Proceedings of the Conference on Membranes in Drinking and Industrial Water Production, Volume 1, pages 421–432ISBN 0-86689-060-2, October 2000, Desalination Publications, L’Aquila, Italy

Presented at the Conference on Membranes in Drinking and Industrial Water Production, Paris, France, 3–6 October 2000International Water Association, European Desalination Society, American Water Works Association, Japan Water Works Association

The effect of shear rate on controlling the concentrationpolarization and membrane fouling

R. Biana, K. Yamamotoa, Y. Watanabeb*

aProduct Development Department, Environmental System Division, Shinko Pantec Co. Ltd.,Kokusai-Hamamatsucho Bldg., 9-18, 1-Chome, Kaigan, Minato-Ku, Tokyo 105-0022, Japan

Tel. +81 (3) 3459-5941; Fax +81 (3) 3437-3256; e-mail: r.bian@pantec.co.jpbDepartment of Environmental Engineering, Hokkaido University, Kita 13, Nishi 8, Sapporo 060-8628, Japan

Tel. +81 (11) 706-6275; Fax +81 (11) 706-7890; -email: yoshiw@eng.hokudai.ac.jp

Abstract

This paper deals with the results from experiments concerning the effects of an increasing shear rate at the edge of themembrane on reducing concentration polarization and on controlling membrane fouling during filtration of river water.Concentration polarization of humic substances in NF and MF membranes can be reduced by increasing the shear rate.The concentration polarization model can predict the removal efficiency of humic substances successfully. The highremoval efficiency of humic substances in NF membrane filtration processes can be sustained even when the waterrecovery rate reaches to 96%, if the membranes are vibrated with the maximum vibratory amplitude of 1". A cake layerformation on the NF membrane surface due to deposition of suspended colloids and humic substances dominates NFmembrane fouling. NF membrane fouling can be evaluated by the cake filtration model and controlled by increasing theshear rate. Humic substances with molecular weight of more than 6,000 Da are transported away from the membranesurface by the shear-induced diffusion. Humic substances with molecular weight of 2,000 Da and with molecular weightof less than 500 Da are transported away from the membrane surface not only by the shear-induced diffusion, but also byBrownian diffusion.

Keywords: Nanofiltration; Shear rate; Concentration polarization; Membrane fouling

1. Introduction

Membrane processes are becoming increas-ingly attractive as an alternative to conventionalwater and wastewater treatment. A major_________________________

*Corresponding author.

obstacle in applying membrane processes forpotable water supplies and wastewater treatmentis the permeate flux decline due to membranefouling. This is a problem because the capitaland operational costs of membrane systems aredirectly dependent on the membrane permeateflux. Raw waters contain a wide distribution of

R. Bian et al. / 421–432422

particle size. The membrane fouling mechanismsby small molecular substances, macromoleculesand colloids are all different. The smallmolecular substances can pass through themembrane and become absorbed inside themembrane pores. Macromolecules and colloidsare rejected on the membrane surface and tend toform a cake layer. Authors [1] report that forriver water filtration the cake formation on themembrane surface results in more serious UFmembrane fouling than the absorption of smallsubstances inside the membrane pores.

The removal of dissolved materials such ashumic substances in membrane processes is alsoimportant when selecting the membrane. Duringmembrane filtration, materials dissolved in thefeed water are convectively driven to themembrane surface where they build up aconcentration polarization boundary layer nearthe membrane surface. The formation ofconcentration polarization boundary layer resultsin increasing concentration of dissolvedmaterials near the membrane surface; as a result,the removal of dissolved materials declines withtime.

The formation of a cake layer on themembrane surface and concentration polarizationboundary layer near the membrane surfacedepend on the back diffusion phenomenon duringthe filtration process. The back transportmechanisms of small molecular substances,macromolecules and colloids are all different [2].Large particles are preferentially back-transported by shear-induced diffusion, whereassmall materials are transported from themembrane by Brownian diffusion. The backtransport mechanisms also depend on the shearrate at the membrane surface.

To control the concentration polarization andmembrane fouling, several practical approachessuch as modifying the surface chemistry ofmembrane have been pursued. This study focuseson increasing the back-transport of particles awayfrom the membrane by increasing the shear rate

to counteract the problems. The effects of theshear rate on improving removal of humicsubstances and controlling membrane fouling arediscussed in this paper.

2. Experimental methods

2.1. Source water

Chitose River water was used as experimentalraw water. The concentration of humic sub-stances and small colloids in this water isrelatively high. The annual average water quali-ties are: dissolved organic carbon (DOC) =3.1mg/L, UV absorbance at 260 nm (E260) =0.12cm-1, and turbidity = 25 NTU. After the riverwater was filtered through 0.45µm membranefilters, DOC and E260 were measured by aShimadzu, Model TOC-5000, and by a HitachiU-2000 spectrophotometer with a 1-cm cell at260 nm, respectively. Fig. 1 shows the correlationbetween DOC concentration and E260 of ChitoseRiver water during the period of October 1994, toDecember 1999. A good linear relationship,about 32, can be seen between DOC and E260.These results indicate that humic substances arethe major components of the natural organicmatters in Chitose River water [3].

FR

ig. 1. Correlation between DOC and E260 of Chitoseiver water during October 1994–December 1999.

R. Bian et al. / 421–432 423

Fig. 2. App

HPLC molecularsubstancespark coluphotometrsubstanceinto three The appasecond, anapproximarespectiverespectivetotal humi

2.2. Expeprocess

A vibr[4]) was uthe Chitostreatment.system is is composdriving smembranetransfers va system f

arent molecular weight distribution of humic substances in Chitose River water.

was used to determine the apparent weight distribution (AMWD) of humic in Chitose River water. A Hitachi gelmn and a commercial UV spectro-ic detector were used. The humics in Chitose River water can be dividedgroups by HPLC, as shown in Fig. 2.rent molecular weight of the first,d third groups are more than 6,000Da,tely 2,000Da, and less than 500Da,ly. The first, second, and third groups,ly, occupy 30%, 60%, and 10% of thec substances.

riments of vibratory shear enhanced

atory shear enhanced process (VSEPsed for the membrane process to treate River water directly without any pre- The schematic flow diagram of VSEPshown in Fig. 3. The VSEP apparatused of four main components, i.e., aystem that generates vibration, a module, a torsion spring whichibration to the membrane module, andor controlling vibration. It can vibrate

Fig. 3. Schematic flow diagram for the VSEP system.

the membrane with a frequency of 60Hz andmaximum vibratory amplitude of 1". A NFmembrane (NTR7450) made of sulfonated poly-thersulfone with 50% rejection of NaCl and anMF membrane made of Teflon with nominalpore size of 0.45µm were used.

The shear rate (γ, s-1) at the membranesurface can be calculated by Eq. (1):

scalelength scalevelocity =γ (1)

Thus the shear rate at the membrane surface seton the VSEP can be calculated by Eq. (2):

R. Bian et al. / 421–432424

Ff

wtvtcfVratc

0ooaVa8ftmoo

3. The effect of shear rate on reducing concen-

ig. 4. Comparison between shear rate of cross flowiltration and of membrane vibration when using VSEP.

Pf5.0

5.05.14µ

ρπγ = (2)

here f is the frequency of vibration (Hz), ρ ishe density of solution (water, units: kg/m3), μ isiscosity of solution (water, units: Pa s) and P ishe vibratory amplitude (m) [5]. Fig. 4 shows aomparison between the shear rate of cross flowiltration and of membrane vibration when usingSEP. It shows that the VSEP generates a shear

ate of about 120,000s-1 on the membrane surfacet the maximum vibratory amplitude; this is 20imes greater than the shear rate obtained byross flow filtration with fluid velocity of 1m/s.

A flat MF and NF membranes with an area of.045m2 were mounted on the membrane modulef the VSEP. The vibratory amplitude at the rimf the membrane module was set at 0, 1/4, 1/2,nd 1" to evaluate the effect of vibration. TheSEP membrane apparatus was operated under

constant transmembrane pressure of about50kPa for NF and 60 kPa for MF. The permeatelow rate, transmembrane pressure and tempera-ure of the feed water were measured everyinute. The VSEP membrane apparatus was

perated for about 100h without any hydraulicr chemical cleaning.

tration polarization

3.1. Concentration polarization and removal ofhumic substances

In membrane filtration processes, some of thecomponents in the solution are rejected by themembrane and accumulate near the membranesurface. Before reaching a steady state theconvective flow of the components to the mem-brane surface is larger than that due to diffusionback-flow to the bulk solution. This phenomenonis called concentration polarization. It is often aserious problem in membrane operations due toits negative influence on the removal of thecomponents and on the permeate flux [6]. Asshown in Fig. 5, at the steady state the convectivecomponents movement to the membrane surfaceis equal to the permeate flow and the diffusiveback transport of components into the bulksolution.

( )xCCCJ p d

d−=− (3)

where J is the permeate flux (m/s), C is thecomponents concentration in the bulk solution(mol/m3), Cp is the concentration in the permeate(mol/m3), D is the diffusion coefficient (m2/s),and x is the distance from the membrane surface(m). The diffusion coefficient is assumed to be aconstant, so that the following well-knownequation can be obtained:

−−

=

−−

=pb

pm

pb

pm

CCCC

kCCCCDJ lnln

δ(4)

where δ is the thickness of the boundary layer(m), k is the mass transfer coefficient, and Cm

and Cb are the concentrations at the membranesurface on the feed side and in the bulk solution,respectively. The mass transfer coefficientdepends on the molecular weight of the

R. Bian et al. / 421–432 425

F

cdvmcc

orhocewadrhtpt

3h

pt

ig. 5. Concentration polarization.

omponents and on the shear rate. It can beetermined by experiment with different fluidelocities of the tangential flow over theembrane surface. Then the concentration of

omponents on the membrane surface can bealculated from Eq. (4).

There are three ways to evaluate the removalf humic substances in membrane filtration: trueemoval efficiency based on the concentration ofumic substances on the membrane surface,bservable removal efficiency based on theoncentration in the feed water and removalfficiency based on the concentration in rawater. In this paper the true removal efficiency

nd observable removal efficiency are used toiscuss the concentration polarization, theemoval efficiency based on the concentration ofumic substances in raw water (hereafter referredo as removal efficiency) is used to evaluate theerformance of membrane filtration for waterreatment.

.2. Reduction of concentration polarization ofumic substances in NF membrane filtration

It has been considered that concentrationolarization arises because of the convectiveransport of solute to the membrane surface. It is

Fha

totssroeoscwvergwhrhVrfirsm

ig. 6. Relationship between the removal efficiency ofumic substances in the NF membrane and the vibratorymplitude.

herefore important to increase the back transportf solute to the bulk solution in order to be ableo decrease the accumulation at the membraneurface. This can be achieved by increasing thehear rate. The usual way of increasing the shearate is to make the feed solution flow tangentiallyver the membrane surface [6]. In this studyxperiments for evaluating the effect of vibrationn inducing concentration polarization of humicubstances in NF membrane filtration werearried out. The NF membrane set on the VSEPas vibrated with a frequency of 60Hz and aibratory amplitude of 0, 1/4, 1/2, and 1". In thesexperiments permeate of NF membrane waseturned to the reservoir. The areas of chromato-raphs of raw water and permeate by HPLCere used to evaluate the removal efficiency ofumic substances in each group. Fig. 6 shows theelationship between the removal efficiency ofumic substances and the vibratory amplitude ofSEP. It shows that the first group can be

emoved completely by the NF membraneiltration and that the removal efficiency isndependent of the vibratory amplitude. Thisesult shows that the molecular size of humicubstances in the first group is larger than the NFembrane pore size. The removal efficiencies of

R. Bian et al. / 421–432426

humic substances in the second and the thirdgroups increases with increasing vibratoryamplitude of VSEP.

Eq. (4) can be rewritten to show the relation-ship between observable removal efficiency, trueremoval efficiency and shear rate as thefollowing Eq. (5):

kJ

RR

RR

+−=− 1ln

1ln

obser

obser (5)

where

b

pb

cCC

R−

=obser (6)

m

pm

cCC

R−

= (7)

abk γ= (8)

where Robser and R are the observable removalefficiency and true removal efficiency,respectively.

The mass transfer coefficient of the secondgroup of humic substances, which occupiesabout 60% of total humic substances in ChitoseRiver water, was determined by a combinationof Eqs. (5)–(8). Fig. 7 shows the relationshipbetween the mass transfer coefficient of thesecond group and the shear rate at the membranesurface. It shows that the mass transfercoefficient of the second group increases with anincreasing shear rate. The relationship betweenthem obtained from our experiments can bewritten as Eq. (9):

5.17100.2 γ−×=k (9)

The ratio of the concentration of the secondgroup on the membrane surface to the concen-tration in the feed water can be calculated by a

Fig. 7. Influence of shear rate on the mass transfercoefficient of humic substances of the second group.

Fig. 8. Influence of shear rate on the ratio ofconcentration of humic substances of the second groupat the membrane surface to the concentration in thefeed water.

combination of Eqs. (4) and (9) as shown inFig. 8. It shows that the concentration of thesecond group of humic substances on themembrane surface decreases with increasingshear rate. This result proves that the concen-tration polarization of humic substances can bereduced by increasing the shear rate at the edgeof the membrane.

The water recovery rate is also an importantparameter for water treatment. A commonproblem has been that the removal efficiency ofsolute decreases with increasing water recovery

R. Bian et al. / 421–432 427

rate during membrane filtration. The concen-tration of solute in the permeate can be predictedby a combination of Eqs. (5)–(7) and (9) asEq. (10):

( )( )( )( )RKJR

RkJCC b

p −+−

=1/exp

1/exp(10)

Then the removal efficiency can be estimated byEq. (11):

( )( )( )( )RkJR

RkJR−+

−−=1/exp

1/exp1obser (11)

The relationship between the water recoveryrate of NF membrane filtration and the removalefficiency of humic substances in the secondgroup was calculated by a combination ofEqs. (9) and (11) as shown in Fig. 9. It showsthat the removal efficiency of the second groupof humic substances decreases with increasingwater recovery rate. The high removal efficiencyof the second group could be sustained evenwhen the water recovery rate reached 96%, if themembranes were vibrated with the maximumvibratory amplitude. The larger the vibratoryamplitude, the higher the removal of humicsubstances. The correlation between removalefficiency in the second group and water recoveryobtained in our experiments is also shown inFig. 9. It shows that the concentration polarizationmodel [Eq. (2)] predictions are consistent withthe experimental results. These results also provethat the concentration polarization can bedecreased by increasing the shear rate at the edgeof the membrane, and it can be predicted by theconcentration polarization model.

3.3. Reduction of concentration polarization ofhumic substances in MF membrane filtration

Fig. 10 shows the effect of membranevibration on the removal efficiency of humic

Fig. 9. Relationship between the water recovery of NFmembrane filtration and the removal efficiency of

Fig. 10. relationship between the removal efficiency ofhumic substances in MF membrane and the vibratoryamplitude.

substances in MF membrane filtration process.The removal efficiency increases with increasingshear rate at the edge of the MF membrane. It hasbeen pointed out that the concentration of humicsubstances in Chitose River water was evaluatedby E260, which was measured after the river waterwas filtered through 0.45µm membrane filters.The humic substances are not usually removed byMF membrane filtration with a nominal pore sizeof 0.45µm. However, as shown in Fig. 10, theremoval efficiency of humic substances reached

humic substances in the second group.

R. Bian et al. / 421–432428

60% when the MF membrane was vibrated at themaximum vibratory amplitude. The removalefficiency of humic substances in the threegroups is also shown in Fig. 10. The humicsubstances in the first group can be completelyremoved at the maximum vibratory amplitude.The removal efficiency of humic substances inthe second and third groups increases withincreasing shear rate. One possible explanationof these results is that the shear rate has an effecton reducing the concentration polarization asdiscussed above. There may be some othermechanisms to explain the improvement of theremoval of humic substances in MF membranefiltration process by membrane vibration, andmore investigation of this phenomenon is needed.

4. The effect of shear rate on controllingmembrane fouling

4.1. Cake layer formation on the membranesurface

Concentration polarization not only results indecreasing the removal of dissolved materials,but also results in increasing filtration resistancesdue to the formation of a concentration polari-zation boundary layer and a cake layer on themembrane surface. There are many existingmodels developed to predict flux decline duringmembrane filtration. The oldest model in theresistance model based on the cake filtrationtheory [7]. It has been successful in describingflux decline during dead-end MF/UF membranefiltration of particulate suspensions. It has also,however, been considered that this model cannotbe applied to cross-flow filtration where the feedsolution continuously recirculates. This isbecause after the initial cake build-up the cakegrowth on the membrane surface can be arrestedby the action of the tangential flow [8]. Inmembrane filtration for river waters treatment,the membrane filtration process is confrontedwith a mixture of suspended colloids and natural

organic materials such as humic substances.Furthermore, the suspended colloids and naturalorganic materials in waters have a wide sizedistribution, which results in differing diffusionaction near the membrane surface. This meansthat small particles are deposited into the initialcake layer as the permeate flux declines. Theporosity of cake layer decreases with thedeposition of small particles, which results in anincrease in the resistance of the cake layer.Therefore, in membrane filtration for river waterstreatment, the cake layer thickness growth maybe arrested after initial cake build-up, but thecake layer resistance cannot be arrested, even ina cross-flow membrane filtration process. Basedon the above discussion, the resistance modelbased on the cake filtration theory may alsoapply for the river water treatment in the cross-flow filtration process.

Previous research carried out by the authors[1,9,10] pointed out that the UF membranefouling was dominated by the cake layerformation caused by accumulation of dissolvedorganic materials and suspended colloids in theraw water. The particles are driven to themembrane surface by the permeate flow to forma cake layer on the membrane surface, unless theshear rate is sufficiently high to prevent cakeformation. The undetachable cake layer, whichcannot even be removed by back washing and/orair scrubbing, accumulates on the membranesurface in every filtration cycle and results inmembrane fouling in the long-term operation. Inthe cross flow UF membrane filtration under aconstant pressure, the filtration process is dividedinto the following two stages: accumulation stageof the undetachable cake layer, and a secondstage where accumulation and detachment ofcake layer reach equilibrium. When the filtrationprocess reaches the equilibrium stage, the fluxbecomes too small and chemical cleaning isneeded. In the dead-end UF membrane filtrationunder a constant permeate flux, the filtrationprocess is divided into the following two stages:

R. Bian et al. / 421–432 429

accumulation stage of the undetachable cakelayer, and compression stage of the accumulatedcake layer. When the filtration process reaches thecompression stage, the transmembrane pressurebecomes too high and chemical cleaning isneeded. The formation of the undetachable cakelayer is influenced by the concentration and sizedistribution of suspended particles and humicsubstances in the raw water by filtration pressureand by permeate flux. Based on the cake filtrationtheory, the undetachable cake layer model wasdeveloped by the authors [8]. It has beensuccessful in evaluating the membrane foulingand in predicting the resistance of the undetach-able cake layer during continuous UF membranefiltration of river water with hydraulic cleaningsuch as backwash and/or air scrubbing.

The authors [10] also presented three methodsfor controlling membrane fouling caused by cakeformation:

1. Pre-coagulation to flocculate foulants toform micro-flocs, resulting in higher backtransport velocity and lower cake specificresistance.

2. Enhancement of shear rate at the mem-brane surface to prevent the attachment offoulants by increasing back transport velocity.

3. Improvement of the hydraulic cleaning toremove the accumulated cake layer on themembrane surface.

It was pointed out by the authors [11] thatmembrane fouling in the cross flow UF mem-brane filtration under a constant pressure can becontrolled effectively by pre-coagulation with anAl dosage which coagulates the high molecularhumic substances. However, the success of pre-coagulation on controlling the membrane foulingdecreases if the Al dosage is more than thedosage needed for coagulating the highmolecular humic substances. In the dead-end UFmembrane filtration under a constant permeateflux, pre-coagulation is not effective for con-trolling membrane fouling.

The effect of the enhancement of the shearrate at the NF membrane surface to prevent thecake layer formation is discussed below.

4.2. Effect of shear rate on controlling cakelayer formation in NF membrane filtration

A series of experiments was conducted toexamine the effect of shear rate on controlling thecake layer formation. The permeate flux declineof NF membrane is shown in Fig. 11. It showsthat the permeate flux of NF membrane increasedwith increasing vibratory amplitude. This isbecause the strong shear rate produced by highvibratory amplitude prevented foulants such assuspended particles and the humic substancesfrom accumulating on the NF membrane.

In the long-term continuous membrane filtra-tion under a constant pressure without anyhydraulic cleaning, the undetachable cake modelcan be written as Eq. (12):

00 J

PAVKRR

JP

cc µµ+=+= (12)

Fw

ig. 11. Decline of permeate flux of the NF membraneith and without vibration.

R. Bian et al. / 421–432430

where P is filtration pressure (Pa), J0 is the initialpermeate flux of the new membrane (m/s), R0 isthe resistance of the membrane (m-1), V is thevolume of the permeate (m3), A is the area of themembrane (m2) and Kc is the specific resistancecoefficient of the cake layer accumulated on themembrane surface (m-2). The specific resistancecoefficient of the cake layer can be defined asfollows:

CK c α= (13)

where α is the well-known specific resistance(m/kg) and C is the concentration of thematerials found in the feed water form the cakelayer (kg/m3). C is difficult to determine for theriver water filtration process, so we defined thespecific resistance coefficient to evaluate themembrane fouling in our research.

Fig. 12 shows the results of analysis of theexperimental data using the cake formation model[see Eq. (12)]. It shows that there is a good linearrelationship between the filtration resistancesand the accumulative permeate volume. Thespecific resistance coefficient decreases withincreasing vibratory amplitude of the membrane.These results indicate that the cake formation onthe NF membrane surface results in seriousmembrane fouling which can be effectivelycontrolled by membrane vibration.

The back transport model can be used toexplain the mechanisms of controlling membranefouling by increasing the shear rate at the edge ofthe membrane. Three back transport models havebeen developed: the well-known Browniandiffusion for small molecular substances [12], theshear-induced diffusion model for macro-molecules [13], and the lateral migration modelfor colloids [14]. These back transport modelspredict that the steady-state permeate fluxincreases with shear rate and particle size.

For the size distribution range of colloids andhumic substances in river water, Brownian

Fig. 12. Analysis of permeate flux data by the cakefiltration model.

Fig. 13. Condense factor of humic substances in thefirst group during NF membrane filtration.

diffusion and the shear-induced diffusion areimportant to evaluate the back transport awayfrom the membrane surface. As the particle sizeor molecular weight of the substances decreases,the Brownian diffusion coefficient increases,whereas the shear-induced diffusion coefficientdecreases. The effective diffusion coefficient isthe sum of those two diffusion coefficients.Figs. 13–15 show the condense factors of humicsubstances in the three groups during NF

R. Bian et al. / 421–432 431

Fs

Ft

mTsiiawspii

substances in the first group cannot be concen-

ig. 14. Condense factor of humic substances in theecond group during NF membrane filtration.

ig. 15. Condense factor of humic substances in thehird group during NF membrane filtration.

embrane filtration of Chitose River water.hey show that the condense factors of humicubstance in the three groups increase withncreasing vibratory amplitude. These resultsndicate that the humic substances back transportway from the membrane surface to the feedater and transport velocities of humic

ubstances increase with increasing shear rate. Itroduces evidence to indicate that the shear-nduced diffusion coefficient increases withncreasing shear rate. Fig. 13 shows that humic

trated in the feed water when the membrane isvibrated at a vibratory amplitude of less than1/4". It indicates that humic substances in thefirst group cannot be back transported by onlyBrownian diffusion because its Browniandiffusion coefficient is too small. However, thehumic substances in the second and third groupscan be concentrated in feed water (see Figs. 14and 15) even when the membrane is vibrated at avibratory amplitude of less than 1/4". Thisindicates that humic substances in the secondand third groups can be back transported by onlyBrownian diffusion because their Browniandiffusion coefficients are larger than those of thehumic substances in the first group.

5. Conclusions

Concentration polarization not only results ina decrease of the removal of dissolved materials,but also in increase of filtration resistances. Thispaper dealt with the results from experimentsconcerning the effects of an increasing shear rateat the edge of the membrane on reducingconcen-tration polarization and on controllingmembrane fouling. Concentration polarization ofhumic substances in NF and MF membranes canbe reduced by increasing the shear rate. This hasbeen proved by the increase in mass transfercoefficient and the decrease in the concentrationon the membrane surface with increasing shearrate. The concentration polarization model cansuccessfully predict the removal efficiency ofhumic substances. The high removal efficiencyof humic substances in NF membrane filtrationprocesses can be sustained even when the waterrecovery rate reaches 96% if the membranes arevibrated with the maximum vibratory amplitude.

A cake layer formation on the NF membranesurface due to deposition of suspended colloidsand humic substances dominates NF membranefouling. NF membrane fouling can be evaluated

R. Bian et al. / 421–432432

by the cake filtration model and controlled byincreasing the shear rate. Humic substances inthe first group are transported away from themembrane surface by the shear-induceddiffusion. Humic substances in the second andthird groups are transported away from themembrane surface not only by the shear-induceddiffusion, but also by Brownian diffusion.

Acknowledgements

This research has been supported by the CoreResearch for Evolutionary Science and Tech-nology (CREST) of Japan Science and Tech-nology Corporation (JST) and by the AdvancedAqua Clean Technology 21st Centenary(ACT21) research project of the JapaneseMinistry of Health and Welfare.

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