Further Reading - index-of.co.uk/index-of.co.uk/Tutorials-2/Microfiltration.pdf · ial and yeast...

glass membranes were produced by Corning(Vycor�), Schott, and PPG. Glass membranes aretypically made as discs, tubes or hollow-Rbres. Toproduce microporous glass membranes, a homogene-ous melt consisting of 70 wt% SiO2, 23 wt% B2O3

and 7 wt% Na2O is formed between 1300 to 15003C.Phase separation of the initially homogeneous glassmelt occurs by lowering the temperature to about8003C. One phase consists primarily of insoluble sili-con dioxide. The other phase, rich in alkali borate,can be leached from the heterogeneous glass by treat-ment with a mineral acid. After removal of the alkaliborate phase, a microporous silica membrane isformed.

Future Developments

During the past forty years membranes have gainedsigniRcant importance in a wide variety of industrialseparations. Currently, polymeric membranes aremost commonly used for commercial applications.However, recent developments on inorganic mem-branes are very promising and such membranes maybroaden the separation spectrum of membranes forseparations. The wide-spread use of inorganic mem-branes in industrial applications is currently limitedby their poor mechanical stability and very high pro-duction costs. If these problems can be solved infuture work, inorganic membranes will present a newgeneration of high-performance membranes for thenext millennium.

Further Reading

Baker RW, Cussler EL, Eykamp W et al. (1991) MembraneSeparation Systems } Recent Developments and FutureDirections. Park Ridge, NJ: Noyes Data Corporation.

Bhave RR (1991) Inorganic Membranes. New York:Van Nostrand Reinhold.

Burggraaf AJ and Cot L (1996) Fundamentals of InorganicMembrane Science and Technology. Amsterdam:Elsevier.

Cabasso I (1987) In Encyclopedia of Polymer Science andEngineering, Vol. 9, pp. 509}579. New York:John Wiley and Sons.

Kesting RE (1971) Synthetic Polymeric Membranes.New York: McGraw-Hill Book Company.

Kesting RE and Fritzsche AK (1993) Polymeric Gas Separ-ation Membranes. New York: John Wiley and Sons, Inc.

Koros WJ and Pinnau I (1994) In: Paul DR and YampolskiiYP (eds) Polymeric Gas Separation Membranes,pp. 209}271. Boca Raton: CRC Press.

Lloyd DR (1985) Materials Science of Synthetic Mem-branes. ACS Symp. Ser. 269. Washington DC: ACS.

Mulder M (1996) Basic Principles of Membrane Technology,2nd edn, Boston, MA: Kluwer Academic Publishers.

Petersen RJ and Cadotte JE (1990) In: Porter MC (ed)Handbook of Industrial Membrane Technology,pp. 307}348. Park Ridge, NJ: Noyes Publications.

Pinnau I (1994) Polym. Adv. Techn., 5, 733.Strathmann H (1979) Trennung von molekularen Mischun-

gen mit Hilfe synthetischer Membranen. Darmstadt:Dr. Dietrich Steinkopff Verlag.

Strathmann H (1990) In: Porter MC (ed) Handbook ofIndustrial Membrane Technology, pp. 1}60. ParkRidge, NJ: Noyes Publications.

Micro\ltration

I. H. Huisman, AMKM, TNO Voeding, AJ Zeist,Holland

Copyright^ 2000 Academic Press

Introduction

MicroRltration is a separation technique for remov-ing micron-sized particles, like bacteria, yeast cells,colloids, and smoke particles, from suspensions orgases. The process uses membrane Rlters with poresin the approximate size range 0.1 to 10 �m, which arepermeable to the Suid, but retain the particles, thuscausing separation. Examples of particles with sizesin the microRltration range are presented in Figure 1.

MicroRltration membranes were Rrst commercial-ized in the 1920s, and were at that time mainly usedfor the bacteriological analysis of water. After 1960the number of successful microRltration applications

grew rapidly, and nowadays microRltration processesare operated in such different Relds as the biotech-nological, automobile, electronics, and food industry.Examples of applications are the harvesting of bacter-ial and yeast cells, the recovery of latex pigmentsfrom paints, and the puriRcation of water for theelectronics industry. In the food industry, microRltra-tion is used in the clariRcation of fruit juices, wine,and beer, in fat removal from whey and in removal ofbacteria from milk.

MicroRltration is the largest industrial marketwithin the membrane Reld, responsible for about40% of total sales, both in Europe and in the USA. In1997, the US microRltration membrane marketamassed revenues worth about $400 million, growingat an average annual growth rate of 6.6%. MicroRl-tration can be carried out in two different operationmodes: dead-end (in line) Rltration and cross-Sow

1764 II / MEMBRANE SEPARATIONS / Micro\ltration

Figure 1 Particles in microfiltration size range.

Figure 2 (A) Dead-end filtration and (B) cross-flow microfiltra-tion using a tubular membrane.

(tangential Sow) Rltration (Figure 2). In dead-end Tl-tration the main Sow direction is perpendicular to themembrane. The suspended particles are continuouslydragged towards the membrane and deposit on thesurface or inside the membrane pores. The depositionof particles leads to a continuously increasing resist-ance to Sow and thus to a continuously decreasingpermeate Sux rate. To reduce this deposition process,microRltration is often carried out in the cross-Uowmode (tangential Sow) in which the main Sow direc-tion is tangential to the membrane. The Sow ‘scours’

away particles from the membrane surface, and thuslimits particle deposition.

Micro\ltration Membranes

Two main types of membrane Rlters exist: screenTlters and depth Tlters. Screen Rlters contain capil-lary-type pores; particles are retained on the mem-brane surface primarily by a sieving mechanism.Depth Rlters contain a random, tortuous porousstructure; particles are retained through adsorptionand mechanical entrapment within the bulk of theRlter. Screen Rlters are absolute: particles larger thanthe pore size are retained, whereas particles smallerthan the pore size can pass relatively easily throughthe membrane. Particle retention of depth Rlters is notthat clearly deRned: retention values increase slowlyover a broad particle size range and only reach 100%for very large particles. Depth Rlters are often usedfor dead-end Rltration, as they can retain a highparticle load.

Membrane Materials and Membrane Preparation

MicroRltration membranes are available in a widevariety of materials and methods of manufacture.Many membranes are made of polymers, such ascellulose acetate, polysulfone, and polyvinylidene Su-oride (PVDF). Most of these membranes are solventcast, through a phase inversion process. Other prep-aration techniques are stretching (polytetraSuoro-ethylene, PTFE, membranes) and track-etching (poly-carbonate membranes). The track-etching processresults in cylindrical pores with a very narrow sizedistribution.

Other microRltration membranes available aremade from glass, from ceramics, such as alumina,titania, and zirconia, and from metals, such as silverand stainless steel. Advantages of these inorganicmaterials are their higher stability towards extremeprocess conditions, such as high temperature, ex-treme pH values, and solvents different than water.Most metal and some ceramic membranes are pro-duced by a sintering process, whereas other ceramicmembranes are produced by sol-gel processing or byanodic oxidation. Some novel membranes are pre-pared by lithographic techniques.

In Table 1, a number of different commercialmembranes and some of their key properties are pre-sented, and in Figure 3 SEM (scanning electronmicroscopy) and AFM (atomic force microscopy) im-ages of some membranes are shown. Note that themembranes shown here are only a fraction of the totalnumber of membrane materials and membranemanufacturers available.

II / MEMBRANE SEPARATIONS / Micro\ltration 1765

Table 1 Various microfiltration membranes and their water fluxes

Manufacturer Trade name Material b Preparation method Pore sizea (�m) Water permeability at203C (L m�2 h�1 bar)

US Filter/SCT Membralox] �-Al2O3 Sintering 0.2 2 000Anotec Anopore] �-Al2O3 Anodic oxidation 0.2 3 600Carbon Lorraine Carbon Pyrolysis 0.2 1 500Tech Sep Carbosep] ZrO2 Sintering 0.14 400Millipore Durapore] PVDF Phase inversion 0.22 5 900

Fluoropore] PTFE Stretching 0.22 12 000MF-Millipore] Mixed cellulose

estersPhase inversion 0.22 14 400

Osmonics PCTE Polycarbonate Track-etching 0.2 14 600PES Polyethersulfone Phase inversion 0.2 20 500MCS Mixed cellulose

estersPhase inversion 0.22 15 400

Whatman Cyclopore] Polycarbonate Track-etching 0.2 16 000Aquamarijn MicrosieveTM Silicon nitride Photolithography 0.2 87 000

aAll these membranes are available with pore sizes in large ranges. The pore sizes closest to 0.22 �m are mentioned here to comparewater fluxes of the different membranes. bPVDF, polyvinylidene fluoride; PTFE, polytetrafluoroethylene.

Membrane Characterization

Originally the main goal in characterization ofporous membranes was to determine the pore-sizedistribution. It has however been realized more re-cently that membrane surface properties, such as hy-drophobicity, zeta potential and surface roughness,play an important factor in fouling and retentionproperties of membrane processes. Characterizationis therefore nowadays performed by various tech-niques, measuring different structural and physico-chemical parameters. The relatively novel techniqueof AFM microscopy has been shown to provide in-formation on many membrane properties of interest:pore size distribution, surface roughness, and ad-hesion behaviour. In Table 2, various measurementtechniques are summarized.

Dead-end Micro\ltration

In dead-end Rltration, the Suid is forced perpendicu-larly through the membrane, while all or most of theparticles are retained (Figure 2a). If screen Rlters areused, these particles build a cake layer on the surface,which causes an additional resistance to Sow. If depthRlters are used, these particles Rll the voids within themembrane bulk, and in this way cause an increasedresistance. For both types of Rlters, the increasedresistance causes a continuous decline in Sux if a con-stant transmembrane pressure is used (Figure 4).After some time, the Sux has been reduced to unac-ceptably low levels, and the membrane has to becleaned or replaced.

Dead-end Rltration is preferred over cross-Sow Rl-tration in situations where the concentration of par-ticles to be removed from the Suid is very low, as is

the case for sterile Rltration in the pharmaceuticalindustry, for gas cleaning, and for guard-Rlterspositioned as last step in a high-purity water unit.Dead-end Rltration is also used in situations wherebackSush techniques and gas sparging are soeffective that the use of a cross-Sow is not necessary,as found in some wastewater-treatment plants.

Fluid Flow through Membrane Pores

The capacity of a microRltration process is expressedas Sux, J, which is the volume of permeate passingthrough the membrane of area Am and per unit time:

J" 1Am

dVdt

[1]

where V is the volume of permeate, and t is time:Most commercial liquid microRltration processesoperate at Suxes of typically about 10�4 m s�1

(360 L m�2 h�1).The driving force for this Sux is the transmembrane

pressure (most commonly written as �P), the pressuredifference between feed side and permeate side,which results from applying either suction to thepermeate side or pressure to the feed side, or both.Transmembrane pressures in liquid microRltrationare typically 5}100 kPa (0.05}1 bar). It was foundphenomenologically that the Sux increases linearlywith the transmembrane pressure (Darcy’s law):

J" �PRm ) �0

[2]

where �0 is the permeate viscosity, and Rm is thehydraulic resistance of the membrane against


Figure 3 SEM (A}C, E}H) and AFM (D) of surfaces and cross-section of different membranes. (A) Durapore membrane, rating0.22 �m, PVDF solvent cast membrane (Millipore). (B) Fluoropore membrane, 0.1 rating, stretched PTFE (Millipore). (C) Polycarbonatetrack-etched membrane (Osmonics). (D) Anopore membrane, 0.1 �m rating, anodically oxidated Al2O3 (Anotec). (E) Microsieve,photolithography, silicon nitride (Aquamarijn). (F) Silver membrane (Millipore). (G) AP15 glass fibre depth filter (Millipore). (H)Cross-section of a P series membrane, solvent cast polyethersulfone (Osmonics). (A), (B), (F) and (G) were kindly supplied by theMillipore corporation. (C) and (H) were kindly supplied by Osmonics; (D) was kindly supplied by the Group of Membrane Science andTechnology, University of Valladolid, Spain; (E) was kindly supplied by Aquamarijn.

permeate Sow. The permeability of the membrane isdeRned as the inverse of its resistance (1/Rm).MicroRltration membranes have permeabilities oftypically 10�11 m.

The permeability is related to the pore size. Theexact relation between permeability and pore sizedepends on the geometry. For straight cylindricalpores, the Hagen}Poiseuille equation yields:

Rm" 8l�mr2

p[3]

where l is the membrane thickness, �m is themembrane porosity, and rp is the pore radius. Formembranes comprised of sintered spheres, theKozeny}Carman equation may give a better approxi-mation:

Rm"45(1!�m)2l�3

ma2m

[4]

where am is the radius of the particles that constitutethe membrane.


Figure 3 Continued


Figure 3 Continued

Screen Filters: Cake-layer Build-up

The Sux calculated by eqns [2]}[4] is the so-called‘pure water Sux’. During Rltration, fouling and cake-layer build-up continuously decrease the Sux to valuesmuch lower than the pure water Sux. Darcy’s law(eqn [2]) can be written for a fouled membrane as:

J" �PRtot ) �0

[5]

where Rtot is the total hydraulic resistance. It can bedivided into the membrane resistance (Rm), the resist-ance caused by fouling (Rf), and the resistance causedby the cake layer (Rcake):

Rtot"Rm#Rf#Rcake [6]

Fouling can be caused by processes such as the ad-sorption of macromolecules or bacteria. It is difRcult


Figure 3 Continued

to predict the extent of fouling quantitatively; aqualitative description is given in a later section.The cake resistance can be calculated by the Kozeny}Carman equation, eqn [4], where the cake’s voidfraction �, the cake-layer thickness �c, and theparticle radius a are to be inserted for �m, l andam respectively.

The void fraction of the cake layer, �, may dependon various parameters, such as transmembranepressure, particle size distribution, shape, andcompressibility, and the effect of particle}particle in-teractions. Often a value between 0.3 and 0.4 isfound for �.

A model for the time dependent dead-endRltration Sux is obtained by combining eqns [4]}[6]with a mass balance describing cake layer build-up:

�d�c

dt#J��b"(1!�)

d�c

dt[7]

where �b is volume fraction of particles in the bulk.If a constant �P is applied, the Sux is given by:

J(t)" �P�0Rm �1# 2RK c�b�P ) t

(1!�!�b)�0R2m�

�1/2

[8]

where RK c is the speciRc cake resistance ("Rc/�c). Caremust be taken when using eqn [8] as � and RK c oftendepend on time (cake compaction).

Depth Filters

Particle retention in depth Rlters is based on variousmechanisms. In the case of gas cleaning, the two


Figure 3 Continued

most important mechanisms are particle capture byinterception and particle capture by diffusion. Inter-ception occurs when a particle follows a Suid stream-

line, which at some point passes close to the Rltersurface at a distance less than the particle radius, thuscausing contact between the particle and the Rlter.


Table 2 Membrane characterization methods

Method a Parameters obtained Description/remarks

Microscopic techniques ‘Direct’ observation by microscopes.SEM, TEM, FESEM(#image analysis)

Pore-size distribution, poremorphology (surface roughness)

Although these methods have many advanced possibili-ties, they are mostly used for determining the pore-sizedistribution in the membrane surface. Preparation ofsample necessary

AFM (#image analysis) Pore-size distribution, morphology,surface roughness, particle}membrane interactions

See SEM (no preparation technique is necessary)

Liquid penetration methods Liquids will fill larger pores at low pressures. To fill smallerpores, however, higher pressures are needed

Bubble point method Largest pore available Simple method, contact angle of membrane}liquid needsto be known

Extended bubble point method Pore-size distribution See bubble point methodMercury porometry Pore-size distribution High pressures are necessary that may damage the mem-

brane structure

Permporometry Pore-size distribution Vapour condensation in pores is measured. Rather com-plicated method

Solute retention Pore-size distribution (‘cut-off’) Membranes with smaller pores retain solutes of smallersizes. Simple method. More often used for ultrafiltrationthan for microfiltration

Contact angle measurementsSessile drop, Wilhelmy plate Contact angle, surface tension,

hydrophobicityDirect methods that measure the contact angleliquid}air}membrane. Give qualitative infomation on hy-drophobicity

Electrokinetic methodsElectroviscous method Zeta potential, surface charge density Experimentally simple: measurement of water flux at vari-

ous ionic strengths. Interpretation of results more difficultStreaming potential,electroosmosis

Zeta potential, surface charge density Direct measurements of electrokinetic effects. Interpreta-tion of results sometimes complicated

aSEM, scanning electron microscopy; TEM, transmission electron microscopy; FESEM, field effect scanning electron microscopy;AFM, atomic force microscopy.

Figure 4 Flux versus time for the dead-end microfiltration ofa silica particle suspension.

Capture by diffusion occurs when the Brownianmotion of the particle results in contact between theparticle and the Rlter matrix.

Interception is the dominant capture mechanism forlarge particles; Brownian diffusion is the dominantcapture mechanism for smaller particles. Capture istherefore least effective for intermediate size particles,leading to the existence of a ‘most penetrating particlesize’ (Figure 5). The exact value of this most penetrat-ing particle size depends on the membrane pore dia-meter and the Sow velocity. It has been found, how-ever, that capture of particles from gas streams bymembranes of pore diameters of about 0.2 �m is soeffective that essentially all particles are retained.

For depth Rltration of liquids, the situation is dif-ferent, as physicochemical (charge) effects alter therelative magnitudes of the capture mechanisms de-scribed above. If physicochemical conditions are fa-vourable, capture efRciencies in liquids can be similarto those in gases. If conditions are less favourable,capture efRciencies for the smaller particles decrease

rapidly. Under these conditions sieving (entrapment)is the only effective particle capture mechanism, mak-ing the membrane permeable for all particles smallerthan the pore size.


Figure 5 Schematic representation of efficiency of capture byinterception and capture by diffusion versus particle size. Themost penetrating particle size is obtained by combining bothmechanisms.

Figure 6 Flux versus time for the cross-flow microfiltration ofa silica particle suspension.

Cross-]ow Micro\ltration

Dead-end microRltration, as stated, may suffer fromdramatic Sux loss because of deposition of particleson the membrane surface and fouling phenomena.Therefore microRltration is often carried out in thecross-Uow mode (Figure 2b). The tangential Sow(cross-Sow) ‘scours’ away particles from the mem-brane surface, and thus limits cake-layer build-up andfouling. Another advantage of cross-Sow Rltration isthe possibility for continuous operation. Cross-SowRltration is used in most industrial large-scale micro-Rltration plants. For cross-Sow microRltration, screenRlters are mainly used.

Cake-layer Build-up and Fouling

During a cross-Sow microRltration process, a Suxbehaviour is often observed as shown in Figure 6. TheSux declines at Rrst rapidly with time; then the speedof Sux decline decreases, and Rnally a steady state isreached where the Sux does not decrease anymore.The decrease in Sux is commonly ascribed to twophenomena: cake-layer build-up and fouling.

When Rltering a suspension, the membrane retainssuspended particles. The particle concentration nearthe membrane will therefore gradually increase.Cake-layer build-up will occur when the particle con-centration near the membrane surface reaches themaximum packing density (0.6}0.7). Cake-layerbuild-up is thus caused by the particles that areretained by the membrane based on their size,independent of any speciRc interaction between these

particles and the membrane. Cake-layer build-up inmicroRltration is a phenomenon similar to concentra-tion polarization in ultraRltration.

Fouling, on the other hand, is based on a directcontact between solutes and the membrane surface.The term ‘fouling’ includes many processes, such asadsorption and deposition of macromolecules, bac-teria, or small organic molecules on the membranesurface or within the pores. Fouling increases the hy-draulic resistance against permeate Sow, and thus re-duces the capacity of the microRltration process. More-over, fouling in general increases the observed retentionof the membrane as it reduces the effective pore size.

If one plots the steady-state Sux for crossSow micro-Rltration versus transmembrane pressure (�P) oftena curve as given in Figure 7 is obtained. Three regimescan be observed. For low values of �P, the Sux in-creases linearly with �P and often equals the purewater Sux. For higher values of �P, the Sux curvebends, because of cake-layer build-up, and Suxes be-come less than the pure water Sux. The point wherethe deviation from the straight line starts is oftenreferred to as the critical Uux. For even higher �P, theSux is independent of the pressure. This pressure inde-pendent Sux value is referred to as the limiting Uux.

Factors In]uencing Membrane Fouling andCake-layer Build-up

The extent of membrane fouling and cake-layerbuild-up depends on many parameters, which can begrouped in three main contributors:� properties of the membrane,� properties of the suspension, and� properties of the process (hydrodynamics).

Membrane properties of importance are hydro-phobicity, surface charge (zeta potential), surface


Figure 7 Steady-state flux versus �P for the cross-flow micro-filtration of a silica particle suspension. **, water; - - - � - - -,silica particle suspension.

roughness, and pore-size distribution. In general,macromolecular adsorption is more severe for hydro-phobic than for hydrophilic membranes. Fouling bynegatively charged colloids is less for negativelycharged membranes than for uncharged or positivelycharged membranes. As most colloids in practicalsuspensions acquire a negative charge, negativelycharged membranes are preferred in general. Mem-brane fouling is further reduced by choosingmembranes with smooth surfaces, small pore sizes,and narrow pore size distributions.

Feed suspension properties of importance are par-ticle concentration, particle charge (zeta potential),ionic strength, and overall composition. The amountof cake-layer build-up increases with particle concen-tration. Charge effects can reduce fouling by mem-brane-particle repulsion, and can reduce cake-layerbuild-up by particle}particle repulsion. Such chargeeffects are less pronounced at high ionic strength, asthe ions present in solution ‘shield’ the charge ofmembrane and particles. Overall composition of thefeed suspension is of great importance for the foulingbehaviour. Fouling may be caused not only by themain particles retained, but also by macromoleculesand small organic molecules, which ‘geometrically’should pass through the pores easily.

Process properties of importance are the transmem-brane pressure and the cross-Sow velocity. Low foul-ing normally occurs at low transmembrane pressuresand high cross-Uow velocities. More detailed in-formation is given in a later section.

Calculating the Limiting Flux

To calculate the limiting steady-state Sux, local massbalances near the membrane surface are used. It is

then assumed that the limiting Sux is reached whenthe amount of particles transported towards themembrane by the permeate Sux (convection) equalsthe amount of particles transported away from themembrane by the cross-Sow. The cross-Sow cancause back-transport by at least four different mecha-nisms:

� Brownian diffusion,� shear-induced diffusion,� inertial lift, and� surface transport.

In the following, these mechanisms will be ex-plained. It is assumed throughout this section that theparticles are spherical and monodisperse, and thatlong-term fouling and physicochemical interactionsare negligible.

Brownian diffusion If back-transport is caused byBrownian diffusion the standard concentration polar-ization theory can be used, employing the Browniandiffusion coefRcient for spherical particles:

D" kT6��0a

[9]

where k is the Boltzmann constant, T is temperature,and a is the particle radius. By numerical calculations,using a suspension viscosity that depends on the par-ticle concentration, it can be shown that the Sux isgiven by:

J"0.0769 ��wk2T2

�30a

2L �1/3

�1/3b [10]

where �w is the wall shear stress and L is the mem-brane length.

Eqn [10] predicts Suxes of the right order of mag-nitude for suspensions of small particles (up to about10 nm). It under-predicts Suxes by one or two ordersof magnitude if applied to suspensions of larger par-ticles. This discrepancy is called the ‘Sux paradox’.This paradox is explained by assuming that there areother mechanisms for back transport, apart fromBrownian diffusion.

Shear-induced diffusion When a shear Reld is ap-plied to a layer of particles, the particles will tumbleover one another, leading to a more loosely packedlayer. Obviously the particles must move perpendicu-lar to the applied shear stress to achieve this. Theresulting particle migration can be described byemploying an effective diffusion coefRcient, and iscalled shear-induced diffusion.


Figure 8 Torque balance for the surface transport model.F�"horizontal drag force caused by the cross flow; FJ"verticaldrag force caused by the permeate flux J ; Fi"particleIparticleinteraction force; �"angle of repose.

It can be calculated, using an empirical value ofthe shear-induced diffusion coefRcient, that the limit-ing Sux is given by:

J"0.060�w

�0 �a4(1!3.8�b)

�bL �1/3

[11]

valid for �b(0.2, i.e. for all practical applications.Eqn [11] has been shown to give good Sux predic-tions for suspensions of hard spherical particles, andreasonable Sux predictions for complex bioSuidssuch as milk. Although eqn [11] is derived for localviscous Sow, Sux calculations have also been re-ported to be accurate for many turbulent Sowprocesses.

Inertial lift If a diluted suspension of particles Sowsthrough a duct, particles present close to the wall willmigrate towards the centre, perpendicular to thestreamlines. This migration, caused by complex hy-drodynamic interactions, is called inertial lift. Incross-Sow microRltration, inertial lift may be able toprevent particles from depositing onto the membrane.To model this phenomenon, it is assumed that a cakelayer builds up during microRltration until the con-vective velocity towards the membrane (the Sux J)equals the lift velocity, vL, away from the membrane:

J"vL"0.036�0a

3�2w

�30

[12]

The inertial lift theory neglects the inSuence of a par-ticle on the motion of another particle, resulting ina Sux equation which does not depend on the particleconcentration. The inertial lift model is therefore onlyvalid for very low particle concentrations. As the Suxpredicted by eqn [12] increases with the cube of theparticle size and the square of the wall shear stress,inertial effects are expected to be important only forlarge particles ('5 �m) and high cross-Sow vel-ocities (�w'10 N m�2).

Surface transport A particle on top of a Rlter cake issubject to different forces, as shown in Figure 8. Thehorizontal drag force caused by the cross-SowF� exerts a clockwise torque on the particle, and thevertical drag force caused by the permeate SuxFJ exerts a counterclockwise torque. If the torquecaused by the cross-Sow is larger than the torquecaused by the permeate Sux, the particle can roll overthe cake layer to the outlet of the membrane. Thismechanism of transport is called surface transport.

Equating the clockwise torque with the anticlock-wise torque, an equation for the limiting Sux is

obtained:

J" 2.36a�w

�0 tan �(a2RK c)2/5 [13]

where � is the angle of repose (see Figure 8).Just as for the inertial lift model, the present model

neglects the inSuence of a particle on the motion ofanother particle, resulting in a Sux equation whichdoes not depend on the particle concentration.Eqn [13] overpredicts Suxes for typical microRltra-tion conditions by an order of magnitude or more.Two of the models described above, the Browniandiffusion model and the shear-induced diffu-sion model, use a continuum approach. The othertwo, the inertial lift model and the surface transportmodel, are based on a single-particle approach. Thesingle-particle approach is only valid for low particleconcentrations and large particles.

In Figure 9, the Suxes predicted by the two con-tinuum models are given as a function of particle sizefor typical cross-Sow microRltration conditions. TheSux predicted by the inertial lift model is plotted inthe same graph to indicate the order of magnitude ofinertial effects. For small particle sizes, Brownianeffects dominate and the Sux decreases withparticle size. For intermediate particle sizes, shear-induced diffusion dominates and the Sux increaseswith particle size. For large particle sizes ('5 �m)inertial effects dominate causing the Sux to increaseeven faster with particle size.

The combined effect of Brownian and shear-in-duced diffusion can be described by:

JBo#SI"�J2Bo#J2

SI [14]


Figure 9 Flux calculated according to different models asa function of particle diameter. Calculations were performed for�w"32 N m�2, �b"10�3, and L"1.2 m, using eqns [10]}[12]for the Brownian, shear-induced, and inertial-lift models, andusing eqn [14] for combining Brownian and shear-induced diffu-sion, - - - -, Brownian diffusion model; ) ) ) ) ) ) , shear-induceddiffusion model;*, Brownian and shear-induced diffusion model;22, inertial lift model.

Figure 10 Flux and amount of matter deposited on the mem-brane as a function of time for the filtration of a suspension of0.48-�m silica particles. Circles represent experimental values fora particle concentration of 1.7 kg m�3, a transmembrane pres-sure of 0.42 bar and a cross flow velocity of 1 m s�1; lines repres-ent model calculations.

Figure 11 Feed-and-bleed operational configuration for cross-flow microfiltration.

where JBo is the Sux according to Brownian theory,eqn [10], and JSI is the Sux according to shear-induced theory, eqn [11]. Predictions according toeqn [14] are also given in Figure 9.

Calculating the Transient Behaviour ofCross-]ow Micro\ltration

The time dependence of the Sux can be predictedusing an approach as outlined in the section on dead-end Rltration, yet allowing for back-transport accord-ing to the particle transport mechanisms describedabove. Such descriptions are rather complicated, andwill not be treated here.

A simple but effective approach to model the tran-sient behaviour of the permeate Sux is the use ofa combination of transient dead-end Rltration theoryand a cross-Sow Rltration model for the steady-state(limiting) Sux. While the cake is initially developing,the effect of the cross-Sow is small and can be neglect-ed, so that cross-Sow Rltration theory can be approxi-mated by dead-end Rltration theory. Upon approach-ing the steady state, the cross-Sow begins to arrest thecake growth and dead-end Rltration theory is nolonger accurate. However, near the steady state theSux shows only minor time dependence, and the Suxcan be approximated by its steady-state value.

The procedure to predict the total transient behav-iour of the permeate Sux is thus to use dead-endRltration theory (see the section on dead-end microRl-tration) until the time the steady-state Sux is reachedand then use the steady-state Sux predicted by

a steady-state cross-Sow Rltration model. This ap-proach is illustrated in Figure 10, modelling the tran-sient Sux and cake-layer build-up in the cross-SowmicroRltration of a suspension of silica particles.

Process Considerations

Cross-Sow microRltration is usually carried out in thefeed-and-bleed mode, shown in Figure 11. The use ofa retentate recycle makes it possible to work at highcross-Sow velocities (high Qc) while having lowretentate Sows (i.e. high volumetric concentrationfactors Vc"1#QP/QR). When high concentrationfactors are desired, several recirculation loops may beplaced in series, or in even more complicatedschemes, with loops both in parallel and in series(Christmas tree design).

In many cross-Sow microRltration systems and insome dead-end systems, backUushing is applied toremove the fouling layer from the membrane. Back-Sushing is achieved by forcing the permeate period-ically back through the membranes. Effective back-Sushing is obtained by using high counterpressures


Figure 12 Microfiltration flux when filtering a particle suspen-sion, with and without backflush.

(about 0.5 bar) for several seconds every few minutes(Figure 12).

Fouling is reduced by high cross-Sow velocities andlow transmembrane pressures. High cross-Sow vel-ocities cause high-pressure drops along the membrane,which cause the �P to be undesirably high at theentrance of the membrane module. Therefore microRl-tration processes have been developed which facilitatea cross-Sow both on the feed side and on the permeateside. The pressure drops on both sides are similar inmagnitude, guaranteeing a uniform transmembranepressure. This method of operation has been shown tobe effective in many dairy applications.

Other process techniques to reduce fouling are theuse of pulsed Sow, gas sparging, and electric or acous-tic Relds, and the use of Sow geometries that createsecondary Sows or vortices resulting in high shearrates (e.g. the use of ‘turbulence promoters’ or curvedchannels).

Conclusions

Over the last 70 years, microRltration has developedfrom a small specialized technology used only in

laboratories to a multibillion dollar industry forseparation and puriRcation of liquid and gasstreams. Especially since the 1980s, exciting newapplications have become possible, due to improvedmembranes (for example, ceramics) and improvedtechnologies (for example, backpulsing, uniformtransmembrane pressure). Still, great challengesexist, for example in the processing of beverages,such as fruit juices, milk, and beer, wheremembrane fouling seriously impairs the economy ofthe process.

To overcome these problems, researchers and en-gineers are becoming increasingly interested in hybridand combined processes. Combining microRltrationwith good pre- and post-treatments or with otherseparation processes may result in better and moreeconomic separations.

See also: II /Membrane Separations: Filtration.

Further Reading

Belfort G, Davis RH and Zydney AL (1994) The behaviorof suspensions and macromolecular solutions in cross-Sow microRltration. Journal of Membrane Science 96:1}58.

Bowen WR and Jenner F (1995) Theoretical descriptions ofmembrane Rltration of colloids and Rne particles: anassessment and review. Advances in Colloid and Inter-face Science 56: 141}200.

Ho WSW and Sirkar KK (1992) Membrane Handbook.New York: Van Nostrand Reinhold.

Howell JA, Sanchez V and Field RW (1993) Membranesin Bioprocessing } Theory and application, 1st edn.London: Chapman and Hall.

Mulder M (1992) Basic Principles of Membrane Techno-logy, 1st edn. Dordrecht: Kluwer Academic Publishers.

Scott K (1995) Handbook of Industrial Membranes.Oxford: Elsevier Science.

Zeman LJ and Zydney AL (1996) MicroTltrationand UltraTltration. Principles and Applications.New York: Marcel Dekker.

Pervaporation

H. E. A. BruK schke and N. P. Wynn,Sulzer Chemtech GmbH, Neunkirchen, Germany

Copyright^ 2000 Academic Press

Development

In 1917 PA Kober published a paper in which hedescribed his observation that ‘a liquid in a collodion

bag, which was suspended in the air, evaporated,although the bag was tightly closed’. Kober was notthe Rrst researcher to observe this phenomenon, butthe Rrst to realize its potential for the separation ofliquid mixtures which otherwise are difRcult to separ-ate, and to separate them under moderate conditions.He introduced the terms ‘Pervaporation’, and ‘Perstil-lation’, and the Rrst term is now in use to describe in

II / MEMBRANE SEPARATIONS / Pervaporation 1777

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