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Wall shear stress: effective parameter for thecharacterisation of the cross-flow transport in turbulent

regime during skimmed milk microfiltrationGeneviève Gésan-Guiziou, Georges Daufin, Evelyne Boyaval, Olivier Le Berre

To cite this version:Geneviève Gésan-Guiziou, Georges Daufin, Evelyne Boyaval, Olivier Le Berre. Wall shear stress:effective parameter for the characterisation of the cross-flow transport in turbulent regime duringskimmed milk microfiltration. Le Lait, INRA Editions, 1999, 79 (3), pp.347-354. <hal-00929657>

Lait (1999) 79, 347-354© InralElsevier, Paris

347

Note

Wall shear stress: effective parameterfor the characterisation of the cross-flow transport

in turbulent regime during skimmed milkmicrofiitration

Geneviève Gésan-Guiziou*, Georges Daufin, Evelyne Boyaval,Olivier Le Berre

Laboratoire de recherches de technologie laitière, Inra, 65, rue de Saint-Brieuc,35042 Rennes cedex, France

(Received 2 July 1998; accepted 60ctober 1998)

Abstract - Sorne experimental evidence is accumulating in the literature which shows that themean cross-flow velocity is not an effective parame ter for the characterisation of the cross-flowtransport in membrane separation processes. The aim of this work was to determine the most appro-priate parameters (among the wall shear stress, tw' the wall shear rate, y, the Reynolds number, Re,and the mean cross-flow velocity, v) that should be used to assess the limiting and critical fluxes inturbulent regime. The experiments were applied to skimmed milk microfiitration (MF) using a tubu-Jar ceramic membrane (0.1 IJ.mmean pore diameter) for the separation of casein micelles from thesolluble proteins. These experiments were conducted with several membrane geometries (seven or19 channel s, 40 or 85.6 cm long) and seve rai rigs. Unlike Re and v, tw made it possible to assess theIimiting and critical permeation fluxes in milk MF (0.1 IJ.m),whatever the membrane geometry. It wasconsequently concluded to be an effective parameter to account for cake filtration and to study the cross-flow filtration scale-up. The wall shear rate, calculated by assuming the turbulence damped at the mem-brane surface and the flow laminar, was not suitable for the assessment of the Iimiting and critical fluxesin turbulent regime. © Inra/Elsevier, Paris.

wall shear stress / hydrodynamics / critical permeation flux / cross-flow microfiltration /skimmed milk

Résumé - La contrainte de cisaillement à la membrane: paramètre pertinent pour caracté-riser l'écoulement tangentiel en régime turbulent durant la microfiltration tangentielle de laitécrémé. L'objectif de ce travail est de montrer que la contrainte de cisaillement à la membrane est unparamètre approprié pour caractériser l'écoulement tangentiel dans les opérations de séparations parmembranes en régime turbulent. Les expériences de microfiltration tangentielle de lait écrémé sur une

* Correspondence and reprints. gesan@labtechno.roazhon.inra.fr

348 G. Gésan-Guiziou et al.

membrane de 0,1 micromètre de diamètres de pores (séparation micelles de caséines / protéines dulactosérum) ont été réalisées avec différentes géométries de membranes et différents pilotes de filtrationen utilisant la circulation du perméat à cocourant du rétentat. À la différence du nombre deReynolds et de la vitesse moyenne d'écoulement tangentielle, la contrainte de cisaillement à la mem-brane permettait de déterminer les flux de perméation limite et critique quelle que soit la géométriede la membrane (nombre de canaux, diamètre hydraulique, longueur). Cette grandeur était donc per-tinente pour rendre compte des performances des séparations sur membranes et pour étudier leschangements d'échelle. Le taux de cisaillement à la membrane, calculé en faisant l'hypothèse d'unécoulement laminaire à la surface de la membrane, n'était pas approprié à l'évaluation des flux de per-méation critique et limite en régime turbulent. Des études complémentaires devront être réalisées pourdéterminer la possible pertinence de ce paramètre vis-à-vis de la caractérisation de l'écoulementtangentiel. © InralElsevier, Paris.

contrainte de cisaillement / hydrodynamique / flux de perméation critique / microfiltrationtangentielle / lait écrémé

1. INTRODUCTION

The practical application of micro filtra-tion (MF) is often limited by severe foul-ing of the membrane. To reduce this fouling,MF is often carried out in cross-flow modein which a tangential flow transports mate-rial away from the membrane. Many mech-anisms (Brownian diffusion, hydrodynamicdiffusion, erosion, etc.) have been suggestedto explain the steady-state flow commonlyobserved in cross-flow MF, which occursin spite of the continuous convective solidsmass towards the membrane. Ali of themodels predict that the limiting flux (llim'

which is the permeation flux independentof the pressure and obtained when hightransmembrane pressures are applied)depends on cross-flow transport [3]. How-ever, according to the models, the variablecharacterising the cross-flow transport is

different. The aim of this work was to showthat the wall shear stress ('tw) is an appro-priate parameter for the assessment of Jlimand the critical flux (lcrit) compared to theReynolds number (Re) and the mean cross-flow velocity (v), and that they can be usedfor filtration scale-up. The experiments wereapplied to skimmed milk MF using a tubu-lar ceramic membrane (0.1 um mean porediameter) for the separation of caseinmicelles from the soluble proteins.

2. EXPERIMENTAL

2.1. Fluids

Skimmed milk, heat treated at 63 "C for 15 s,was provided by Compagnie laitière européenne(Montauban-de-Bretagne, France). It was heatedto 50 "C 30 min before MF experiments, and0.2 g·L-1 sodium azide was added to it to pre-vent any microorganism development.

List of symbols: di: initial diameter of the tubular membrane (m); dl: hydraulic diameter thatremains open to flow (m); Fa: Fanning factor (-); J: permeation flux (m-s! or L·h-1·m-2);

lcri': critical permeation flux (m-s:" or L·h-l·m-2); llim: limiting permeation flux (rn-s! orL·h-l·m-2); L: length of the membrane tube (m); n: channel number (-); Qr: retentate flow rate(m3·s-I); Re: Reynolds number (-); T: temperature (OC); v: mean cross-flow velocity (m-s:"):Ad: variation of the hydraulic diameter (%); t1P: transmembrane pressure (Pa or bar);t1PI.: pressure drop along the membrane (Pa or bar); y: wall shear rate (s'): YL: wall shear ratedefined in laminar regime according to equation (5) (s "): YT: wall shear rate defined fromequation (4) (S-I); Ilr: dynamic viscosity of the retentate (Pa-s:"); Pr: density of the retentate(m--kg'"); 'tw: shear stress at the membrane wall (Pa).

Shear stress in cross-f1ow microfiltration

Water used in the MF rigs came from the lab-oratory tap water network and was filtered on5 um, then on seriai cartridges of 1.0 and 0.2 um,

The cleaning solutions were: Alkaline:P3-Ultrasil 13 (Henkel-Ecolab SNC; lssy-Ies-Moulineaux, France), 0.15 % v/v; temperature(T) = 50 "C; v = 6 rn-s "; 15 min without perme-ation, 15 min with permeation flux (1) =240 L·h-1·m-2• Acid: HN03 (purity 58 %; Lan-glois Chimie, Saint-Jacques-de-la-Lande, France)0.1 % v/v; T = 50 "C; v = 6 m-s:"; 15 min withoutpermeation, 15 min with J = 240 L·h-1·m-2•

2.2. Microfiltration rig, membranesand operating procedure

Three filtration pilot rigs were used. Ail ofthem could operate either at controlled trans-membrane pressure (t1P) or at controlled J. Ail

349

the experiments were performed using the co-CUITentmode. This mode of operation consistsof the circulation of the permeate co-current to theretentate in order to create a permeate pressuredrop equal to the retentate pressure drop, so as toget no t1P difference along the hydraulic path[16].

Rig 1 consisted of the slightly modified rigdescribed previously [6]: the retentate valve usedto maintain the mean retentate pressure as con-stant during an experiment was replaced by acentrifuge feed pump and a relief valve. The usedmultichannel tubular Kerasep membranes(ORELIS, 01 Miribel, France) have the samemembrane characteristics (alumina membraneon an alumina support, mean pore diameter0.1 um) but different geometries (see table 1).The initial diameter of the cleaned membraneswas determined in laminar regime using sac-charose solutions of different viscosities. The

Controlled variable Geometry

Table I. Operating parameters for the experiments performed with different membrane geometries.Tableau I. Conditions opératoires des expérimentations réalisées avec différentes géométries demembranes.

7 channelsd, = 4.35 10-3 mL

I= 0.856 m

Wall shear stress, 'w'w= 100± 8 Pa(YT = 168000 ± 14000 S-I)

YL = 10 100± 200 S-1

Re = 41 500 ± 800v = 5.50 ± 0.05 m·s-1

JUin = 76 ± 2 L-h-i·m-2

'w = 100 ± 8 PaYT= 168000 ± 14000 S-1

Re = 41 500 ± 800v = 5.50 ± 0.05 m·s-iJUin = 76 ± 2 L-h-i·m-2

'w = 100± 8 PaYr = 168000 ± 14000 S-i

YL = 10 100± 200 S-1

v = 5.50 ± 0.05 m.s-iJUin = 76 ± 2 L·h-i·m-2

t = 100+8 Pay;= 168000 ± 14000 S-1

YL= 10 100± 200 S-I

Re = 41 500 ± 800J. = 76 ± 2 L·h-i·m-2

IIm

Wall shear rate, yYL = 10 ISO ± 250 S-1

Reynolds number, ReRe = 42 200 ± 1200

Cross-flow velocity, vv = 5.50 ± 0.05 m-s'

7 channelsdi = 4.33 10-3 mL= 0.40 m

19 channelsd = 2.75 10-3 mL=0.856m

YL = 9 900 ± 200 S-1

Re=40 loo±800v = 5.35 ± 0.05 m-s'J'iln = 75 ± 2 L·h-i·m-2

YL = 14800 ± 300 S-I

Re = 24 200 ± 500 m·s-iv = 5.09 ± 0.05 m-s"J. = 74 ± 2 L·h-i·m-2

1""'w = 55 ±4 PaYT = 926 000 ± 7 000 S-1

Re = 16700 ± 300v = 3.50 ± 0.05 m-s:'JUin = 40 ± 1 L·h-i·m-2

'w = 275 ± 20 PaYT = 464 000 ± 34 000 S-I

YL = 26 300 ± 600 S-I

v = 9.05 ± 0.05 m·s-IJUin = unstable

'w= 117 ± 8 PaYT= 197000 ± 14000 S-1

YL = 16000 ± 200 S-I

Re = 26 180± 500Jliln = 83 ± 2 L·h-i·m-2

350

4Qrv=--

nnd,2

with n, the channel number and dl' the hydraulicdiameter that remained open to flow during theexperiment. dl corresponds to the initial mem-brane diameter reduced by the deposit thickness(see the Calculations section).

'tw whieh represents the forces applied by thefluid tlowing tangentially to the membrane onan element of membrane area, was experimen-tally determined according to:

G. Gésan-Guiziou et al.

operating conditions of the experiments are givenin table /. The experiments consisted of varia-tions of L'iP(0.0-1.0 x 105 Pa) at constant v (forexperiments performed at constant Re, v or YL'

wall shear rate defined in the laminar regimeaccording to equation (5); (see further in theCalculations section) or longitudinal pressuredrop (L'iPL) (for experiments performed at con-stant 'tw or YTwall shear rate defined from equa-tion (4); (see further in the Calculations section)with 10 min duration at each step. Before eachexperiment, the skimmed milk was concentratedup to a volume reduction ratio (VRR) of2 (L'iP= 0.1 x 105 Pa, duration about 45 min).This level of the VRR was maintained as con-stant during ail of the experiments by runningMF in a feed and bleed mode of operation. Theseexperiments made it possible to assess llim' Alithe experiments were performed in duplicate.

Rig 2 [10] was an MFS 1 type (MicroFiltrationSystem, Alfa-Laval, Lund, Sweden) equippedwith a multichannel membrane consisting of an{X-alumina filtering layer on an alumina support(Membralox" membrane; SCT, Bazet, France:19 channels, inner diameter 4 mm, length 0.85 m,membrane area 0.2 m2, mean pore diameter0.1 um), This pilot rig was composed of threepumps: a centrifuge feed pump maintaining theretentate pressure and two volumetrie pumps forthe circulation of fluids in the retentate and per-meate compartments.

Rig 3 [6] was equipped with a monotubeMernbralox" membrane (SCT, Bazet, France)consisting of an {X-alumina filtering layer on analumina support (inner diameter 6.8 mm, length0.75 rn, membrane area 1.60 x 10-2 m2, meanpore diameter 0.1 um),

The experiments with rigs 2 and 3 were per-formed over the course of time at various constantpermeation fluxes and two cross-flow velocities.These experiments made it possible to defineleril according to the methodology proposed by LeBerre and Daufin [II J. leril is defined as the per-meation flux below which there is no depositionon the membrane surface. Under leri! filtrationperformance is satisfactory (long MF time withslow increase of fouling and high solute trans-mission), and above leri. performance is altered.

2.3. Calculations

The mean v was calculated from the reten-tate flow rate (Qr) as Iollows:

(1)

d,APLr =--w 4L

(2)

where L'iPL, is the longitudinal pressure drop andL is the length of the membrane tube. The pres-sure drop that should be used in equation (2) isthat due to the flow through the filter tube.Bernouilli's equation has then been used to cal-culate the longitudinal pressure drop along themembrane tube once the pressure losses due torecirculation of flow before and after the filterhave been removed l'rom the measured value ofpressure drop. Bernouilli's equation gave com-parable results (5 %) to pressure corrections basedon a hydrodynamic study of the module [7].

Re wa calculated as follows:

p,vd,Re= --

Jir (3)

where Pr and J.lr are the retentate density anddynamic viscosity, respectively. Whatever theexperiment, the regime was turbulent (Re »4000;see tahle 1).

The wall shear rate (y) was calculated in twodifferent ways:

- directly from 'tw and J.lr measurementsassuming the tluid to be newtonian at the mem-brane surface, YT:

(4)Yr=Jir

- by assuming a laminar velocity profile: theturbulence is severely damped at the membranesurface and the flow behaves as a laminar flow insome respects, yI.:

(5)

Piron et al. [13] apply equation (5) for theapproximation of yin turbulent regime, assumingthe retentate viscosity constant and the turbu-

Shear stress in cross-flow microfiltration

lence damped in the neighbourhood of the mem-brane.

The diameter that remains open to flow, dl'decreased during the experiment due to the depo-sition of microorganisms, casein micelles, etc., atthe membrane surface. The relation betwecn 'wand the Fanning factor (Fa) (equation 6) and theapproximation of Blasius in turbulent flow,assuming the membrane to be a smooth tubularelement (equation 6), enable dl to be worked out.

Far = - P V2w 2 r

Fa = 0.08 Re-ll.25

The rugosity of the clean Kerasep membrane,calculated with the Churchill correlation [14],was found to be 3 x 10-6 m. Since the rugosity islikely to decrease as a result of the deposition ofcase in micelles during the experiment, the diam-eter is given with a 5 % accuracy and the pressuredrop with an 8 % accuracy.

The maximum variation of hydraulic diam-

eter, ~d (%) = dl~ di X 100 (di initial hydraulic1

diameter of the clean membrane) over the courseof the experiment was taken into account in theerror specified for each variable (v, Re, 'w' YLand YT) in table 1.

3. RESULTS AND DISCUSSION

Figure J shows the evolution of the per-meation flux versus ~P for experiments per-formed at similar v, Re, YL, YT and Lw withdifferent membrane geometries. Apart fromexperiments performed at very high crossflow (LW = 275 Pa, Re = 42 200, YL = 26300 S-I, v = 9.05 m-s"; table 1), a limitingflux can be observed. This limiting flux isdue to the deposit of casein micelles,microorganisms in the neighbourhood ofthe membrane [9, II] and further investi-gations are in progress to understand theapparent instability of the deposit at highcross-flow transport.

As shown infigure J, Lw and YTproved tobe the most appropriate parameters toaccount for milk MF performance, sincewhatever the membrane geometry, the lim-

351

(6)

iting flux was similar contrarily to what hap-pened with v, Re and y. Moreover, when LW(or YT'directly calculted from Lw) increased,the limiting flux increased (table 1). Theseresults contrasted strongly with thoseobserved by Samuelsson et al. [15], whoshow that the limiting flux is a Iinear func-tion of Re: in this work, two experimentsperformed with different membrane geome-tries and similar Re gave significantly dif-ferent limiting fluxes.

The large discrepancy in the resultsobserved with YT and YL (table J,figure J)emphasised the difficulty of evaluating thewall shear rate in turbulent regime. The cal-culation of the wall shear rate by assuminga Poiseuille flow (equation 5), as suggestedby Piron et al. [13], was inaccurate: the meancrossflow velocity of the viscous sub-Iayer(difficult to determine) should have beentaken into account in the calculation insteadof v. The calculation of y from Lw and theretentate dynarnic viscosity (equation 4) alsohas limitations when the layers depositedon the membrane have a non-newtonianbehaviour, which is the case in skimmedmilk MF. y, difficult to calculate in turbulentregime, could therefore not be consideredin this work as an reliable parameter. Furtherinvestigations should be carried out in lam-inar regime to know whether is an effectiveparameter for the assessment of J1im. Suchexperiments are, however, beyond the scopeof this work since milk MF operations aremainly carried out in turbulent regime.

Although sorne authors believe that thedecisive variable in the cake cross-flow fil-tration is v [2], experimental evidence isaccumulating in the literature and supportsour results. Lu et al. [12] show, for example,that a decrease of the hydraulic diameter ofthe membrane under a given cross-flowvelocity, which leads to an increase ofmem-brane shear stress, improves performance.Aubert et al. [1] use Lw to characterise thedeposit thickness of carbon particles at thesurface of a rotating membrane. Benkahla etal. [4] suggest that the cake growth limit

(7)

352 G. Gésan-Guiziou et al.

140

120

rf' 100E

-' 80:.cd 60-. 40 v = 5.50 ± 0.05 m.s'

20

o 1 1 1

0.0 0.2 0.4 0.6 0.8 1.0 1.2

LlP (l05 Pa)

140

120

rf'looE_. 80

:.cd 60-. 40

YI.= 10150 ± 250 S·I20

1 1 1

0.2 0.4 0.6 0.8 1.0 1.2

LlP (l05 Pa)

140

120

~ 100'1:; 80

:.c 60d-. 40

20Re =42200 ± 1200

0.4 0.6 0.8

LlP (l05 Pa)1.0 1.2

140

120

rf' 1001:; 80

:.c 60....i'-'-. 40

20

~w = 100 ± 8 PaY1= 168000 ± 14000 S·I

0.2 0.4 0.6 0.8LlP (l05 Pa)

1.2

Figure 1. Permeation flux (l) versus transmembrane pressure (dP) for experiments performed withdifferent membrane geometries at constant cross-flow velocity (v), Reynolds number (Re), wallshear rates (YT)(cg. 4) and YL (eq, 5) and wall shear stress (lw)' (-): 7 channels, 0.4 m; (_):19 channels, 0.856 m; (-): 7 channels, 0.856 m.Figure 1. Densités de flux de perméation, 1 en fonction de la pression transmembranaire, dP pour desexpérimentations réalisées avec différentes géométries de membranes à même vitesse moyenned'écoulement tangentiel, v, même nombre de Reynolds, Re, même taux de cisaillement à la membraneYT(Eq, 4) et YL(Eq, 5) et même contrainte de cisaillement, "w' (-) 7 canaux; 0,4 m (-) 19 canaux;0,856 m ; ( - ) 7 canaux; 0,856 m.

can be attributed to the Coulomb failure cri-terion defined by a relation taking intoaccount shear and normal stresses acting onthe cake as weil as the friction coefficientand the cohesion of the deposit. Accordingto Wu et al. [17], 'tw should be employed tocharacterise the cross-flow transport becauseit considers the changes in modules charac-teristics and cross-flow velocity but also thechanges in viscosity in the course of anexperiment.

The representation of Jeril (under whichfouling is low) vs. 'tw (or YT ranging l'rom

125000 ta 250 000 S-I) demonstrated a goodcorrelation between experimental dataobtained with two different rigs and mem-brane geometries (figure 2), contrary to likev, Re and YL''tw consequently seemed ta bean appropriate parame ter ta study filtrationscale-up since it made it possible ta deter-mine the cri tic al operating conditions of asystem (Jeril' J'lm)' whatever the geometryof the membrane and the membrane sur-face. Recent publications painting out theexistence of a Jcr/'tw ratio [5, 8, Il] rein-forced this result.

Shear stress in cross-flow microfiltration 353

125 a a 125 b a

,....., ,.....,"i "i 100E; 100 E;:.c:: :.c::c!- a c!- a •75 • 75jj "B... ...• •

50 505 5.5 6 6.5 7 30000 50000 70000

v (m.s") Re

125 C a 125

,....., ,.....,"i 100 "iE; E; 100:.c:: :.c::c!- • a c!-jj 75 'Ë 75... • ...

50 500 5000 10000 15000 75 100 125 150

Yds·l) 'tw(Pa)

Figure 2. Critical permeation fluxes (Jeri') obtained with two different membrane geometries: (0) rnul-tichannel, 19 channels (0.2 m-; initial diameter of the membrane tube [dd = 4 x 10-3 m; length of thetube [L] = 0.85 m); (.) monotube (0.02 ml; di = 6.8 x 10-3 m; L = 0.75 m) versus a) mean cross-flowvelocity (v); b) Reynolds number (Re); c) wall shear rate (YL' eq. 5); and d) wall shear stress ('tw)'

Figure 2. Densités de flux de perméations critiques obtenues avec deux géométries de membranes:(0) multicanal, 19 canaux (0,2 ml; di = 4 x 10-3 m ; L = 0,85 m) ; (. ) monotube (0,02 ml;di = 6,8 x 10-3 m ; L = 0,75 m) en fonction de : a) vitesse moyenne d'écoulement tangentiel, v ;b) nombre de Reynolds, Re ; c) taux de cisaillement à la membrane, YI.(Eq. 5) ; d) contrainte decisaillement à la membrane, 'tw'

4. CONCLUSION

Unlike Re and v, which are parametersclassically used to characterise cross-flowtransport, 'tw made it possible to assess thellim and lcri! in milk MF (û.l um), whateverthe membrane geometry (length, channelnumber, hydraulic diameter). 'tw was con-sequently an effective parame ter to charac-terise the cross-flow transport, to accountfor cake filtration and to study the cross-flow filtration scale-up.

The wall shear rate y, cafculated byassuming the turbulence damped at the

membrane surface and the flow behaviourlaminar, was not a satisfactory parameterfor controlling the process in turbulentregime. It proved y to be difficult to calculatein turbulent regime, and further investiga-tions should be performed in order to clarifyits effectiveness in controlling the process.

ACKNOWLEDGEMENTS

We thank M. Garnier for technical assistancewith the rig built-up and D. Jacob for setting upthe regulations of microfiltration operating con-ditions.

354 G. Gésan-Guiziou et al.

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[1] Aubert M.C., Elluard M.P., Barnier H, Shear tration of skimmed milk: transition to irreversible

stress induced erosion of filtration cake studied deposition, J. Membrane Sci. (1999) in press.

by a Ilat rotating disk method, J. Membrane Sei, [10] Le Berre O., Microfiltration tangentielle de lait84 (1993) 229-240. appliquée à la séparation des micelles de caséine

[2] Baker R.J., Fane A.G., Feil C.J.D., Yoo B.H., des protéines solubles: aspects hydrodyna-Factors affecting Ilux in crossflow filtration, miques et physico-chimiques, thèse ENSA,Desalination 53 (1985) 81-93. Rennes, France, 1996.

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[5] Boyaval P., Lavenant C; Gésan G., Daufin G., filtration model based on integration of the massTransient and stationary operating conditions transport equation, J. Membrane Sei. 108 (1995)on performance of lactic acid bacteria crossllow 57-70.microlïltration, Biotechnol. Bioeng., 49 (1996)

[14] René F., Leuliet J .C., Delplace F., Friction fae-78-86.[6] Daulin G., Radenac J.F., Gésan G., Kerhervé F.L.,

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Le Berre O., Michel F., Merin D., A novel rig 175-182.design for ultra and microfiltration experiments,

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[8J Gésan G., Daufin G., Merin U., Performance of [17] Wu D., Field R., Howell J., Filtration behaviourwhey microfiltration during transient and sta- of baker' s yeast suspensions at very high con-tionary operating conditions, J. Membrane Sci., centrations, Separ. Sei. Technol. 30 (1995)104 (1995) 271-281. 1473-1490.