversal is a potentially attractive alternative. This type of process was first applied to reverse osmosis membranesby Spiegler et al. (1981). Both electro-osmotic and osmotic backwashingwere considered and collectively termed molecular washing. The electricallydriven process was found to be most effective and had the importantadvantage that only periodic application of the electric field was required.

An innovative process development based on electro-osmotic backwashing, though with the continuous application of the electric field, isshown in Fig. 8.11. The process feed is fed to alternate membrane pairs.Under the influence of the applied electric field, negatively charged

286

Filtrate

Cathode

W. R. Bowen

Concentrate

+ Anode

Feed

Electrolyte

M- Ultrafiltration membraneC - Ion permeable cellulose membrane

Fig. 8.11. Multiple stack cross-flow electrofiltration and electro-osmotic backflushingequipment with frequent polarity reversal arrangement (after Visvanathan and Ben Aim

(1990)).

particles are electrophoretically transported away from the membrane onthe cathode side of the pair, reducing concentration polarisation. However, they are at the same time transported to and deposited on themembrane on the anode side of the pair. Hence, to run the processeffectively, the polarity of the electrodes is reversed at a frequency in therange of 0·1-2·0 Hz. This prevents excessive deposition of particles on themembrane surface, and the induced electro-osmotic flow backwashes themembrane and creates a perturbation in the boundary film. Results fordispersions of inorganic colloids have shown that this process can give adoubling of the membrane flux compared to a purely pressure drivenprocess.

The main types of electrically enhanced microfiltration and ultrafiltration processes are summarised in Table 8.3.

8.8.5 Conclusions

Electrochemical effects can playa major role in determining the performance of conventional microfiltration and ultrafiltration processes. Inoptimising such processes it is always beneficial to consider the nature andmagnitude of electrochemically controlled interactions in the process feedand between components of the process feed and the membrane. Suitablemethods for the electrochemical materials characterisation are available. Atheoretical analysis of the process significance of the various phenomena isbeing established.

The application of external electric fields can give substantial improvements in the performance of cross-flow microfiltration and ultrafiltration

Tab

le8.

3M

ain

Typ

esof

Ele

ctri

cally

Enh

ance

dM

icro

filt

rati

onan

dU

ltra

filt

rati

onPr

oces

ses

Pro

cess

nam

eN

atur

eo

fM

embr

ane

Spec

ial

adva

ntag

esel

ectr

icfie

ldty

pe

Con

vent

iona

lC

onti

nuou

sP

olym

eric

orR

educ

tion

inco

ncen

trat

ion

pola

risa

tion

elec

trof

iltr

atio

nin

orga

nic

and

foul

ing,

impr

oved

sele

ctiv

ity.

Pul

sed

elec

trop

hore

tic

Pul

sed

Pol

ymer

ico

rR

educ

tion

info

ulin

g,lo

wpo

wer

cons

umpt

ion,

clea

ning

inor

gani

cm

inim

alch

ange

sin

feed

due

toel

ectr

olys

is.

Ele

ctro

lyti

cm

embr

ane

Pul

sed

Ele

ctri

cally

Red

ucti

onin

foul

ing,

low

pow

erco

nsum

ptio

n,cl

eani

ngco

nduc

ting

wor

ksin

all

cond

ucti

vity

rang

es.

Ele

ctro

lyti

cm

embr

ane

Pul

sed

poly

mer

ic,

inor

gani

cC

lean

ing

ofm

embr

anes

unde

rm

ildch

emic

alre

stor

atio

nor

elec

tric

ally

cond

itio

ns.

cond

ucti

ng

Ele

ctro

-osm

otic

Pul

sed

orpo

lym

eric

orR

educ

tion

info

ulin

g,lo

wpo

wer

cons

umpt

ion,

back

was

hing

cont

inuo

usin

orga

nic

min

imal

chan

ges

infe

eddu

eto

elec

trol

ysis

.

~ ~ '" .Q., ~ ;:;. i :::- ~ o' " tl 5- ~ .g, ~ §. IV 00 .....

288 W. R. Bowen

through reduction of concentration polarisation, control of membranefouling and improvements in membrane selectivity. A number of innovative processes that eliminate the disadvantages of conventional electrofiltration are under development. Pilot plant equipment is in operation in anumber of industries, and such equipment is commercially available.

Finally, it is worth noting that the use of electric fields for somemembrane processes is already well established. The purely electricallydriven process of electrodialysis (that is well described by Lacey (1988» isused on a large scale industrially with over 700 plants in operationworldwide for the purification of brackish water and brine concentrationand with more than 40 plants in operation for the demineralisation ofwhey solids. The engineering knowledge gained in the design and operation of electrodialysis plants should be of significant benefit in the futuredevelopment of electrically enhanced microfiltration and ultrafiltration.

NOMENCLATURE

A p projected area of particle (m2 )

a particle radius (m)Cb solute concentration in bulk (-)Cr bulk retentate concentration (-)Cu bulk ultrafiltrate concentration (-)Cm solute concentration at membrane (-)D dielectric constant (-)E mean electric field gradient (Vm -1)e electronic unit of charge (C)F numerical factor HI current density (A m - 2)J membrane flux (permeation rate) (m s- 1 )

J m membrane flux in absence of electric field (m s- 1)J Oc cake flux in absence of electric field (m s- 1 )

J Om membrane flux in presence of electric field (m s- 1)

ko Boltzmann constant (J K - 1)k mass transfer coefficient (m s - 1 )

np bulk concentration of ions (m - 3)~p hydraulic pressure difference (N m - 2)Pe electrostatic pressure (N m - 2)R rejection or retention coefficient (-)Rc resistance of deposited layers (m - 1)Rr resistance of film layer (m -1 s)Rm resistance of membrane (m -1)


R l total resistance to flow (m - I )

r pore radius (m)T temperature (K)x distance (m)Ue electro-osmotic mobility (m 2 S-l V-I)

Uec filter cake electron-osmotic mobility (m2 s - I V - I)

Uem membrane electro-osmotic mobility (m2 S-I V-I)

up electrophoretic mobility (m2 s - 1 Y- 1)

Veo electro-osmotic flow rate (m s- 1 )

Ue electro-osmotic velocity (m s - 1 )

Up particle velocity (m s - 1 )

Ur radial migration velocity (m s - 1 )

z ion charge (-)

a specific cake resistance (m kg - 1 )

al selectivity factor (-)() thickness of boundary film (m)e electrolyte permittivity (F m - 1 )

eo vacuum permittivity (F m - 1 )

( zeta-potential (Y)Ie (double-layer thickness) - 1 (m - 1 )

,10 bulk electrolyte conductivity (S m - 1 )

J1 viscosity (N s m - 2)

t/J electric potential (Y)

REFERENCES

Bowen, W. R. & Clarke, R. A. (1984). Electro-osmosis at microporous membranes and the determination of zeta-potential. J. Colloid Interface Sci., 97,401-9.

Bowen, W. R. & Cooke R. J. (1990). Properties of microfiltration membranes.Computer automated determination of the zeta-potential of ceIlulose nitratemembranes, Proceedings of the Vth World Filtration Congress, Nice, pp. 231-9.

Bowen, W. R. & Cooke, R. 1. (1991) Properties of microfiltration membranes.Computer automated determination of the electrokinetic properties of polycarbonate membranes, J. Colloid Interface Sci., 141, 280--7.

Bowen, W. R. & Goenaga, X. (1989). ElectricaIly enhanced membrane filtration.Cross-flow microfiltration and e1ectrofiltration at aluminium oxide membranes.Proceedings of the International Congress on Inorganic membranes, ed. L. Cot.and 1. Charpin, MontpeIlier, pp. 411-14.

Bowen, W. R. & Goenaga, X. (1990). Properties of microfiltration membranes.Effect of physicochemical conditions on cross-flow microfiltration at aluminiumoxide membranes. I. Chem. E. Symposium Series, No. 118,8.1-8.12.

290 W. R. Bowen

Bowen, W. R. & Hughes, D. T. (1990). Properties of microfiltration membranes.Adsorption of bovine serum albumin at aluminium oxide membranes. J.Membr. Sci., 51, 189-200.

Bowen, W. R. & Hughes D. T. (1991). Properties of microfiltration membranes.The surface electrochemistry of anodic film membranes. J. Colloid Interface Sci.,143, 252-65.

Bowen, W. R. & Jacobs, P. M. (1986). Electro-osmosis and the determination ofzeta-potential: the effect of particle concentration. J. Colloid Interface Sci., Ill,223-9.

Bowen, W. R., Goenaga, X. & Sabuni, H. A. M. (1989a). Electrically enhancedmembrane filtration-construction and operation of an automated laboratorytest-rig. I. Chern. E. Symp. Series, No. 112, 251-62.

Bowen, W. R., Kingdon, R. S. & Sabuni, H. A. M. (1989b). Electrically enhancedseparation processes: the basis of in-situ intermittent electrolytic membranecleaning (IEMC) and in-situ electrolytic membrane restoration (IEMR). J.Membr. Sci., 40, 219-29.

Cheryan, M. (1986). Ultrafiltration handbook, Technomic Publishing Company,Lancaster.

Fane, A. G. (1986). Ultrafiltration: factors influencing flux and rejection. InProgress in Filtration and Separation, ed. R. J., Wakeman, Vol. 4, Elsevier,Amsterdam, pp. 101-79.

Henry, J. D. (1984). Novel solid-liquid separation processes. In Perry's ChemicalEngineers Handbook, 6th edn, McGraw Hill, New York, pp. 17.51-17.56.

Henry, J. D., Lawler, L. F. & Kuo, C. H. A. (1977). A solid/liquid separationprocess based on cross-flow and electrofiltration. AIChernE J., 23, 851-9.

Hunter, R. J. (1981). Zeta Potential in Colloid Science, Academic Press, London.Ibanez, J. A., Forte, J., Hernandez, A. & Tejerina, F. (1988). Streaming potential

and phenomenological coefficients in Nuclepore membranes. J. Membr. Sci., 36,45-54.

James, A. E. & Williams, D. J. A. (1992). Improved calculation of electrokineticflow parameters for porous media, AIChemE Journal, in press.

Kimura, S. & Tamano, A. (1986). Separation of amino acids by charged ultrafiltration membranes. In Membranes and Membrane Processes, ed. E. Drioli & M.Nakagaki, Plenum, New York, pp. 191-7.

Lacey, R. E. (1988). Dialysis and electrodialysis. In Handbook of SeparationTechniquesfor Chemical Engineers, cd. P. A. Schweitzer, 2nd edn, McGraw-Hill,New York, pp. 1-479-1-495.

Lee, C. K. & Hong, J. (1988). Characterisation of electric charges in microporousmembranes. J. Membr. Sci., 39, 79-88.

Levine, S., Marriott, J. R., Neale, G. & Epstein, G. (1975). Theory of electrokineticflow in fine capillaries at high zeta-potentials. J. Colloid Interface Sci., 52,136-49.

Masse, P., Martinez, P., Verdier, A. & Choe, T. B. (1988). Fouling in ultrafiltrationof macromolecular solutions. The role of ionic environment. Stud. Environ. Sci.,34,235-44.

Matthiasson, E. (1983). The role of macromolecular adsorption in fouling ofultrafiltration membranes. J. Membr. Sci., 16, 23-36.

McDonogh, R. M., Fane, A. G. & Fell, C. J. (1989). Charge effects in thecross-flow filtration of colloids and particulates. J. Membr. Sci., 43, 69-85.


McDonogh, R. M., Fell, C. D. & Fane, A. G. (1984). Surface charge andpermeability in the ultrafiltration of non-flocculating colloids. J. Membr. Sci.,21,285-94.

Nakao, S., Osada, H., Kurata, H., Tsura, T. & Kimura, S. (1988). Separation ofproteins by charged ultrafiltration membranes. Desalination, 70, 191-205.

Nystrom, M., Lindstrom, M. & Matthiasson, E. (1989). Streaming potential as atool in the characterisation of microfiltration membranes. Colloids Surfaces, 36,297-312.

Radovich, J. M. & Sparks, R. E. (1979). Electrophoretic techniques for controllingconcentration polarisation in ultrafiltration. In Ultrafiltration Membranes andApplications, ed. A. R. Cooper, Plenum Press, New York, pp. 249-67.

Radovich, J. M., Mason, N. S. & Sparks, R. E. (1980). Coupling electrophoresiswith ultrafiltration for improved processing of plasma proteins. Sep. Technol.,15, 1491-8.

Rios, G. M., Rakataoarisoa, H. & Tarado de la Fuente, B. (1988). Basic transportmechanisms in ultrafiltration in the presence of an electric field. J. Membr. Sci.,38, 147-59.

Smoluchowski, M. (1914). In Handbuch der Elektriziat und des Magnetismus, ed. B.Graetz, Vol. 2, Liepzig, p. 366.

Shaw, D. 1. (1969). Electrophoresis, Academic Press, New York.Spiegler, K. S. & Macleish, 1. H. (1981). Molecular osmotic and electro-osmotic

backwash of cellulose acetate hyperfiltration membranes. J. Membr. Sci., 8,173-91.

Visvanathan, C. & Ben Aim, R. (1990). Enhancing electrofiltration with the aid ofan electro-osmotic back washing arrangement. Filtr. Sep., 27, 42-4.

Vivoni-Assice, D. (1989). Influence d'un champ electrique continu sur Ie transfertde solvant en ultrafiltration, These du grade de Docteur de I'Universite PaulSabatier, Toulouse.

Wakeman, R. J. & Tarleton, E. S. (1987). Membrane fouling prevention incross-flow microfiltration by the use of electric fields. Chern. Eng. Sci., 42,829-42.

Wijmans, J. G., Nakao, S. & Smolders, C. A. (1984). Flux limitation in ultrafiltration: osmotic pressure model and gel layer model. J. Membr. Sci., 20, 115-24.

Yukawa, H., Shimura, K., Suda, A. & Maniwa, A. (1983). Cross-flow electroultrafiltration for colloidal protein solution. J. Chern. Eng. Jpn., 16,305-11.

Chapter 9

THE USE OF PERVAPORATION IN BIOTECHNOLOGY

H. STRATHMANN* & R. M. McDoNOGHt

Institut fUr Chemische Verfahrenstechnik, Universitiit Stuttgart,Boblinger StrajJe 72, D-lOOO Stuttgart 1, Germany

9.1 INTRODUCTION

One of the major problems in modern industrial scale biotechnology is theseparation, concentration and purification of the bioreaction products.This mass separation task, generally referred to as 'downstream processing', is often particularly difficult. As stated by Wang (1987) this is becausemost microbiological processes are carried out in dilute solutions with theactual product in rather low concentration in mixture with large amountsof water, biomass and other by-products. The relative magnitudes typically encountered in a microbiological production process are shownschematically in Fig. 9.1.

Waste AirWater SUbstrate Air

MicrobiologicalProduction

Processc=~~~~.... Product

Waste Water

Fig. 9.1. Schematic drawing illustrating a typical microbiological production process.

Bioreactor constituents such as microorganism, proteins, enzymes etc.are thermally and chemically very sensitive. Therefore many of the conventional separation techniques, such as distillation, chemical precipitationetc., often cannot be used in downstream processing. Other separation

·Present address: Faculty of Chemical Engineering, University of Twente, PO Box 217,7500 Enschede, The Netherlands.tPresent address: Schleicher & Schuell GmbH, Hahnestrabe 3, W-3354 Dassel, Germany.

293

294 H. Strathmann & R. M. McDonogh

procedures, such as gel-chromatographic, electrophoresis etc., are notsuited for large industrial scale application.

In the search for better and more efficient methods for the downstreamprocessing of bioreactor constituents, membranes are receiving increasingattention. Membrane related processes are particularly suited for applications in large scale bioproduction processes. Their advantages are easy tosee, since they are generally operated at ambient temperature and theseparation is achieved by physical means, there is no thermal stress on, andno chemical alteration of the various components of a mixture. Furthermore, the mass separation properties of membranes can be adjusted over awide range to suit specific requirements. Their use is also relativelyeconomic, the scale of operation having little effect (Lonsdale, 1982).

While, as noted in Chapter 1, membranes and several membraneprocesses, such as micro- and ultrafiltration, have been used for manyyears, others, such as pervaporation, have only recently been introduced.See, for example, Neel (1991), one of the major developers of this process.

Pervaporation is a process which combines the evaporation of volatilecomponents with their permeation through semipermeable membranes. Thecauses of its late introduction to biotechnical separation problems lie bothwith the technology and the application. The process itself has only reachedlarge scale industrial application in the last few years. The application of pervaporation is limited to the separation of volatile components only. Itcannot be applied to the vast majority of commercial bioproducts, such asproteins, enzymes, antibodies, hormones, amino acids because these components do not evaporate readily, they cannot be separated by pervaporation.

There is, however, one area of application where pervaporation couldplay an important role, that is the continuous removal of biosolvents withinhibitory effects on the production rate, such as ethanol, butanol, acetoneetc. from fermentation broths. By integrating a pervaporation unit into abioreactor to selectively remove volatile inhibitory substances Strathmannand Gudernatsch (1991) have shown that significantly better bioconversion rates and lower downstream processing costs may be achieved.

9.2 FUNDAMENTALS OF PERVAPORATION

Before considering the application of this process to the specific realm ofbiotechnology, the principle of pervaporation and the key parameterdetermining its performance shall be summarised. A fuller introduction isgiven in Chapter 3. However, it is considered that some repetition will beuseful for reasons of continuity and because the nomenclature of thischapter is somewhat unusual. The extensive use of super and subscripts

Pervaporation in Biotechnology 295

will, it is hoped, bring greater clarity. A list of symbols is given at the endof the chapter.

9.2.1 Mass Transfer in Pervaporation and its Mathematical Description

In pervaporation the components that vaporise must traverse a selectivebarrier, a semi-permeable membrane, as illustrated schematically in Fig. 9.2.A liquid feed stream containing volatile components contacts a semipermeable membrane separating the liquid from a gas phase. If a driving forceacross the membrane, i.e. a difference in the partial pressure for a volatilecomponent (pfeed > prermeate), is established, the component tends to movefrom the liquid to the vapour phase passing through the membrane phase.

The mass transport of a species in pervaporation can then be viewed asa three-step process schematically shown in Fig. 9.3. Following Neel et at.(1985) we have:

absorption of the component from the liquid phase at the membrane-feed solution interface;diffusion of the absorbed species through the polymer matrix to thegas-membrane interface;release of the species into the gas phase, desorption and evaporation.

Feed Retentale

Permeate

f PPi > PI

Fig. 9.2. Schematic diagram illustrating the operating principle of pervaporation (Pi refersto the partial pressure of a volatile component).

IIII

F~~dMixlur~

X' p~I

TAY

m~mbrQne

1xP pP

I IP~17MQr~

PIII

Fig. 9.3. Schematic diagram illustrating the mass transport in pervaporation.

Mass transport through membranes can be described by variousmathematical relations, varying from the rigorous to the empirical. Thoseinterested in a comprehensive description can consult Strathmann (1990).

In most membrane separation processes of practical relevance only thematerial fluxes are of concern, and direct kinetic coupling of individualcomponents can be neglected. Also in pervaporation no ionic compoundsare transferred. Electrical potential gradients can therefore be neglected asdriving forces. Since the membranes used in pervaporation are of asolution-diffusion type, no convective flux is obtained. Thus the masstransport in a pervaporation membrane can be described as a function ofthe chemical potential gradient only:

(9.1)

(9.2)

Expressing the chemical potential of the component Pi as a function of thestate variables temperature, pressure and composition leads to:

d - MJi=Lid/-siT+ ViP+RTlnai)

where J i is the flux, L i a phenomenological coefficient, R the gas constant,T the absolute temperature, Vi the partial molar volume, P the pressure, sthe partial molar entropy, a the activity and y the directional coordinateperpendicular to the membrane surface. The subscript 'i' refers to thepermeating component.

Since in pervaporation - Si T < ViP ~ R T In ai, the flux of a component'i' through the membrane can following Katchalsky and Curran (1967) beexpressed, to a first approximation, as:

which reduces to:

d MJ.= -L·RT-(ln a· )

I I dy I(9.3)

(9.4)-LjRT da~

J i = M -dai Y

The direction y is perpendicular to the membrane. If a linear variation ofactivity in the direction y perpendicular to the membrane surface isassumed, eqn (9.4) reduces to:

-LiRT L\a~J j = M ~ (9.5)

ai UY

where a~ is the average activity of the component 'i' in the membrane, L\a~

is the activity difference of the component 'i' between the membrane feedand permeate side, and L\y is the thickness of the membrane.


If we assume there to be local equilibria between the membrane surfaceand both the feed and permeate phases, the activity of component 'i' in themembrane can be related to its vapour pressure and concentration in theouter phases.

At the feed-membrane interface:

a~eed = y~eed. x~eed = a~(feed)I • I •

At the membrane-permeate interface:

P!'erm • m!,erm

aperm _. 't' 1 = a~(perm)

j - p? 1

(9.6)

(9.7)

The combination of eqns (9.5), (9.6) and (9.7) gives an expression for theflux of component 'i'. Here aj"(feed) and aj"(perm) refer to the activities of thecompound 'i' in the membrane at the feed solution and the permeatemixture interfaces.

_ L. R T 1 p!,erm. m!,erm _ y~eed. x~eedp9J.= J _.' ..,..... • • I

1 aj" ~y p? (9.8)

Noting that the diffusion coefficient Dj" of component 'i' in the membrane,as defined by Fick's law (Strathmann, 1979) is:

(9.9)

and the distribution or partition coefficient, Sj, between the membrane andadjacent phases of feed and the permeate is given as:

(9.10)

(This is the inverse of Henry's law coefficient, when it is expressed in termsof pressure and molar concentrations.)

Remembering that aj" = yj" C~ V~, equation (9.8) can now be written as

P!'erm. m!,erm _ y~eed. x.p9J.=D~ 1 't'l • • 1

1 1 ~y(9.11)

As noted earlier in Chapter 3 this equation tells us that the molar flux of acomponent 'i' through a dense membrane is determined by its diffusioncoefficient in the membrane and its distribution between the outer phasesand the membrane.


9.2.2 Reliability and Relevance of the Mass Transport Equations

Equation 9.11 describes the mass transport in solution-diffusion membranes for a steady state by a mechanistic model where the key parametersare the diffusivity and the solubility of the various components in themembrane polymer matrix. Thus the transport properties of the membrane depend not only on the intrinsic properties of the polymer but alsoon the conditions of the outside phase. Although the relations expressed ineqn (9.11) seem to be logical, it has to be kept in mind that several grossassumptions have been made in its derivation. This matter was discussedat the end of Section 3.3.4.

9.2.3. Membrane Performance Parameters

In any application the purpose of the membrane is to separate variouscomponents from a mixture with others. So for practical purposes theseparation efficiency of the membrane is a crucial parameter. Despite thelimitations in eqn (9.11), it is used as the basis for the characterisingparameters.

The selectivity of a membrane to various components of a mixtureis defined as the ratio of the permeabilities of the individual components. The permeability of a component 'i', Pi, is defined from eqn (9.11)as

and the selectivity Zi,j of a membrane for i with respect to j is:

p.z· .=-!.

',J p.J

(9.12)

(9.13)

The selectivity is defined to be always larger than 1, i.e. the permeability ofthe permeating component is always in the numerator.

In general, diffusion and partition coefficients and hence the permeabilities of the various components in the membrane are not a constant but afunction of their composition. The selectivity is a useful parameter tocharacterise a membrane and for selecting the proper membrane for agiven separation problem. For design and adapting an actual process to aspecific problem, the actual increase in concentration of a particularcomponent is most important. This is the enrichment factor p:

x~erm

p= x'feed with p~ 1., (9.14)


Different authors report this as a mole fraction or mass fraction ratio. Therelative enrichment or separation factor of two components, (Xij, is definedas:

(9.15)

It should be clear that the enrichment factor Pand the separation factor (X

are related, i.e.:

(9.16)

and:

(9.17)

Obviously, both (Xij and Pi are greater than or equal to 1.For binary systems a further relationship can be developed based on

eqn (9.11). It can be shown that the separation factor, (Xij, is related to themembrane selectivity, Zi.j, by the following equation:

x~eed x~eedy~eedp9 _ xpermppermmpermZ) I 1 1 1 I 'f'1

(Xij = i.j xfeed • x~eedy~eedpO _ xpermpl'erm{lll'erm1 )) ) ) ) 'f')

(9.18)

(9.19)

Equation (9.18) summaries the influences on the separation in pervaporation. This is a convenient equation as it separates membrane behaviourfrom effects due to the feed components. It can be seen that the separationfactor depends not only on the selectivity of the membrane, Zij, but is alsodetermined by the activity coefficients of the components i and j, Yi and Yj,

in the feed solution, their saturation vapour pressures and the total vapourpressure on the permeate side of the membrane.

Assuming vanishingly low pressure on the permeate side of the membrane, i.e. pr

erm and pyerm--+o, the separation factor in eqn (9.18) reduces to:

y~eedp?

(Xij=Zij feed 0Yj Pj

The separation factor (Xij consists of the product of the ratio of thesaturation pressures of the pure components i and j times the ratio of theiractivity coefficients, and the membrane selectivity Zi.j which is onlydetermined by the properties of the membrane. The ratio Meed p? )/(y~eed p7)

(9.20)

represents the separation obtained due to evaporation, that is the distillation selectivity.

Thus the pervaporation separation factor, (Xii> may be either larger thanthe separation factor obtained by distillation, when Zi,j> 1, or it may besmaller, when Zi,j< 1.

9.2.4 Characterisation of Pervaporation Membranes

A pervaporation membrane is characterised by its permeability andselectivity. Two simple tests are conducted for each of the particularcompounds of interest to determine the relevant membrane properties. Tomeasure the permeability coefficient, the membrane is challenged with apure vapour of the particular compound i, at a particular pressure, preed• Adriving force of a pressure drop across the membrane is established bymaintaining a vacuum on the permeation side of the membrane. Thepermeating species is collected at a cold trap, and its mass flux per unitarea of the membrane is found. The steady state pressure on the downstream side is due to the vapour pressure of the liquid in the cold trap. Thepermeability coefficient prerm is simply the flux over the driving force, herethe pressure gradient, Jd(Ap/Ay).

The distribution and diffusion coefficients Si and D~ can be determinedfrom sorption experiments (Crank & Park, 1968). The steady state mass ofcompound absorbed by a particular volume of the membrane polymergives the concentration in the membrane (mole adsorbed per volumepolymer). Knowing the partial pressure during the experiment leads to thecalculation of the distribution coefficient Si'

CiP·=HC·=-

1 I Si

Here is Ci the concentration of the component 'j' in the polymer and Pi itspartial pressure above the membrane.

If the rate of absorbtion is also monitored, then the diffusion coefficientof the volatile component in the polymer can be estimated. Otherwise eqn(9.11) can be used to estimate it. Fugacity and activity coefficient can befound from the literature. In general fugacity of gases is close to one anddoes not influence the calculation significantly. This, however, is not thecase for the activity coefficient of components in a liquid mixture, and theymust be considered as they can vary substantially from one. Knowing J i ,

S; (and/or Di ) means all the quantities can be estimated.Using the vapour of pure components on feed side in determining the

membrane transport properties results, of course, in the permeabilitycoefficients of the pure components, which can be, and usually are, very


different from those obtained with mixtures. To obtain realistic data forthe membrane separation capability, measurements should be carried outwith mixtures, the composition of which should be selected as close aspossible to the practical application in mind.

9.2.5 Further Considerations

Effects that exist in other membrane processes exist here as well, forexample concentration polarisation and fouling. As specific topics thesewill not be discussed per se. However, where they occur in conjunctionwith other aspects they will be described.

It is now appropriate to tackle some exercises. If exercise 3.5 has notbeen tackled this should be done first. Solutions are appended.

Exercise 9.1

The rate of uptake of ethanol by the polymer PDMS was measured. Asample of polymer, 1·3 g, was placed on a microbalance in a saturatedatmosphere of ethanol at 35°C. The change in weight of the sample wasmonitored with time. The following results were obtained.

Time Mass(mins) (g)

0·0 1·3000·4 1·3170·8 1·3251·7 1·3352·5 1·3433·3 1·3494·2 1·3555·0 1·3605·8 1·3656·7 1·3707·5 1·3748·3 1·378

12·5 1·39616·7 1041020·8 1042325·0 1·43529·2 1·44633-3 1'45637'5 1'46641·7 1·475

302 H. Srrathmann & R. M. McDonagh

Using only this data, calculate the partition and diffusion coefficients forethanol in this film. Compare the estimate of the diffusion coefficienthere with that obtained using eqn (3.58) (or eqn (9.20».

Exercise 9.2

The steady state absorptions of the other compounds were as follows(units are grams of compound per gram of polymer): methanol 0,030,n-propanol 0'276, water 0·0033. Calculate the partition and diffusioncoefficients for each of these using this and data from Question 1.

Assume that the fugacity coefficient in each case is 1. The activitiescoefficient for each compound in its pure state, at 35°C is: methanol0'944, ethanol 1,057, n-propanol 0·806 and water 0·821.

Exercise 9.3

In the above exercises there is data on four compounds; for eachpossible pair estimate

(a) membrane selectivity Zi.j;(b) membrane separation factor (Xij; and(c) distillation selectivity.

9.3 PERVAPORATION MEMBRANES

For a membrane to be useful in any application, it needs to have a highselectivity for the components to be separated and a high flux for thepreferred components. It should also maintain its integrity for a longperiod under operating conditions.

To achieve high fluxes the membrane must be as thin as possible.According to eqn (9.15), the transmembrane flux is inverse proportional tothe membrane thickness. Extremely thin separation layers can be produced as so-called integral asymmetric membranes (Lloyd, 1985), ormembranes can be made by coating a dense separating layer on to the topsurface of a porous substructure which then acts merely to support thedense selective coating layer mechanically. The material of each layer canbe selected and optimised separately to its specific function. Alternativelyintegral asymmetric membranes can be made by the so-called phaseinversion process in which a skin-type asymmetric structure is precipitated


from a polymer casting solution by addition of a non-solvent. However,the majority of today's pervaporation membranes are composite structures. The preparation of an effective composite pervaporation membraneis a two-part process; the first part involves the development of theselective layer and the second part the development of a suitable microporous structure which supports the selective layer without effecting itstransport properties (Strathmann et aI., 1988). A typical composite membrane consisting of a polydimethylsiloxan selective layer and a microporous polysulfone support structure is shown in the scanning electronmicrograph of Fig. 9.4.

Fig. 9.4. Scanning electron micrograph showing the cross-section of composite membraneconsisting of the same polydimethylsiloxane (PDMS) layer on microporous polysulphone

support structure. Scale-bar = 211m.

9.3.1 Selective Layer

According to eqn (9.11), the flux of a component through a polymer layeris dependent on the product of the diffusion in the polymer matrix and thepartition coefficients of the component between the outer phases and thepolymer. It has been shown by Bell et at. (1988) that the diffusivity of amolecule is dependent on its size and the physical structure of the polymermatrix. For example, small molecules like hydrogen and nitrogen havehigh diffusion coefficients in almost all polymers, whereas larger moleculeslike carbon dioxide or organic solvents diffuse at much slower rates.


However, the decrease in the diffusivity coefficient with increasing diameter of the permeating components is generally higher in glassy than inrubbery polymers. In opposition to this, the partition or solubility isdetermined primarily by the chemical interaction between the mobilemolecule and the polymer matrix. Such that, contrary to diffusive transport, solubility is generally increasing with the 'condensibility' of thepermeating component, i.e. boiling temperature (Baker et aI., 1987). Thussmall non-organic molecules are poorly soluble in polymers, whereas CO2

and organic solvents are generally highly soluble.Strathmann et al. (1990) have shown that the classes of the polymers can

be shown to also play general roles. Elastomers like polydimethylsiloxane(PDMS) show a higher permeability to higher molecular components dueto the fact that in elastomers the solubility contribution to the permeability is much higher than the diffusive part. Whereas for glassy or semicrystalline polymers, e.g. cellulose, the reverse is the case, as the diffusioncomponent dominates. Whether it is serendipity or not, the range ofcharacteristics of varying polymers offers a wide spectrum of differentseparation possibilities.

9.3.2 Support Layer

While the selective layer is most important, properties of the support alsoinfluence the effectiveness of the membrane as a whole. Gudernatsch et ai.(1991) have shown that the extent is sometimes dramatic.

The task of the sublayer is to provide a stable mechanical support to theselective layer, without effecting its transport properties. Thus the poroussupport structure has to meet certain requirements in order to fully utilisethe properties of the barrier polymer: (1) the hydrodynamic resistance ofthe support should be small compared to the resistance of the top layer;and (2) the surface porosity should be as high as possible in order not toreduce the permeate flux and selectivity of the membrane. The structure ofa composite membrane and possible pathways of components through themembrane are shown schematically in Fig. 9.5.

As indicated there are two possible pathways through a compositemembrane. The first goes through the selective coating layer of themembrane into a pore of the substructure. The second pathway goesthrough the coating layer ending at the pore-free surface of the supportstructure To reach a pore a permeating component has to diffusethrough the top layer and a layer of the support structure. The twopathways through the membrane can be described by a resistance model.This model shows that the total flux of a composite membrane for agiven component is a function of the permeabilities of the selective


Fig. 9.5. Schematic drawing illustrating two possible paths of a component through acomposite membrane with a support material of finite permeability.

coating layer and the suport structure polymer, their thicknesses and thesurface porosity of the support structure. It can be shown that, for givenintrinsic properties of the barrier and the support sructure polymers, thefluxes of individual components and thus the selectivity of the compositemembrane depends on the surface porosity of the substructure. Highsurface porosity means that the selectivity of the top-layer polymerdetermines the selectivity of the composite membrane. For vanishingporosity the selectivity is determined by the properties of the substructure polymer.

If the selective layer and the support structure polymer show thesame permeabilities or preferences in the permeability of different components, the selectivity of the barrier polymer is obtained or even increasedin the composite membrane. If, however, the permeabilities of the barrierand support structure polymers are different or even inverse, Gudernatsch et at. (1991) have found that the selectivity of the compositemembrane can be rather different or even reverse from that of theselective layer. This is illustrated in Fig. 9.6 which shows a typicalMacCabe-Thiele diagram determined for the pervaporation of an ethanolwater mixture through composite membranes, which consist of a polydimethylsiloxane selective layer on a microporous polysulfone substructure. The porosity of the substructure is varied from 1 to O. Theselectivity of the composite membrane changes from that of an ethanolselective homogeneous unsupported polydimethylsiloxane film to that ofa water selective polysulfone film. Depending on the porosity of thesupport layer selectivities between these two extreme values can beobtained. By selecting the proper polymers for the barrier layer and thesupport structure and by varying the surface porosity of the supportstructure composite membranes can be tailored for specific separationproblems.

H. Slralhmann & R. M. McDonagh

Porosity '"l00~ l-- ----;.."..- ~ '7-/ ,/'-S3~ V

I{ /' VIV ./II V .....V

V V S.z...~

II L.~...-7t}~ 63~\. 1.

f/ - O~

306

1,0w

p

0,8

0,6

0,4

0,2

0,00,0 0,2 0,4 0,6 0,8 1,0

Fig. 9.6. Composition of the permeate, as a function of the feed solution composition,obtained by pervaporation of an ethanol water mixture through composite membranesconsisting of an ethanol-selective polydimethylsiloxane layer on a water-selective polysul-

phone substructure of varying surface porosity (after Gudernatsch et al. (1991».

9.3.3 Membrane Module

The development of a suitable membrane for any particular applicationstarts with lab scale experiments, but to be applied on technical scale itmust be incorporated into a suitable device, normally a self-contained unitreferred to as a module.

The fundamental considerations determining any module design are lowmanufacturing costs and the requirement of a low as possible hydraulicresistance on the permeate side of the membrane. But also to be considered, on the feed side, is the reduction of concentration polarisation andfouling, and very important to pervaporation is the creation of effectiveheat transfer. These engineering aspects have been discussed by Rautenbach et al. (1990). Another fact to be kept in mind for the development ofmodules to be used in biotechnological applications is the ease with whichthe integral sterility of a system can be maintained.

In pervaporation, the transport of permeate usually takes place underreduced pressures (10-100 mbar) so here the basic rule of vacuum technique applies: the bigger the transport orifice the better the transport. Asthe heat of evaporation during pervaporation is drawn from the feedsolution, the feed may be cooled substantially, to such an extent thatintermediate heating may be necessary, so optimal energy input may alsoneed to be considered.

To date, most of the module types applied in other membrane separationprocesses have also been used for pervaporation. Aspects relating to theseare summarised in Table 9.1. Evaluating all the considerations above, i.e.

Pervaporation in Biotechnology

Table 9.1Effectiveness of Pervaporation Modules

307

Module Supplierconfiguration

CapiIlary Sempas

Plate and Frame GFTGKSS

Spiral Wound MTRNitto

Advantages

large surface area to volume,membrane requires no support

easy membrane replacementgood control of concentrationpolarisation

large surface area to volume ratio,low costs

Disadvantages

restricted feedsolution pressure

restrictedpermeate flow,high costs

supoortedmembranes,restricted permeateflow,poor control ofmembrane fouling

good permeate transport properties, fouling and concentration polarisation control by proper flow velocities, sterility, easy intermediate heatingand low cost per installed membrane area, the hollow fibre with the feedflowing inside the fibre appears to be a good solution. But as not allpervaporation membranes are available as hollow fibres, other configurations are also used. See, for example the research paper of Sander andSantiago (1988) and the report of Baker (1990).

9.4 THE PERVAPORATION PROCESS AS A UNIT OPERATION

Typical to all membrane processes, there are several technical aspects tomaking pervaporation work. One, already discussed, is that of providing asemipermeable barrier, i.e. the membrane. Another one, considered here, isthat of supplying the driving force-here the chemical potential differenceacross the membrane-and a third aspect is that of system and processdesign.

9.4.1 Pervaporation Process Operating Modes

As shown earlier the chemical potential of a component in the membranecan be related to its concentration and activity coefficient in the liquid feedsolution and to its partial vapour pressure in the permeate. The chemicalpotential is a function of the state variables: pressure, composition andtemperature:

J1= !(p,x, T)

308 H. Strathmann & R. M. McDonagh

Thus differences in the chemical potential of a component in the feed andpermeate mixture can be established by introducing either differences inthe pressure, the composition or the temperature.

In pervaporation all three methods are used to establish a suitablechemical potential gradient in the membrane as driving force for the masstransport. A hydrostatic pressure difference between feed and permeatemixture is established by introducing a vacuum on the permeate side. Inthis case the process is referred to as vacuum pervaporation. An inert gasstream on the permeate side of the membrane can be used to remove thecomponent and thus establish a concentration gradient driving force. Thismode of operation is referred to as sweep gas pervaporation. Finally, if atemperature difference between the feed and the permeate mixture is usedto establish a chemical potential gradient in the membrane, the process iscalled thermo-pervaporation.

These processes are discussed in more detail in turn below with acomparative consideration of their applicability to biotechnological problems. Illustration of each procedure is given in terms of model experimentsusing 5 wt% ethanol water solution with a low ethanol selective hollowfibre membrane (PDMS selective layer on a PES support). This sameset-up was run in each of the described modes, to give a direct comparison.

The respective operating modes are depicted schematically in Fig. 9.7along with the flux and selectivity of each with the major operatingparameter.

9.4.1.1 Vacuum PervaporationThe most obvious way to generate the chemical potential difference is toapply a vacuum on the permeate side, i.e. to lower the partial pressure of acomponent i in the permeate prerm under a given partial pressure in thefeed p~eed. The component i of the feed permeates the membrane along theestablished chemical potential gradient and evaporates into the vacuumon the permeate side of the membrane. Maximum separation is approached as prerm goes to zero.

To achieve this in reality requires substantial pumping, at great cost. Soit is of more interest to have a membrane operating efficiently at a reducedvacuum. The range of variation lies between that of diminishingly smallpermeate vapour pressure and it being identical with the saturationvapour pressure of the feed mixture. The latter being the thermodynamicequilibrium.

In summary:

at the thermodynamic equilibrium, the flux is zero, and the selectivity equals the thermodynamic equilibrium selectivity;


a] Vacuum Pervaporation

0,1---"---+---+--+.---I01020304050

P (mbar)

2 ---+-- ----1--··

8r--.-,-.---.---,B-J-f-- ,-

61--+--I-+--+---1----~ ......_ .

4 -.._. - .. - - .)-

0,1---I---I--+---+.---Io 10 20 30 40 50

P (mbar)

o

Fig. 9.7a. Flow scheme of vacuum pervaporation, and fluxes and enrichment factors as afunction of the permeate pressure.

b] Sweep Gas Pervaporation

J:s=HE ·'m'~·~·"Etlli ~m

o 1000 2000 0 1000 2000

Re Re

Fig.9.7b. Flow scheme of sweep gas pervaporation, and fluxes and enrichment factors as afunction of sweep gas Reynolds number, Re.

c] Thermo ·pervaporation

20 40 60aT (K)

o

8,.......,r-T~-r--,--,

B --f-- - .-- .-_...-.

6t-1'--1-+-+-+--j--1-- - -- --I

4)

0I

( 0o0204060

aT(K)

Fig. 9.7c. Flow cherne of thermo-pervaporation, and fluxes and enrichment factors as afunction of the temperature difference.

at the optimum driving force, prerm-+o, the flux is at its maximumand the system selectivity is the intrinsic membrane selectivity.

This is demonstrated in the model experiments. Figure 9.7(a) shows theeffect of change in permeate side pressure. As pressure is reduced the fluxincreases. The selectivity, however, shows the opposite trends. The minimum selectivity corresponds to the intrinsic membrane selectivity.


9.4.1.2 Sweep Gas PervaporationThis is another method to lower the fugacity of the permeate. In thiscase molecules desorbed from the permeate side of the membrane areremoved by a flow of a gas through the permeate compartment ofthe module. One way to describe this is as drying of the backside of themembrane.

In Figure 9.7(b) fluxes and enrichment factors as function of Reynoldsnumber of the sweep gas are shown, using the same module and membrane and feed mixture as in Fig. 9.7(a). The vapour loaded sweep gasleaving the module was cooled using a liquid nitrogen trap. The vapoursare frozen out and the sweep gas recycled into the module after beingreheated.

The flux can be seen to increase with the sweep gas velocity (i.e. Re).Other experiments showed it to plateau above Re = 2300. As in vacuumpervaporation, the selectivities of the membrane decrease as the flux isincreased, for the same reason as in vacuum pervaporation. As Re-+O, theselectivity approximates to the thermodynamic equilibrium selectivity; theloaded sweep gas leaving the module is then saturated with vapour. WhenRe-+ 2300 a maximum flux is obtained, under these conditions the intrinsicselectivity of the membrane is approached.

9.4.1.3 Thermo-pervaporationThermo-pervaporation is driven by the chemical potential difference thatexists between streams of different temperature.

The experiments were carried out with the module as above. Thestainless steel housing of the module was kept at O°C while the feedmixture was heated. In Figure 9.7(c) it is shown how the flux andselectivity vary with temperature difference across the membrane. The fluxincreases sharply with increasing temperature difference. This is easilyexplained as the feed component vapour pressure depends exponentiallyon the temperature. Fluxes comparable to those of vacuum pervaporationare seen.

The enrichment factor also increases with increasing temperature difference, approaching the sweep gas maximum value-indicating membrane controlled separation is reached when ~T > 50°C. Further increasesin temperature do not see any improved enrichments, but the flux doescontinue to increase. Further, the enrichment factor approaches unity asthe temperature difference goes to zero. This is the reverse of the twoprevious modes. This is attributed to a different controlling mechanismhere. The equilibrium approached now is a liquid-liquid one and notvapour-liquid. The isothermal liquid-liquid selectivity is 1. So, as ~T-+Othe enrichment factor /3-+ 1.


9.4.1.4 Comparison of Operational Modes with Respect to BiotechnologicalRestrictionsConsidering the three possible configurations above, thermo-pervaporationmust be the most favoured due to the easy operation and the extremelysimple permeate transport out of the module. There are, however, some veryserious limiting factors. The temperature difference has to be in the range of50°C in order to generate the high fluxes and maximum selectivities.Cooling at very low temperatures is expensive, so cooling temperatures inthe range of o-15°C are to be favoured. This means a feed temperature of60°C or more. In a continuous fermentation such temperature can only bewithstood by thermophilic micro-organisms. For this reason thermopervaporation might find only limited use in biotechnology.

The module design for thermo-pervaporation is significantly different tothat of vacuum or sweep gas modes. The distance from the membrane downstream side to the condenser wall has to be minimised in order to reducepressure losses along the diffusion path of the permeate. Further, a diffusionpath along constantly decreasing temperature drops must be provided. Theimplication is a low packing density and many cooling walls interspersedbetween the membranes. Both requirements mean more expensive modules,thus a significantly increased capital cost for an installation.

If neither thermophilic micro-organisms nor thermo-pervaporationmodules are available, conventional vacuum pervaporation can do thesame job, provided the additional cost of a vacuum pump is acceptable. Inthis case the condenser may be outside the module as the specificdownstream transport resistance is lowered by the low pressure.

Sweep gas pervaporation requires the cooling of the large volumes ofsweep gas stream. Significantly enlarged condenser areas are neededbecause of the decreased condensing efficiency due to the low concentrations of permeate in the inert sweep gas. Much lower condensationtemperatures are required due to the decreased pressure of the vapours.Economically then, it is only feasible to use sweep gas mode whenpermeate and carrier gas can be vented to the atmosphere. Thus, it cannotbe used efficiently to directly recover organic products, but perhaps as afurther process step, as in the dehydration of organic solvents. In this case,high gas velocities have to be generated to reach the maximum selectivityof the membrane. This requires powerful blowers.

9.4.2 Chemical Engineering Aspects of Pervaporation Process Design

For the performance of pervaporation as a practical mass separationprocess, several chemical engineering aspects are of equal importance tothe development of the proper membrane and membrane module. For


practical purposes it is of interest to know: (1) how far a given mixture canbe depleted of a certain component; (2) how much can a given componentbe enriched in the permeate; (3) how much of the original feed stream canbe recovered as permeate or retentate; and (4) how much membrane area isrequired for this operation.

The depletion or enrichment of a mixture depend not only on membrane performance but also on the recovery rate of the feed stream. Inpervaporation the recovery rate is generally referred to as stage-cut byanalogy to gas, separation. It is obtained from a simple mass balance andcan be expressed by:

Here Hi are the mass flows, and 0 the stage-cut; the subscripts '0' and 'p'refer to the feed and the product mixture. The composition of the retentateand the permeate can be expressed as a function of stage-cut, i.e. theamount of the feed that has been obtained respectively as permeate orretentate. The stage-cut corresponds to the recovery rate used in ultrafiltration and reverse osmosis.

In pervaporation, the achievable separation, i.e. the enrichment of acertain component in the permeate or its depletion in the retentatedepends on: (1) membrane parameters, such as its selectivity and permeability; (2) operational variables, such as temperatures and pressures inthe feed, the permeate and the stage-cut; and (3) the flow pattern of themixture on the feed and permeate sides of the membrane. The flow patterndepends, in turn, on the geometry of membrane module design.

9.4.2.1 Feed and Permeate Flow PatternsThe relations between the achievable separation, membrane properties,operational variables and system design have been studied extensively andare described in the literature by, for example, Rautenbach and Albrecht(1989) and Hwang and Kammermeyer (1975).

In pervaporation, three different feed and permeate flow patterns maybe used as indicated in Fig. 9.8. This shows schematically process designwith: (a) complete mixing of the feed and the permeate; (b) counter-currentflow of feed and permeate; and (c) co-current flow of feed and permeate.

The analytical studies, i.e. determination of the membrane area requirement and separation characteristics for the different flow patterns forbinary and multicomponent mixtures, are described in the literature, andcomputer programs for parametric studies are available for all flowpatterns. The effect of the various flow patterns on the performance of a

Feed


a) complete mixing

Reject

313

Reject

F~ J=~=[R~~·m.c) Co-current flow

Fig. 9.8. Schematic diagram indicating various flow patterns in a pervaporation module.

unit is significant, since membrane permeability and selectivity stronglydepend on the feed and permeate mixture composition.

9.4.2.2 The Permeation CascadeIf a separation obtained in a single permeation stage does not meet therequired permeate composition, it can be multiplied by connecting anappropriate number of stages in series to form a countercurrent permeation cascade. There are two possible arrangements. In the firstarrangement there is no reflux of the retentate.

A typical section of a permeation cascade is shown in Fig. 9.9(a). In thissimple arrangement the permeate from stage n becomes the feed for thenext higher stage n+ 1 and the retentate is disposed off. In the second casethe retentate is refluxed, i.e. the retentate of stage n is mixed with the nextlower stage n-1 and so on. The simple cascade without reflux of theretentate is only of use when the retentate is virtually of no value and largeenrichment factors of the product in the permeate are required. If acascade with reflux of the retentate is used, there are two sectionsdepending on the position where the original feed solution is introducedinto the cascade. One is the so-called enrichment section where theproduct is enriched in the permeate, and the other is the stripping sectionwhere the product is enriched in the retentate.

The subject of cascade operation is of rather fundamental importancefor all separation processes and therefore treated in detail in the corresponding literature.

314

Permeet.

Feed

H. Strathmann & R. M. McDonogh

Feed ----1--1

Fig. 9.9. Flow diagram of permeation cascades (a) without reflux of the retentate and (b)with reflux of the retentate.

9.5 PERVAPORATION IN MICROBIOLOGICALPRODUCTION PROCESSES

Pervaporation can be and has been used successfully in several microbiological production processes. An application of pervaporation whichhas been studied quite thoroughly is the removal of different alcohols fromfermentation broths.

Because of its relevance as fuel and feed stock, the production of ethanolfrom renewable raw materials is of special commercial interest and shall bebriefly reviewed.

9.5.1 The Separation Problem in the Microbiological Production of Ethanol

In fermentation of ethanol the production activity of the microorganismsis inhibited with increasing concentration of ethanol and certain byproducts. For reasons of fermentation efficiency, they should be continuously removed from the fermenter, whereas salts, microorganisms, andnutrients should be kept within. Figure 9.10 depicts the required permeation and rejection properties of the separation unit, using as examplethe ethanol fermentation with Saccharomyces cerevisiae. It is evident that


EtOHH2O

organIc by-productsCOz

salts

proteins

microorganisms(producing)

--~ .._._-------------

microorganisms(contaminating)

fermentation broth permeate side

Fig. 9.10. Required permeation and rejection properties of the separation unit.

the separation unit has to carry out a complex set of single separationtasks simultaneously to keep the fermentation process continuously inaction. To operate under optimum conditions, the ethanol concentrationin the fermentation broth should be kept as low as 5-8 wt% relative towater (Nagashima et ai., 1984).

The ethanol concentration in the product, however, should be muchhigher in order to keep the further processing costs as low as possible.Therefore, a simultaneous preconcentration of ethanol integrated into theremoval step is desirable.

Looking at possible separation processes suitable for the describedapplication, pervaporation across highly permeable solvent-selective membranes seems to be the most attractive solution of the stated separation andconcentration problem. It clearly avoids the high mechanical, thermal orchemical stresses exerted upon the microorganisms by competitive processes such as reverse osmosis, distillation, or solvent extraction and holdsthe biggest potential of simultaneous preconcentration of the product. It isthe only solvent-selective removal process able to keep the fermentationbroth in the separator under exactly identical conditions as in the fermentor.

The process can be operated at low temperatures. Thus, the optimumfermentation temperature can be adjusted. Since the ethanol fermentationprocess is exothermic, pervaporation can take the heat of evaporation ofthe permeants from the feed solution. It can, therefore, at least partially bedriven by the excess heat of the fermentation process.

9.5.2 Integration of Pervaporation into the Fermentation Process

An integrated pervaporation bioreactor system is shown schematically inthe flow diagram of Fig. 9.11. The system is designed as a closed loopconsisting of the bioreactor, the membrane separation unit and

316 H. Slralhmann & R. M. McDonogh

Nutrients Bleed

T

Bioreactor

Sweep Gas OfT-GassesInlet

VI

pvSeparator

Product

Fig. 9.11. Experimental set-up of a fermentation-pervaporation unit.

a circulation pump. It is usually operated in a feed and bleed mode, i.e.nutrients are continuously fed into the reactor and part of the fermentation broth is bled. This is done to avoid the accumulation of certainreactor constituents retained by the membrane. For example, manyreactions have as a biproduct water, so to maintain a constant reactorvolume the water has to be removed-as bleed.

9.5.3 Co-permeation of Organic By-products

The microorganism S. cerevisiae converts glucose not only into ethanoland carbon dioxide but also into organic by-products, such as acetaldehyde, ethyl acetate, isobutanol, or acetic acid. These substances aremuch more dilute than ethanol. In a conventional batch or flow-throughfermentation system, their concentrations are usually too low to seriouslyinhibit the activity of the microorganisms. In a recycling system, however,the danger of accumulation of those trace components to inhibitingconcentration levels exists and they must be removed. Therefore, theco-permeation behaviour of some selected by-products has been investigated. Table 9.2 gives the results of a representative experiment.

Table 9.2 shows that even at very low feed concentrations a copermeation of trace components takes place. Methanol and ethyl acetate areconcentrated from a non-detectable level to a detectable one. Therefore, noenrichment factor can be defined for those two components. Acetic acid,however, is not detectably permeated. This is a drawback, because aceticacid has been identified as the most inhibiting trace component whenaccumulated. If acetic acid cannot be removed simultaneously withethanol from the fermentation broth, Mulder and Smolders (1986) have


Table 9.2Co-permeation Behaviour of Various Organic By-products

Component wJ wp f3 J,omp(kg/m1·h)

Ethanol 4·80E-02 2'6IE-OI 5-44 6'39E-02Acetaldehyde 2'63E-04 2'5IE-03 9·52 6'14E-04Ethyl acetate O'OOE+OO 5'69E-04 1'39E-04Methanol O'OOE+OO 2'36E-04 5'78E-05Isobutanol 9'99E-05 1'I3E-OJ 11·31 2'77E-04Methyl butanol 5'74E-05 5'40E-04 9-42 1'32E-04Acetic acid 7'32E-05 O'OOE+OO 0 O'OOE+OO

317

noted that a feed-and-bleed operation must be installed to keep itsconcentration at tolerable levels.

9.5.4 Membrane and Process Optimisation in Integrated Processes

As previously identified, pervaporation can achieve two solvent recoverytasks, one is the removal of a solvent product and the other the removal ofunwanted volatile organic by-products. The first requires a high-fluxmembrane, the second a high selectivity. Both need tailored membranesand special process conditions are required in order to work with propereconomics. Some of these aspects are demonstrated in the followingexample for ethanol recovery.

9.5.4.1 An Example of Direct Ethanol Recovery Using PervaporationThe most common way to ferment ethanol is the free cell fermentation, i.e.the microorganisms are suspended in an aqueous solution containingnutrients, product, by-product, and cell debris. In this situation the masstransport to and from the cells is convective and diffusive and therefore atits optimum. A direct product recovery unit needs also to operateoptimally.

Take as an example the arrangement of Fig. 9.12, the essential elements of the configuration given in Fig. 9.11 - a loop consisting of thereactor vessel, a recycle pump and the separator. This design allows apermanent transport of the fermentation broth through the separator atdefined velocity, pressure, and temperature. This is a three-pole systemhaving one input and two outputs. The input mass flow F with massfraction of substrate Wf divides into the bleed output B with the productmass fraction Wb and the product output P with the product massfraction wp •

Ideal operation means a mass flow B of zero. All glucose fed into thesystem F' W~luc is converted to ethanol and output as p. w~tOH. The yield

318 H. Slralhmann & R. M. McDonogh

Feed. F Bleed. B

Permeate. P

Fig. 9.12. Simple pervaporation-bioreactor system.

of ethanol from glucose is described by the mass related yield factor A~

defined as:

A PF

mass of ethanol produced mEtOH(9.21)

mass of glucose consumed mgluc

The ideal stoichiometric value for A~ is 0,511, the technical value reportedby Maiorela et al. (1984) is 0-434. Doing the stationary mass balance overthe system shown in Fig. 9.12, shows that there is a maximum ethanolmass fraction W~IOH in the separator output. This maximum concentrationdepends on the feed glucose concentration, as shown in Fig. 9.13.

0,8

0,4

0,2

BFR....----------,----,---,.---,.---,

0,4

0,2

0,0

0,4 0,5

Ws

Fig. 9.13. Maximum ethanol mass fraction in the product output as a function of glucosemass fraction in the substrate at different bleed-to-feed ratios.

Setting the ethanol mass fraction in the fermentation broth to 0·05 andthe glucose mass fraction to 0-45, which would correspond to slightlydiluted molasses, a maximum product mass fraction of w~tOH of 0·3 isobtained at a BFR (bleed-to-feed) of zero. This corresponds to a requiredenrichment factor p of 6.

The product flow p. w~tOH is given by the volumetric productivity VEtOH

of the microorganisms and the volume of the fermentation broth V.A technical value for v is about 20 g EtOH 1- 1 h -1. Values up to


100 g EtOH 1-1 h - 1 resulting from laboratory experiments are reported inliterature. Assuming a VEIOH of 60 g EtOH 1- 1 h - 1 and a volume offermentation broth of 10 m3 the product output flow becomes 600 kg h - 1.

If 500 m2 of membrane were affordable for this plant the required partialethanol flow through a membrane separator would be 1·2 kg m - 2 h - I.

This example demonstrates how the membrane requirements are determined. Two major exercises are given at the end of the chapter.

9.6 CONCLUSIONS AND OUTLOOK

Laboratory scale trials have shown beyond doubt that pervaporation canimprove both overall process efficiencies and product quality in biotechnology. The technology is, however, limited to the removal of volatilecomponents. For a broader application further improvements are needed,both with respect to the membranes in terms of higher selectivities andfluxes, and with respect to the membrane modules in terms of better heatand mass transfer.

There are four major areas of application where pervaporation can besuccessfully utilised to improve the overall process economics, these are:

(1) the direct recovery of bioproducts from the fermentation broth;(2) the removal of process-inhibiting volatile by-products;(3) the concentration and purification of thermally unstable, sensitive

volatile by-products;(4) dehydration of organic solvents.

The draw back in the application of the technology is that each processrequires ajob specific membrane. A membrane needs to be tailored to eachproblem, ranging from high flux membranes with a 'moderate' selectivitywhen organic solvents are to be recovered to membranes with a highselectivity for the removal of process-inhibiting volatile by-products. Forthe dehydration of organic solvents, water-selective membranes with veryhigh selectivity are required. Both water- and solvent-selective membranesare now commercially available. As more and varied membranes becomeavailable this job specific nature will cease to be a limiting factor.

As a phase change is involved in pervaporation, it is crucial to haveadequate heat transfer within the membrane module. Boundary layer effectscan also severely reduce the selectivity as well as the flux in pervaporation.This is particularly the case when components with low solubility or lowconcentration in the feed solution have to be pervaporated. This means thatmass transport in the modules is also of critical importance. Both thesefactors must be considered in the design of a membrane module.


In summary, based on laboratory scale trials, it is clear that pervaporation can improve overall process economics. Its scope of application isrestricted to the removal of volatile components. For a broader use furtherimprovements are needed, both in the membranes in terms of higherselectivities and fluxes, and in the membrane modules in terms of better heatand mass transfer. These developments are the active concern of manypeople and solutions to the problems should appear in the next few years.

Exercise 9.4

(i) Fermentation has often been considered as a renewable source ofliquid fuel, i.e. ethanol. Typical fermentation broths contain ethanolin concentrations of a range of 4-8% by mass. Estimate theconcentration of ethanol in the permeate stream after a single passPV treatment using a composite membrane whose active layer isthat of the polymer discussed in exercises 9.1-9.3, assume a feedconcentration of 5 wt %. What is the enrichment factor for thisprocess?

(ii) For ethanol to be a viable fuel it must be available at concentrations above 95 wt%. How many stages in a simple cascade, withoutpermeate recycle, would be necessary to concentrate the permeateup to burnable concentrations? Assume the separation factor is aconstant with feed concentration.

(iii) If the further concentration was achieved using a water selectivemembrane instead of a ethanol selective membrane, what would bethe required enrichment factor for single pass purification? Assumea mass stage cut of 40% and a mean concentration over theretentate side of the membrane.

(Answer: (i) f3 = 4·18. Concentration of ethanol in the permeate is72 wt%; (ii) the concentration from the second stage is 94·8 wt%. Thethird is 99·3 wt %; and (iii) f3 = 3·3. Solution given in Appendix)

Exercise 9.5

As a simple fermentation system, consider the configuration of reactorvessel, recycle pump and separator in a closed loop, as depicted in Fig.9.12 above. In this case the separator is a PV module. The input massflow F with mass fraction of substrate Wf is divided into a bleed, outputB with the product mass fraction Wb and permeate product stream,output P with the product mass fraction wp '


Perform the stationary mass balance over the system shown in Fig.9.12 and show that the ethanol mass fraction w:tOH in the separatoroutput is given by:

WEtOH = 1 [ 1 _ BFR. WEtOH]p 1- BFR 1- W~IUC B

1+ GlucAPWF F

BFR is the bleed-to-feed ratio defined as BFR = BjFSetting the ethanol mass fraction in the fermentation broth to 0·05

and the glucose mass fraction to 0-45 estimate the maximum productmass fraction of w:tOH

. A~ values are given in the text. If this isseparated using a pervaporation module, what is the required enrichment factor?

The product flow p. w:tOH is given by the volumetric productivityVEtOH of the microorganisms and the volume of the fermentation brothV. Assuming a VEtOH of 60 g EtOHjl . h and a volume of fermentationbroth of 10 m3

, what is the product output flow? If commercialmembranes having an ethanol permeability of 44·5 kg m - 2 h -1 bar- 1

are to be used, assuming an economic operating vacuum of 0·01 bar,what is the required membrane area for the separator? Vapour contentabove 5% ethanol in water is 0·323.

(Answers: Maximum product mass faction is 0·3 and is obtained at aBFR of zero. This corresponds to a required enrichment factor (3 of 6.The product output flow is 600 kg h -1. Membrane needed is 400 m 2

.)

NOMENCLATURE

a activity (- )Lla activity difference (- )C concentration (mol m - 3)D diffusion coefficient (m2 s -1)J flux (mol m - 2 S- 1)tL phenomenological coefficient (mol 2 J - 1 m - 1 S - 1 )

P permeability coefficient (mol m - 2 S - 1 Pa - 1 )

LlP pressure drop across membrane (Pa)p pressure (Pa)R the gas constant (JK - 1 mol- 1 )

322

ReSisTVWXZi,j

X

yLly

Greek{3y

qJ

J..le

Subscriptij,k,m

H. Scrathmann & R. M. McDonagh

Reynold's number ( - )distribution or partition coefficient (mol m - 3 Pa - 1)

partial molar entropy (J K - 1mol- 1)the absolute temperature (K)partial molar volume (m 3 mol- 1

)

mass flux (kg s- 1 )

driving force, as defined in eqn (9.1)the selectivity of a membrane for i with respect to j ( - )mole fraction ( - )directional coordinate perpendicular to the membrane surface (m)thickness of the membrane (m)

enrichment factor (- )activity coefficient (- )separation factor with respect to two components ( - )fugacity coefficient ( - )chemical potential (J mol- 1 )

mass stage cut (- )

permeating componentindividual component

Superscriptfeed in the feedM in the membraneM(feed) at the membrane feed interfaceM(perm) at the membrane-permeate interfaceo at saturationperm in the permeate

APPENDIX: SOLUTIONS TO EXERCISES 9.1-9.4

Exercise 9.1

The solution for Fick's Second for the case of diffusion into a slab, ofthickness Llz, from a constant concentration reservoir gives an expres-

t While derivation of the equations is usually done in terms of molar quantities, for technicalapplications concentrations are often expressed as mass fractions, yield in terms of kg of product etc. Molar quantities must then be converted, by multiplying by the kg molecular weights.


sion relating the mass accumulated with time and the diffusion coefficient of the volatile in the material of the slab as:

mass diffused = jD .Jn~;2

so the slope of a plot of mass versus Jconst • time will give the diffusioncoefficient directly, if the relation fits. The raw data is plotted in Fig.A9.1, the corrected data in Fig. A9.2. The linearity confirms theapplication of the equation. The diffusion coefficient is found from theslope.

o 00

o c0

p

Vv

1,3

Mass (g)

1,5

1,4

2010 30 40 50Time (min)

Fig. A9.1. Mass accumulation with time.

1,2o

DO

o [0

00

DO

~L

DO1,3

Mass (g)

1,5

1,4

10001,2

o 2000 3000 4000i(Constant x Time)

Fig. A9.2. Mass accumulation with function of time -J(16t)/(1t~y2).


The partition coefficient is found using eqn (9.20)

Pi=HCi=C;/Si

If the pressure of the componet i, Pi> is known and the limitingconcentration of the species in the film is found, Ci> then Si is easilyfound. The pressure is the partial vapour pressure. The concentrationmust be converted from gram per gram, to mol/m3

.

Exercise 9.2

Steady state concentrations:

mol. wt Vapor pressat 35°C

Methanol 32 28280Ethanol 46 13332n-propanol 60 5316

Water 18 5555

9 Liquidlg film

0·0300·1190·276

0·0033

Mo/lm 3

944·525864603

185·5

Part coeff.(mo/lm 3

• Pal

0·03340·1940·866

0·0334

In the case where only the limiting flow and partition coefficient areknown, the diffusion coefficient can be calculated, using eqn (9.11)

P!'erm. m !'erm _ yfeed • X. p?J.=DMS. ' 'Y, I "

, " ~y

and literature data for the activities and fugacities.

Part Coeff Permeability F/ux Activity Diffusion(mo/lm 3

• Pal (mo/'ml (mollm]ls) (m]Is)m]'s'Pa)

Methanol 0·0334 1'33IE-II 0·03761 0·944 4'22E-1OEthanol 0·194 2'05E-II 0·02733 1·057 I'OOE-IOn-Propanol 0·866 4'87IE-II 0·02588 0'806 6'98E-Il

Water 0·0334 8'66IE-12 0·004810 0·821 3'16E-1O

Solution to Exercise 9.3

Using the answers from Exercise 9.1 as data, the values of membraneselectivity can be calculated using equation 9.13

p.Z··=~.,J p.

J


Selectivity for:

MethanolEthanoln-Propanol

Water

with respect to: Methanol

1'()()

1·543-66

0·65

Ethanol

0·651'()()

2'38

0'42

n-Propanol

0·270·421'()()

0'18

Water

1·542-375·62

1'()()

Using the data in Exercise 9.1 and the values of Zi.j, the remaining valuescan be calculated using eqn 9.19.

Distillation with respect to: Methanol Ethanol n-Propanol Waterselectivity for:

Methanol 1'()() 1·89 6·23 5·85Ethanol 0'53 1'()() 3·29 3·09n-Propanol 0·16 0'30 1'()() 0·94

Water 0·17 0·32 1·06 1'()()

Membrane with respect to: Methanol Ethanol n-Propanol Waterseparationfactors for:

Methanol ).()() 1·23 ),70 9'()()Ethanol 0·81 1·00 1·38 7·32n-Propanol 0·59 0·72 1·00 5·28

Water 0·11 0·14 0·19 1·00

For the cases of organic mixtures the distillation selectivity is larger thanthe separation factor for the pervaporation membrane. The reverse is thecase for water organic mixtures. This means that this particular PVmembrane is a better separator only for water organic mixtures.

Exercise 9.4

(i) The enrichment factor is

If the enrichment factor is known along with the feed concentration,then permeate concentration can be estimated. The separation factorhas previously been estimated as 7·32 (assume it is constant). The


separation factor and the enrichment factor are related, in terms only ofthe feed concentration, by:

ex ijf3i= 1+(exij_l)x~eed

Hence f3 can be estimated without further information and this leads toan estimate of the permeate concentration.

Separation factorFeed cone.EtOH/H2 0

Cone in perm.

7-320·05

mass fraction

0·4959mole fraction

0·119mole fraction

0·715mass fraction

gives beta as 4'18

(ii) This calculation is essentially the same as the above. The feedconcentration and separation factor are known. The calculation of eachstage uses the result of the previous stage. An expression could bedeveloped to estimate the number directly, but as concentration is rapidit is simpler to do the calculation of output concentrations directly.

M ass fraction M ole fraction Fraction mole Mass

Initially Feed 0·05 0·11 beta 4·18 cone. in perm. 0-496 0·715Second 0·496 beta 1·77 0·878 0·948Third 0·878 beta 1·112 0·981 0·993

Fourth Feed 0·981 beta 1·02 0·997 0'999

(iii) Overall mole balance

Qfeed = Qret +Qperm

Q perm = Qfeed _ Qret

Mole balance on the water:Q is molar flow rate, X w is mole fraction of water in feed (feed), permeate(perm) and retentate (ret).

so

Qfeed xfeed _ Qretxret

x perm = w wW QPerm

Q feedx~ed _ Q ret X ~t

Qfeed_Qret

Stage cut:


mass flow permE>=---------,~

mass flow feed

mass flow feed - mass flow ret= mass flow feed

mass flow ret= 1- ------,,.........,

mass flow feed

= 1- Qret((I-X:;t)MwtEtOH + X:;tMwtWat)Qfeed((I-x~ed)MwtEtOH+ X~edMwtWat)

Qret-1-A--- Qfeed

327

((I-X:;t)MwtEtOH + X:;tMwtWat)where A = ..,...:-:-----..-'--;-'-,----=--=-=---;-,..,--.,------'----

((1- X~ed)MwtEtOH+ X~edMwtWat)

so

Q feedQret=_(I_E»

A

All quantities are now known or calculable, the feed (0·504), retentate(0·020), stage cut (0·5). Set feed molar flow to I, so the permeateconcentration is calculated (0·856). Hence the required enrichment is:

x perm{3 - w 3-27- xfeed+xret

w w

2

REFERENCES

Baker, R. W. (1990). Membrane Separation Systems - A research needsassessment, Report to U.S. Department of Energy, Office of Energy Research,April.

Baker, R. W., Yoshioka, N., Mohr, J. M. & Kahn, A. J. (1987). Separation oforganic vapors from air. J. Membr. Sci., 31, 259-71.

Bell, C.-M., Gerner, F. J. & Strathmann, H. (1988). Selection of polymers forpervaporation membranes. J. Membr. Sci., 36,315-29.

Crank, J. & Park, G. S. (1968). Diffusion in Polymers, Academic Press, NewYork.

Gudernatsch, W., Menzel, Th. & Strathmann, H. (1991). Influence of compositemembrane structure on pervaporation. J. Membr. Sci. (in print).

Hwang, S.-T. & Kammermeyer, K. (1975). Membranes in Separations, John Wiley& Sons, New York.


Katchalsky, A. & Curran, P. F. (1967). Non-Equilibrium Thermodynamics inBiophysics, Harvard University Press, Cambridge, Mass.

Lloyd, D. R. ed. (1985). Materials Science of Synthetic Membranes, ACS Symposium Series 269, American Chemical Society, Washington.

Lonsdale, H. K. (1982). The growth of membrane technology. J. Membr. Sci., 10,81-181.

Maiorela, B. L., Blanch H. W. & Wilke, C. R. (1984). Economic evaluation ofalternative ethanol fermentation processes. Biotechnol. Bioeng., 26, 1003-25.

Mulder, M. & Smolders, C. A. (1986). Continuous ethanol production controlledby membrane processes. Process Biochem. (April).

Nagashima, M., Azuma, M., Nagudi, S., Inuzuka, K. & Samejima, H. (1984).Continuous ethanol fermentation using immobilized yeast cells. Biotechnol.Bioeng. 26,992-7.

Neel, J. (1991). Introduction to pervaporation. In Pervaporation MembraneSeparation Processes, ed. R. Y. M. Huang, Elsevier, Amsterdam, pp. 1-109.

Neel, J., Aptel, P. & Clement, R. (1985). Basic aspects of pervaporation. Desalination, 53, 297-326.

Rautenbach, R. & Albrecht, R. (1989). Membrane Processes, John Wiley & Sons,New York.

Rautenbach, R., Herion, C. & Meyer-Blumenroth, U. (1991). Engineering aspectsof pervaporation: calculation of transport resistances, module optimization andplant design. In Pervaporation Membrane Separation Processes, ed. R. Y. M.Huang, Elsevier, Amsterdam, pp. 181-223.

Sander, U. & Santiago, P. (1988). Design and operation of a pervaporation plantfor ethanol dehydration. J. Membr. Sci., 36, 463-75.

Strathmann, H. Trennung von molekularen Mischungen mit Hilfe synthetischerMembranen, D. Steinkopff Verlag, Darmstadt (1979).

Strathmann, H. (1990). Membranes and membrane separation processes. InUllmanns Encyclopedia of Industrial Chemistry, Vol. A 16, pp. 187-263.

Strathmann, H. & Gudernatsch, W. (1991). Continuous removal of ethanol frombioreactors by pervaporation. In Extractive Bioconversions, ed. B. Mattiasson& O. Holst, M. Dekker, New York, pp. 67-89.

Strathmann, H., Bell, C.-M. & Kerres, J. (1990). Gas separation and pervaporation membrane module development. Desalination, 77,259-78.

Strathmann, H., Gudernatsch, W., Bell, C.-M. & Kimmerle, K. (1988). DieEntwicklung von losungsmittelselektiven Membranen und ihre Anwendung inder Gastrennung und Pervaporation. Chem.-Ing.-Tech., 60,590-603.

Wang, D. I. C. (1987). Separations for biotechnology. In Separations for Biotechnology, ed. M. S. Verrall & M. 1. Hudson, Ellis Horwood, Ltd., Chichester, U.K.

INDEX

Acrylonitrile (AN), 254Activity coefficients, 86Adsorption, 25, 204, 205, 207-11

proteins, 222, 227, 272-3Adsorption coating, 32Adsorption isotherms, 216Aggregation, 204, 205

proteins, 211-13Aliphatic polyamides, 29Amino acids, rejection of, 274Amorphous polymers, 26Association, 212Asymmetric membranes, 3, 18, 22

Backflushing, 247-8Baffles, 62-3, 250-2BASIC program, 166Batch concentration, 178Batch plant, single-stage, 166--8Beverage industries, 158Bioproducts, 13-14Bioreactor constituents, 293Biosensors, 156Bioseparations, 13Blasius correlation, 146Bleed plant, 162--4

two-stage, 164-6Blood processing, 157Boundary conditions, 64Boundary layer, 89, 101Bovine serum albumin (BSA), 37, 222,

227-8, 231, 235, 236, 259Bubble-point method, 38--40, 230Bulk concentration, 91

and limiting flux, 89versus flux, 143, 145

Capillary condensation techniques, 230Captive bubble method, 225Carman-Kozeny equation, 34-5, 72, 73,

233,234Cascade systems, 11

mathematical design approach, 168-76Cell debris separation, 153Cell separation, 153Cells, fouling of membranes by, 213-14

Cellulose, 49chemical structure, 19-20

Cellulose acetate, 1, 3, 20, 49Cellulose derivatives, 20Cellulose diacetate, 23Cellulose esters, 20Cellulose nitrate, 20Cellulose triacetate, 23Cellulosics, 19, 29Chain flexibility, 26Chemical potential, 2, 5, 78, 307-8Chemically stable polymers, 28Chlorine, 190Chlorolignin, ultrafiltration of, 221Clarification of biofluids, 114Cleaning agents, 25Cleaning and membrane lifetimes, 151-2Coagulation, 212Colloids

influence of physico-chemistry ontransmission, 125-6

membrane filtration of, 274-6Complexation, 212Composite membranes, 18-19, 23-5, 100,

304, 305Concentration, 14Concentration boundary layers, 56--60, 90Concentration build-up in hollow fibres,

102Concentration driven membrane processes,

8-9Concentration effect on flux, 142-6Concentration polarisation, 60, 127-8, 142,

301Concentration profile, 60, 61, 90, 103Contact angle, 46

hysteresis, 230measurement of, 224-6

Control software, 178-9Convection in a pore, 118-19Convective flow, 55-60

of solvent through porous membranes,71--4

Cooling system, 177Copermeation of organic by-product,

316--17Counter-current mode, 135-6Cross-current mode, 134-5

329

330 Index

Cross filtration of mycelial cells, 193-20 Iconcentration, 196-201cost considerations, 194experimental programme, 194flux versus time, 195operating conditions, 193optimum recirculation velocity, 197-8pore size, 194-5pressure, 196

Cross-flow, 6electrofiltration, 278filtration, 277microfiltration, 284velocity, 67

Crystallites, 26-7Cut-off curves, 230Cytochrome C, 273, 274

Dairy industry, 4Darcy's law, 143, 232Debye length, 124, 215Deposition potential, 235-7Deposition rate, 237Dextran, 125, 126, 144, 254Diafiltration, 7-8, 130-6, 193-20 I

continuous, 130, 134, 135design, 132--4example, 9-10mass balance equations in, 131-2multi-stage counter-current, 135-6multi-stage crossed-current, 134-5

Dialysis membranes, 20Diffusion, in a pore, 118-19Diffusion coefficients, 43, 69, 76, 80, 81,

125, 300, 303--4Diffusion equation, 64Diffusive flow, 55-60Diffusive, flux, 62Diffusivity, 76Dimpled/furrowed membranes, 249-50Distribution coefficient, 300Distribution of residence times, 65-6Disulphide bonding, 211Dittus-Boelter relationship, 66DLVO theory, 124,205,215Downstream processing, 293Drinking water, ultrafiltration system,

179-93Driving forces, 5-6

Electrical double layer, 265-7Electrically enhanced membrane processes,

265

Electrochemical effects, 271-6Electrochemical interactions, 266Electrochemical properties, 215-23,

265-91measurement of, 269-70

Electrocoat paint industry, 4Electrocoat paint recovery, 271-2Electrodialysis, 3Electrofiltration, 265

applications, 281-8conventional, 281-3module design, 279-81theory, 277-9

Electrokinetic effects, 267-9Electrolysis, 280Electrolytic membrane cleaning, 283-5Electron microscopy, 230Electro-osmosis, 268-9Electro-osmotic backwashing, 285-6Electrophoresis, 267Electrophoretic paints, 220Electrostatic forces, 205, 216Electrostatic interaction, 215, 220Electro-ultrafiltration, 281Energy consumption, estimation of, 184Enhancement, 75Enrichment factor, 298, 299Entrance length, 149Ethanol

direct recovery using pervaporation,317-19

pervaporation in microbiologicalproduction, 314-19

separation problem in microbiologicalprod uction of, 314-15

Ethylene-vinylacetate (EVA), 29Ethylene-vinylalcol (EVAL), 29Eureka Programme, 179

Feed-membrane interface, 79Feed plant, 162--4

two-stage, 164-6Feed pressures, 177Feed pump, 176-7Feed rates, 177Fick's law of diffusion, 80, 237Film model, 61-3Flat sheet membranes, 161-3Flexible polymers, 43Flow reversal, 62, 248Flowing cakes, 70Fluid dynamic calculations, 184Fluid flow patterns, 63Fluid mechanical phenomena, 56

Index

Flux, 7concentration effect on, 142-6control, 232-3enhancement, 243-64

hydrodynamics, 243-52surface modifications, 252-51

measurement, 67pressure effect on, 142-6reduction, 221versus bulk concentration, 143, 145versus concentration, 196-2, 201versus time, 151,201see also Limiting flux

Food processing, 157-8Food processing in, 1Fouling, 129-30, 150-1, 189, 203--41, 253,

301approaches to combat, 243by precipitates, 213convection-controlled deposition, 237definition, 203experiments, 186influence of charge, 220-3influence of hydrophilicity, 226-9influence of pore size, 231layer structure, 212-13mechanisms, 203-5models, 232-7physico-chemically limited mechanism,

234-5prevention, 186-7rate, 195reaction model, 237re-entrainment controlled deposition,

235-7research, 186resistance, 235unstirred cake filtration model,

233--4see also Surface phenomena

Fractionation, 14Frame assemblies, 161-2Friction factor, 146, 245Fruit juices, 100, 157

Gass absorption modelling, 63Gas flux measurements, 35-6Gas recovery, 155Gas separation, 4, 10-12, 59, 159Gel-polarization model, 89Gel theory, 93Gelatin, ultrafiltration of, 94Glass transition temperature, 26, 27Glassy polymers, 26

331

Hagen-Poiseuille equation, 34-5, 71, 115,209

Hamaker constant, 225-7Heat transfer, 89-90Heat tansfer equation, 106Hg-intrusion methods, 230Holding vessels, 177Hollow fibre modules, 159-60Hollow fibre systems

backflushing, 247versus other geometrics, 184

Hydraulic permeability coefficient, 95Hydrodynamics, 243-52Hydrophilic conditions, 230Hydropholic membranes, 45Hydrophilic monomers, 254Hydrophilic polymers and copolymers, 29Hydrophilicity, 223-9

influence on fouling, 226-9measurement of, 224-6

Hydrophobic forces, 211Hydrophobic membranes, 45Hydrophobic polymers, 46, 254Hydrophobic protein residues, 207Hydrophobicity, 223-9, 253Hydroxyethyl methacrylate (HEMA), 254

Immersion precipitation, 22-3Inorganic membranes, solvent fluxes

through, 95-6Instrumentation, 178Integral asymmetric membranes, 302Interfacial forces, 205-7Interfacial polymerization, 23-5Inter-molecular affinity, 206Internal pore blocking, 210-11Ionic strength, 206, 215,216

Kapton,50Kelvin equation, 40, 41Kidney dialysis machines, 157

p-Iactoglobulin, ultrafiltration of, 228,231-2

Laminar flow, 62, 66, 100, 244Langmuir-Blodgett layers, 259Laplace equation, 279Leveque formula, 102Limiting flux, 86-96

and bulk concentration, 89in ultrafiltration systems, 86-95predicted values of, 92theoretical condition, 91

332 Index

Liquid-displacement method, 39-40Liquid permeation, 34-5Liquid phase permeability, 95

Mass balance equations indiafiltration, 131-2

Mass transfer, 5~70, 101equations, 9~102, 298in pervaporation, 7~82, 295-7in reverse osmosis, 84-5into developing velocity gradient, 105-6mathematical relationships, 77-82through reverse osmosis membranes,

98-100viscosity effect on, 103-5

Mass transfer coefficient, 59, 60, 65, 70,88-91, 94, 101, 145, 146, 148-9

Medical applications, 157Membrane filtration of colloidal

materials, 274-6Membrane material, nature of, 185Membrane morphology, 18Membrane performance parameters,

298-300Membrane-permeate interface, 79Membrane processes, 1-3

advantages, 14-15disadvantages, 15electrically enhanced, 265generalised system, 2history, 3-4schematic representation, 15

Membrane reactors, 155-6Membrane resistance, 8Membrane selectivity, 299Membrane-solute interactions, 215-17Membrane surfaces

dynamic modification, 257-9with inorganic compounds, 258-9with Langmuir-Blodgett layers, 259with polymers, 257-8

effects of solution conditions, 259-60modification, 252-61

before membrane casting, 253-5permanent modification, 253-7

after casting, 255-7Membrane systems

cast study, 193-201configuration selection, 162-76cost, 141design, 141-202

case study, 179-93detailed considerations, 152-62examples, 162

factors influencing, 146information required, 142

experimental trials, 141-2module configuration, 158-62module geometries, 184-5operation/design, 174-6performance, 141pilot system, 176process selection in biotechnology,

153-8project definition, 179-83see also Cross filtration of mycelial cells;

Water treatmentMembranes

asymmetric, 3, 18, 22choice of, 13definition, 3, 15-19in food processing, Imaterial selection, 25, 28-9nature of, 13-54preparation, 19-25see also under specific type of

membraneMemtec system, 248Microbial cells, 265-7Microfiltration, I, 114, 193

electrically enhanced, 287electrochemical aspects, 265-91flux versus concentration, 146history, 3-4shear diffusion in, 69tubular pinch in, 68-70

Microfiltration membranes, 15, 16, 128preparation techniques, 20

Molecular affinity for membrane, 206Molecular shape and integrity, 207Molecular size, 206Molecular washing, 285Molecular weight, 43Molecular weight cut-off (MWCO), 41-5,

273Mycelial cells, cross filtrations.

See Cross filtration of mycelial cellsMyoglobin, 273, 274

Nanofiltration membranes, 17, 222preparation, 23water flux data, 95

Navier-Stokes equation, 279Nomex,50Non-porous membranes, 16

permeation through, 74-6Nylon 6,6, 50

Index 333

Orange juice, reverse osmosis of, 248Osmosis, 82-6

phenomenon of, 82Osmotic backwashing, 285Osmotic flow, 82Osmotic pressure, 2, 82-6, 143-5

measurement of, 82models, 89of fruit juices, 100phenomenon of, 82thermodynamic relationship, 83

Particle diffusion, 66-70Peclet number, 118PEG, 125, 126, 260Permeability coefficient, 8, 75, 300Permeability methods, 34-7Permeate, 7Permeation, 70-82

related characterisation methods, 38--40through non-porous membranes, 74-6through porous membranes, 71--4

Permporometry, 40-1Permselective barrier, 57Permselective membranes, 15Permselectivity, 75Pervaporation, 4, 55, 59, 293-329

as unit operation, 307-13biotechnological restrictions, 311

chemical engineering aspects of processdesign, 311-13

copermeation of organic by-products,316-17

direct recovery of ethanol, 317-19feed and permeate flow patterns, 312-13fundamentals, 294-302heat transfer within membrane module,

319in microbiological production processes,

314-19integration into fermentation process,

315-17mass transfer in, 76-82, 295-7mass transport in modules, 319mathematical description, 295-7membrane and process optimisation in

integrated processes, 317-19membrane characterisation, 300-1membrane model, 306-7membrane requirements, 302-7module configurations, 306-7operating modes, 307-11operating principle, 77overall process economics, 319-20

permeation cascade, 313product quality improvement, 319

pH effects, 126, 206, 217, 218, 221-3, 227,231, 233, 236, 259-60, 265, 272-3

pH meter, 218Phase inversion, 3, 21, 30Phenomenological coefficient, 78Photogrammetry, 230pI effect, 222-3Pilot system, 176pK values, 259Plasma treatment, 31-2Plasmapheresis, 157Plasticising, 8-9Plate assemblies, 161-2PLC type controllers, 178Plug flow, 62Poisson-Boltzmann equation, 266Polyacrylamide (PAAm), 49Polyacrylic acid (PAA), 49Polyacrylonitrile (PAN), 30, 49Polyamide, 28, 254Polyamideimide, 28Polybenzimidazole (PBI), 49Polycarbonate (PC), 49Polydimethylsiloxane, 49Polydimethylsiloxane (PDMS), 81, 303, 304Polyelectrolytes, 221Polyester, 28Polyether, 28Polyetheretherketone (PEEK), 27, 29Polyetherimide (PEl), 30, 37Polyethersulphone (PES), 30, 50, 123Polyethylene (PE), 46, 49Poly(ethylene imine) (PEl), 221Poly(ethylene oxide) (PEO), 227Polyhexamethylenedipamide, 50Polyimide, 28, 30, 50Polymer blends, 30Polymer state, 25-8Polymeric degradation, 29Polymeric membranes, 15, 19Polymethacrylate (PMA), 227Poly(methacrylic acid), 227Poly(methyl methacrylate) (PMMA), 50,

227Polyoxyethylene (POE), 254Poly(oxyethylene glycol) (POE-OH), 254Polyphenylene, 28Poly m-phenylene isophtalimide, 50Polyphenylene oxide (PPO), 50Polyphosphasenes, 28Polypropylene (PP), 46, 50, 185Polysiloxanes, 28Polystyrene (PS), 50

334 Index

Polysulphones, 30, 31, 50, 152, 185, 228,273, 274, 303

Polytetrafluoroethylene (PTFE), 27, 28,46,51

Poly(vinyl alcohol) (PVA), 185, 254Poly(vinyl chloride) (PVC), 254Poly(vinyl difluoride) (PVDF), 31, 123, 185Polyvinylacetate (PVAc), 51Polyvinylalcohol (PVA), 51, 260Polyvinylamine (PVAm), 51Polyvinylbutyrate, 30Poly(vinylchloride) (PVC), 51, 227Poly(vinylidenefluoride) (PVDF), 46, 51,

220Polyvinylpyrrolidone (PVP), 30, 51, 101,

126Pore blockage, 208-11Pore bridging model, 209Pore size

distribution, 209influence on fouling, 231measurement methods, 229-30

Porous capillary model, 98-9Porous membranes, 16

characterisation, 33, 33-47convective flow of solvent through, 71-4permeation-related parameters, 33permeation through, 71-4selectivity, 114-26

and ionic interactions, 122-5structure-related parameters, 33structures, 114-115

Potential gradient, 5Potentiometric titrations, 218-19Powdered activated carbon (PAC), 189,

190Precipitates, fouling by, 213Precipitation

by controlled evaporation, 21-2from vapour phase, 22

Pressure driven membrane processes, 6-8,17,282

Pressure drop, 146-8Pressure effect on flux, 142-6Prism system, 4Process engineering, 126-36Product removal, 154Proteins

adsorption of, 222, 227, 272-3aggregation, 211-13processing, 154ultrafiltration of, 222, 233

Pulsatile flow, 62with baffles, 250-2

Pulsed electrophoretic cleaning, 283Pulsed flow, 63, 248-9Purification, 14

Radius of gyration, 42-3Recycling, 247Rejection

at ultrafiltration membranes, 273-4of amino acids, 274

Rejection coefficient, 7, 96-8Relative flux reduction (RFR), 36-7Relative permeate flux (RF), 37Resistance models, 89Retentate, 7Retention, 221Retention coefficient, 117, 127Reverse osmosis, 1, 2, 59, 157-8, 159

history, 3-4mass transport in, 84-5of orange juice, 248solution-diffusion model for, 85-6

Reverse osmosis membranes, 17characterising performances, 99mass transport through, 98-100preparation, 23

Reynolds number, 62, 70, 146, 149, 250-2Rotating filter, 63Rotating membranes, 246-7Rubbery polymers, 26

Saccharomyces cerevisiae, 266, 314, 316Scanning electron microscopy, 230Scouring models, 70Sealing problems, 162Selective layer, 303-4Semi-crystalline polymers, 26-7Separation, 13, 113-39

process selectivity, 114Separation factors, 9, 11, 299Sessile drop method, 225Shear diffusion in microfiltration, 69Shear stress, 90, 104Sherwood number, 62, 245Sieving equation, 119-21Sieving mechanism, 17Simpsons Rule, 166Smoluchowski equation, 217, 267, 268Solubility coefficient, 74Solute flow through pore, 116-18Solute-membrane interactions, 215-17Solute rejection measurements, 41-5Solute-solute interactions, 204

Index

Solute-solute separation, 113Solution-diffusion, 8Solution-diffusion model, 74

for reverse osmosis, 85-6Solvation forces, 205Solvent flow through single pore, 115-16Solvent fluxes through inorganic

membranes 95-6Solvent-solute separation, 113Spiral wound membrane system, 158-9,

174-6Steric effects, 229Steric forces, 205-6Steric hindrance, 229Sterilisation, 154-5Sticking bubble method, 47, 225Stokes-Einstein diffusion, 67Stokes-Einstein equation, 67Stokes-Einstein radius, 42, 43Streaming potentials, 217, 218Support layer, 304-5Surface area/volume ratio, 149Surface charges, measurement of, 217Surface concentration, 91Surface modification techniques, 30-2

adsorption coating, 32chemical reaction, 30-1flux enhancement, 252-51plasma treatment, 31-2

Surface phenomena, quantification of,214-32

Surface properties, characterisation of,45-7

Surface renewal model, 63-6Surface roughness

influence on fouling, 232measurement of, 230

Surface tension, 46, 47Surface viscosity, 91Sweep gas pervaporation, 310, 311Symmetric membranes, 18

Taylor vortices, 63Tensile modulus, 26Ternary system phase diagram, 21Thermal precipitation, 22Thermally stable polymers, 28Thermo-pervaporation, 310, 311Thin-film composites (TFC), 23Time frequency diagram, 182Transmembrane pressure, 6Transport equations through pores, 114-26Transport processes, 55-112

335

Tubular pinch, 67in microfiltration, 68-70

Tubular systems, 160-1packing densities for, 161

Turbulence/convection promoters, 244-6Turbulent flow, 62, 66

Ultrafiltration, 1, 60, 100-2, 114drinking water, 179-93electrically enhanced, 287electrochemical aspects, 265-91flux versus concentration, 143history, 3--4limiting flux in, 86-95of p-Iactoglobulin, 228, 231-2of chlorolignin, 221of gelatin, 94of proteins, 222, 233versus other membrane processes, 184

Ultrafiltration membranes, 15, 16, 128preparation, 23rejection at, 273--4

Vacuum pervaporation, 308-9Van der Waals forces, 205, 211, 216van't Hoff equation, 83, 143Velocity gradient, 105-6Vinyl acetate (VAc), 254Vinyl acetate-vinyl chloride, 30Viscosity effect on mass transfer, 103-5Voltage gradient, 279

Water treatment, 179-80advantages and disadvantages of

mebrane filtration, 181bundle geometry, 186choice of membrane type and

configuration, 184-5energy consumption, 191fibre geometry, 186future possibilities, 193ground waters, 187man-power requirement, 191membrane material, 185membrane regeneration

requirement, 190-1membrane replacement, 192module size considerations, 186operating costs, 190-3

336

pilot scale validation, 187-9plant size, performances and limitations,

190process definition and validation, 186-9quality regulation, 180-1quality validation of technical choices,

182-3raw water quality and its consequences,

181-2reagents, 190-2surface waters, 189, 192waste waters and biological processes,

189

Index

Welhelmy method, 225Wettability, 25

measurement of, 224-6Whey protein concentration, 4

Young's equation, 46

Zeta-potential, 217, 218, 221, 267, 268, 270,275, 276

membranes in bioprocessing: theory and applications

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