Particle Back-Transport and Permeate Flux Behavior in Crossflow

These data support a previously hypothesized minimum in particle back-transport from the membrane as a function of particle size. The back-transport o...
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Environ. Sci. Technol. 1997, 31, 819-824

Particle Back-Transport and Permeate Flux Behavior in Crossflow Membrane Filters S H A N K A R A R A M A N C H E L L A M * ,† A N D MARK R. WIESNER Department of Environmental Science and Engineering, Rice University, P.O. Box 1892, Houston, Texas 77251

Particle residence time distributions in a membrane channel are interpreted to elucidate mechanisms of particle transport and colloidal fouling in membrane filtration. A comparison of particle size distributions in the membrane feed suspensions and deposited cakes provides evidence for selective particle transport and accumulation on membranes. These data support a previously hypothesized minimum in particle back-transport from the membrane as a function of particle size. The back-transport of smaller particles is apparently due to Brownian diffusion, while larger macrocolloids are controlled by an orthokinetic mechanism such as shear-induced diffusion. In all cases, cake specific resistances measured in the dead-end mode were higher than those of the corresponding feed suspensions. Also, cake specific resistances measured under a crossflow were higher than those in the dead-end mode. Further, the specific resistance of particle deposits on membranes increased with shear rate and decreased as the initial permeation rate increased, suggesting that cake morphology is an important parameter in determining permeate flux. Thus, the effects of hydrodymamics on cake resistance needs to be established before a comprehensive model for crossflow filtration can be derived.

Introduction The drive to improve the quality of drinking water, recover potential pollutants used in industrial processes, and reuse wastewater have combined with recent developments in membrane science and technology to stimulate interest in the use of membrane processes for environmental quality control at an unprecedented scale. For example, drinking water treatment facilities using low-pressure membrane processes such as ultrafiltration (UF) and microfiltration (MF) have been designed and placed into service in several communities. These installations have also been shown to be effective for the removal of turbidity as well as microbiological contaminants such as Giardia, coliforms, HPC, and viruses (1) and are expected to be cost effective for particle and dissolved organic carbon removal for capacities up to at least 5 million gal/day (2). The economics of low-pressure membrane filtration in the potable water treatment industry are largely dependent on the permeate flux (3). Inherent in UF and MF is the accumulation of rejected components on the membrane surface. Accumulation of rejected materials can decrease the effective permeability and the rejection characteristics of † Present address: Applied Research Department, Montgomery Watson Americas Inc., 560 Herndon Parkway, Suite 300, Herndon, VA 20170. Telephone: (703) 397-0367; fax: (703) 478-3375; e-mail: [email protected].

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 1997 American Chemical Society

the membrane. Some fraction of these materials can be removed by periodic hydrodynamic and/or chemical cleaning whereas adsorbed materials may be irreversibly bound to the membrane matrix (either on the surface or within the pores). This process of membrane fouling may be initiated by many materials in water including dissolved organic material, bacteria, and inorganic colloids. Considerable research has been directed toward understanding the factors that control UF and MF performance (4, 5). In this work, we consider the role of particle size and hydrodynamics on the transport of particles in membrane systems and their subsequent effects on permeate flux. The particle size distribution (PSD) of materials encountered in environmental applications is typically broad, often spanning several orders of magnitude in size. Particle size fractions may differ in their composition and physical characteristics. The interplay between hydrodynamics and particle size is likely to play a role in determining the nature of materials transported to the membrane surface and the resultant effect on permeate flux and membrane fouling. We have earlier reported on convective and inertial effects on particle transport in the membrane far-field region (6). This study focuses on the role of particle size and hydrodynamics in membrane near-field accumulation processes. We analyze particle deposition and subsequent changes in permeate flux during the continuous filtration of suspensions under a wide range of hydrodynamic conditions and PSDs. We also investigate the effect of shear rate and permeate flux on the specific resistance of cakes formed during crossflow filtration of suspensions having either narrow or wide PSDs.

Experimental Section Experiments were conducted in which a pulse of particles was introduced in slow crossflows over a membrane with high permeation rates such that initial transport was dominated by permeation drag. Particle transport mechanisms were surmised through analysis of the particle residence time distributions (RTDs) measured at the outlet of the membrane channel. A second series of experiments employed continuous inputs of particles to the membrane at faster laminar flows, typical of many membrane applications. The goal of the second series of experiments was to investigate particle deposition and subsequent reductions in permeate flux under a range of hydrodynamic conditions and feed suspension PSDs. An important feature of the continuous input experiments reported in this work is that unlike previous studies reported in the literature (e.g., refs 7 and 8), the particle feed suspension was not recycled. This ensured that the composition of the membrane feed water remained constant for the duration of the experiment both in terms of mass concentration and PSD. As the current work will demonstrate, recycling particle suspensions may lead to the enrichment of certain size classes even in membrane filters operating in laminar flow. This artifact may be of critical importance in experiments designed to elucidate particle transport and deposition phenomena in micro- or ultrafiltration. Materials and Methods. Crossflow experiments were conducted using a laboratory-scale apparatus with one porous wall similar to one described in an earlier work (6). Hydrophilic modified polyvinylidene difluoride (PVDF) membranes having a nominal pore diameter of 0.1 µm and thickness of 110 µm were used in all experiments (Durapore, Millipore Corp., Bedford, MA). All experiments were conducted in a rectangular channel 46 cm long and 2 cm wide with an effective filtration area of 88.48 cm2. Ultrapure, organic free water with a pH typically near 6.3 and resistivity greater than

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10 MΩ‚cm was used in all experiments. A near pulse-free crossflow of ultrapure water was achieved using a micropump head fitted on a Ismatec digital variable speed drive (Cole Palmer Instrument Co., Chicago, IL). Permeate flow was continuously collected on a precision electronic balance (FX3000, A&D Co. Ltd., Milpitas, CA) coupled to a SER420 serial 0-5 V converter (Rice Lake Weighing Systems, Rice Lake, WI) to facilitate data acquisition. A data acquisition system (DAS) for the Macintosh computer was used for remote control of instruments as well as analog signal acquisition (MacPacq MP-10, Biopac Systems, Goleta, CA). Macros were written to automate tasks such as digital instrument control and data acquisition. Pulse Input Experiments. Six different spherical monodisperse, latex particles of diameter 0.48, 0.94, 3.2, 7.0, 12.0, and 25.7 µm were used (Seradyn Corp., Indianapolis, IN). The ζ potential of these particles was typically near -33 mV as measured using a Zeta Sizer 2c (Malvern Instruments Malvern, England). Impulse inputs (typically 80 ms duration) of monodisperse latex suspensions were made using a syringe infusion pump (Harvard Apparatus Inc., South Natick, MA) fitted with a 22 gage non-reactive Teflon flexible needle tubing. Particle RTDs were obtained using a flow-through UV-visible spectrophotometer installed at the filter concentrate side and set to a wavelength of 258 nm (Spectra 100, Spectra Physics Inc., San Jose, CA). Thus, only particles that escape irreversible deposition on the membrane contribute to the RTD. RTDs were obtained as volt-seconds plots. Samples were acquired at a constant rate of 10 s-1. A 762 µm thick Teflon feed channel was used. Experiments were conducted at two crossflow Reynolds numbers of 70 and 52 (Re t Uoh/ν). Here, Uo is the average entrance velocity, h is the channel thickness, and ν is the kinematic viscosity of water. A needle valve installed in the concentrate tubing was used to adjust the pressure in the module. The initial permeation rate was varied in the range of 2.6 × 10-3 to 0.015 cm/s. A total of 44 experiments were conducted in this range of hydrodynamic conditions. Each experiment was repeated 6-10 times for a given set of hydrodynamic parameters. Particle transport was analyzed under conditions of constant hydrodynamics. Continuous Input Experiments. Continuous input experiments were conducted using rigid, spherical glass particles (Potters Industries Inc., Parsipanny, NJ) fractionated into either narrow or broad size distributions. In both cases, fine colloids smaller than the membrane pore size of 0.1 µm were removed by repeated sedimentation. This was verified by scanning electron microscopy, which also revealed the particles to be spherical and largely free of surface impurities and defects. The volume-based PSDs of the broad (polydisperse) and narrow (monodisperse) suspensions of glass particles measured using an electric sensing zone device (Coulter MultiSizer, Luton, Beds., England) fitted with a 50µm orifice are shown in Figure 1. The geometric mean diameter weighted by particle volume for the narrowly distributed particles (denoted M) was 2.46 µm whereas the broader, more polydisperse particles (denoted P) had a mean diameter of 9.95 µm. The ζ potential of these particles was typically near -50 mV. Clean water was circulated in the filter for 6 h prior to the introduction of particles. Despite precautions taken in using ultrapure water, the permeate flux dropped before attaining a steady-state value, presumably due to remaining impurities in the feed water, tubing, and connections. Membrane resistance was measured to be virtually constant at various pressures in the range of 7-140 kPa (1-20 psig) and was not found to change significantly during the duration of the experiment. It is therefore unlikely that membrane compaction played a role in this initial decrease in permeate flux. The initial 30 min of these experiments was run without particle feed to measure the resistance of the clean membrane. Particle feed was then initiated and continued for 8 h. A three-roller peristaltic pump

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FIGURE 1. Particle size distributions of glass particles used in continuous input experiments. The volume-weighted geometric mean diameter of the narrowly distributed particles (used in M series experiments) is 2.46 µm and that of the more widely distributed particles particles (used in P series experiments) is 9.95 µm. fitted with a pulse dampener was used to affect continuous inputs of feed suspensions. The contents of the pulse dampener were kept well stirred. The pressure in the filtration channel increased during the course of the continuous input experiments because of particle deposition on the membrane surface. Analyses reported in this work therefore account for the variation of the transmembrane pressure, and we report the transient behavior of the specific permeate flux (defined as the ratio of the instantaneous permeate flux and the pressure). A continuous trace of the pressure was recorded by the DAS using a high-gain strain gage with an amplifier (Cole Palmer Instrument Co., Chicago, IL). Samples were acquired at a constant rate of 0.5 s-1. Teflon feed channels of two different thicknesses, 350 and 762 µm, were used. Feed concentrations (Co) ranged from 0.01 to 1 g/L. The feed water turbidities corresponding to these concentrations are in the range of 7 to 960 NTU. All experiments were run in a laminar crossflow regime typical of hollow fiber and plate and frame modules (Re < 215) corresponding to entrance shear rates (γo t 6Uo/h) of 1157, 2197, and 5486 s-1. Experimental data on cumulative permeate weight were obtained by collecting the filtrate on a digital balance connected to the DAS. Instantaneous values of the specific permeate flux were obtained by numerical differentiation of the smoothed weight data normalized by the pressure. Initial short duration experiments were conducted using the narrowly distributed glass particles to perform a mass balance on the system. Particle feed was maintained for a period of 6380 s, during which time the permeate and reject streams were collected. The cake as well as the reject water were analyzed for solids weight at the end of the experiment (as described in the next section) and compared with that fed to the system. Recoveries were typically between 92 and 94% and are within the range of analytical accuracy. Results from a total of 42 continuous input experiments are reported: 13 with the narrowly distributed particles (denoted M1-M13) and 29 using the more broadly distributed particles (denoted P1-P29). Dead-End Filtration. At the conclusion of every crossflow experiment with continuous particle feed, the surface deposit was carefully washed using a known volume of ultrapure water. This suspension was then sonicated for 1 h to breakup aggregates and then filtered in batch, unstirred, dead-end filtration cells under constant pressure to measure the mass of solids and their specific resistance in the absence of shear. A polycarbonate pressure filter with an effective area of 12.5 cm2 fitted with a membrane having the same characteristics as that used in crossflow experiments was used (Sartorius Corp., Edgewood, NY). Feed and cake specific resistances were measured in the dead-end mode under three different pressures (provided by a tank of compressed air) in the range of 14-128 kPa (2-18.5 psig) at the end of each crossflow

experiment. Air flow to the filter was accurately controlled using a two-way solenoid valve activated using a solid-state relay. A DAS was used for instrument control as well as acquiring pressure and cumulative permeate weight data. Membranes were dried to constant weight at 75 °F for a period of 10 h after dead-end filtration to measure cake mass. (It was previously established that the PVDF membranes did not loose weight on being exposed to 75 °F temperatures for 15 h.)

a

Results and Discussion Particle Back-Transport. When initial transport is dominated by permeation drag, trajectories are expected to bring a fraction of particles in the feed into the near-field region of the membrane. Once in the near-field, chemical and colloidal interactions such as diffuse layer repulsion, dispersion forces, and others will determine if particles are deposited on the membrane. Particles that enter the near-field region may undergo back-transport and be swept axially by the crossflow, eventually exiting the channel. Under conditions of low crossflow velocity, residence times are high and particles may relax to their equilibrium lateral distribution in the membrane module as determined by a balance between convective transport to the membrane and diffusive back-transport away from the membrane. Because near-field tangential velocities are small, particles that are back-diffusing from the membrane should elute at longer times than particles undergoing convective transport in the bulk flow near the center of the channel. For a second peak to occur when particle transport in the far-field is dominated by premeation drag, backdiffusion velocity should be comparable to convective velocity toward the membrane. For a given set of particle and hydrodynamic parameters, back-transport velocities should decrease as the concentration gradient decreases (because of loss of particles from the near-field). The remaining particles occupy lateral positions closer to the membrane. These particles, along with those undergoing surface transport (e.g., “rolling”), will contribute to long trailing edges in the RTDs. RTDs obtained in response to pulse inputs of five macrocolloids are superposed in Figure 2a for conditions of slow crossflow and high permeate velocity (Re ) 70 and Vw ) 0.0115 cm/s). These RTDs (except the one corresponding to 7 µm) are bimodal with a convective first peak and a diffusive second peak. Because multiple transport mechanisms such as convection, Brownian, and/or shear-induced diffusion and surface transport contribute to different sections of these RTDs, peaks can only be arbitrarily delineated to assign areas corresponding to one particular transport mechanism. On the other hand during early times, particle motion is dominated by convection, and hence the height of the first peak should closely reflect the effect of convective drag on transport in the far-field region. Therefore to compare particle size effects on back-transport, experimental data for various particles were adjusted to obtain the same height for the convection peak. As size increases from 0.48 to 0.94 and 3.2 µm, diffusive peaks decrease in height compared to the convection peak, and they take longer to elute. At a particle diameter of 7 µm, the diffusive peak disappears completely. These observations are consistent with the notion that backtransport during the membrane filtration of colloids under these conditions is caused by Brownian diffusion. As particle size is increased further to 12 µm, a second peak is observed to reappear (see Figure 2a). This behavior is consistent with a shear-induced component of back-diffusion for these large particles, moving them from a region of high concentration (membrane near-field) to a region of low concentration (bulk flow). Diffusive peaks are prominent even at low permeate fluxes (low near-field concentrations) as particle size was increased further to 25.7 µm (Figure 2b). This behavior is reasonable

b

FIGURE 2. (a) Particle size effects on back-transport in laminar flow. As size increases beyond 7 µm, the mechanism of backtransport appears to change from Brownian to shear-induced diffusion. (b) Experimental RTD of 25.7-µm particles.

FIGURE 3. Effect of shear rate on the cake PSD during the crossflow filtration of widely distributed particles. since orthokinetic back-transport mechanisms such as shearinduced diffusion typically scale as the square of particle size (9). Consistent with the theory of shear-induced diffusion, these peaks were found to intensify relative to the convection peak and to take longer times to elute when the permeation rate was increased from 0.003 to 0.0041 and 0.0064 cm/s and crossflow velocity was maintained at a constant value (10). Results from experiments performed at a slower crossflow velocity and fixed permeate velocity (Re ) 52, Vw ) 0.0082 cm/s) also suggest a minimum in the back-transport for particles near 7 µm in diameter (10). The effects of particle size and module hydrodynamics on transport were also evidenced in the P series continuous input experiments conducted using feed suspensions with a wide PSD. In all of these experiments, larger particles present in the feed were absent from the cake. The PSD of the feed and cakes formed under two conditions of entrance shear rate are compared in Figure 3. The percentage of fines in the cake is seen to increase with shear. It was also found that increasing the initial permeation rate (Vwo) induces the deposition of larger particles from the feed (10). Thus, the

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TABLE 1. Properties of Feed Suspensions Used in Continuous Input Experiments feed suspension

experiment P series M series

volume-weighted geometric mean diametera (µm)

specific resistanceb (cm/kg)

9.95

2.04 ( 0.54 × 1013

2.46

12.45 ( 1.42 × 1013

wide PSD particles narrow PSD particles

aMeasured bMeasured

using the Coulter Counter fitted with a 50 µm orifice. from dead-end filtration experiments.

PSD of cakes formed during crossflow filtration may differ significantly from the PSD of the feed suspension. Similar to previously published results (7, 8) from experiments conducted in turbulent flow with recycle, fine particles accumulated preferentially in the cake. The preferential deposition of smaller particles in continuous input experiments in conjunction with the disappearance of second peaks for particles of an intermediate size in pulse input experiments appears to validate the concept of a minimum in particle diffusivity (11). The particle size corresponding to a minimum in back-transport is expected to be dependent on feed volume fraction, particle density, applied shear stress, and permeation rate. Specific Resistance of Cakes. Consider dead-end filtration using a membrane of area Am and resistance Rm at a transmembrane pressure ∆P. The permeate flux Vw of a fluid with absolute viscosity µ is related to the membrane and cake resistances by Darcy’s law, giving

Vw )

∆P µ(Rm + R′c)

(1)

The cake resistance R′c is related to the specific cake resistance R, the membrane area, and the mass of cake deposited (M) by

R′c )

(2)

RM Am

Thus, the specific cake resistance is the cake resistance normalized to the cake mass and membrane area and has units of cm/kg. Using eqs 1 and 2, R is calculated as

R)

(

)

Am ∆P - Rm µVw M

(3)

Effects of Operating Conditions on Specific Permeate Flux. Crossflow experiments were conducted to investigate the effects of module hydrodynamics and particle parameters on specific permeate flux. In all cases, particles were found to form incompressible cakes in the range of 14-128 kPa (2-18.5 psig) (10). In addition to the volume-based average diameter measured using an electronic particle counter, the specific resistances of the feed suspensions measured from dead-end experiments are shown in Table 1. In accordance with the results obtained by other researchers (e.g., refs 12 and 13), the specific permeate flux normalized to the initial value in both the M and P series experiments was found to be inversely related to the feed suspension concentration and the initial permeation rate. Increasing the shear rate in experiments using the narrowly distributed particles (M series) as well as the more widely distributed particles (P series) resulted in a decrease in the mass of particles deposited. This is seen in Figure 4, which shows specific permeate flux data from M and P series experiments conducted at a high initial permeation rate (Vwo ) 0.015 cm/s) in which particle feed was terminated after

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FIGURE 4. Effect of shear rate on specific permeate flux decline for M and P series experiments when particle feed was terminated after 16 200 s. For a given PSD, mass of particles deposited decreases with increases in shear. Note that specific permeate flux does not remain steady upon termination of particle feed, suggesting shearinduced changes in cake morphology.

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FIGURE 5. Effect of shear rate on specific permeate flux during P series experiments using widely distributed particles. Cakes with a high specific resistance are formed at low initial permeation rates and high shear, counteracting the benefits of lower deposit mass. 16 200 s. Under these conditions, higher specific permeate fluxes were obtained during continuous particle feed with increases in the entrance shear rate. Specific permeate flux behavior upon termination of particle feed will be discussed in the next section. However, even though an increased shear decreased the mass of particles deposited, thinner cakes did not necessarily result in higher specific permeate fluxes in experiments using the more widely distributed particles (P series) and low initial permeation rates (Figure 5). Replicate experiments produced similar results. Thus, the benefits of a decrease in the cake mass at higher shear rates may be counteracted by an increase in the specific resistance. In other words, the cake specific resistance during the filtration of a polydisperse suspension is dependent on operating conditions. This may be attributed to two phenomena: (1) higher shear rates selected for smaller particles in the cake in these experiments and (2) higher shear rates may favor more dense packing geometries. Effect of Crossflow on Cake Specific Resistance. Specific resistances of cakes formed during the crossflow filtration of rod-shaped bacteria have been found to be higher than those measured from dead-end experiments because of the increased structure brought about by the preferential orientation of the rods in the direction of crossflow (14). Similar results have been reported using large 125-180 µm spheres (15). Experimental fluxes have been over predicted (12) when cake permeability was modeled using an empirical correlation developed for identical latex particles and solution chemistries from dead-end filtration experiments (16). Better agreement

FIGURE 6. Comparison of specific resistances in the crossflow and dead-end modes for glass particles. The specific resistance of the feed suspensions used in M and the P series experiments are shown as horizontal lines. In all cases (1) specific resistance of cakes measured in the dead-end mode are higher than those of the feed suspension and (2) cakes formed in crossflow have a higher resistance than in the dead-end configuration. between theoretical predictions and experimental observations was reported when cake resistance was modeled using the Carman-Kozeny equation, which predicts specific resistances approximately 5 times higher. Thus, even cakes formed in crossflow filtration of monodisperse spherical particles appear to be more resistant than those formed in dead-end filtration. Specific resistances of cakes formed in the crossflow mode in both the M and P series experiments were calculated and compared with measurements obtained from dead-end filtration (Figure 6). Deposits are seen to have a higher hydraulic resistance in the crossflow mode in all cases. The average specific resistance of cakes formed in the M series measured in the dead-end mode is 5.07 × 1014 cm/kg whereas the average specific resistance calculated in the crossflow mode is 15.4 × 1014 cm/kg. In other words, suspensions having identical PSDs formed cakes that were approximately three times more resistant in the crossflow mode in the M series experiments. The average specific resistance of cakes formed in the P series experiments in the dead-end mode is 1.12 × 1014 cm/kg whereas the average specific resistance in the crossflow mode is calculated to be 9.3 × 1014 cm/kg. Thus, in these experiments suspensions having identical PSDs formed cakes that were approximately eight times less permeable in the crossflow mode. We conclude that more structured and compact deposits having a higher resistance to the passage of water are formed under the action of a shear stress, which may have played a role in rearranging particles. Cakes formed in crossflow filtration can therefore be expected to be more compact than those formed during dead-end filtration even for suspensions of spherical particles. This result implies that data obtained from batch dead-end filtration cells may significantly understate the degree of fouling that a given raw water may produce. None the less, the dead-end filtration protocol is the basis for common fouling indices such as the silt density index (SDI). Further, as our experimental data indicate, this increase in the specific resistance becomes more pronounced for feed suspensions with wider PSDs. These results may partially explain the poor correlations between the SDI and membrane fouling. Specific permeate flux was observed to decrease in all M series experiments and in P series experiments conducted at a low shear rate (γo ) 1147 s-1) even upon termination of particle feed (Figure 4). The filtration pressure remained constant after particle feed was stopped. The average absolute deviation in membrane resistance values measured before commencement of particle feed and after carefully washing off the cake deposited on the membrane at the conclusion of the experiment was 6.7%. The continued decrease in specific permeate flux after the particle feed was terminated

FIGURE 7. Effect of shear rate and initial permeation rate on cake specific resistance during the filtration of widely distributed particles. is attributed to the rearrangement of particles in the cake on the membrane surface or perhaps penetration of particle fines into the membrane. Particles were fed only after the clean membrane flux reached a steady value. Hence, changes in Rm appear to be the result of particle penetration into the membrane matrix. Particle movement induced by shear stresses on the cake seems to be manifested either as an increased resistance to water permeation or as the transport of fines into the membrane. Thus, changes in the specific permeate flux after the termination of particle feed are associated with membrane fouling or changes in cake morphology. In all P series experiments conducted at higher values of the entrance shear rate (γο ) 2197 and 5486 s-1), the specific permeate flux was observed to recuperate upon termination of particle feed (e.g., P26 in Figure 4). This increase is attributed to enhanced back-transport of larger particles at high shear rates. Higher hydraulic resistances of deposits in crossflow filtration can only be partially explained by changes in cake structure. As shown earlier in Figure 3, the cake composition is dependent on filter hydrodynamics such that the percentage of fines in the cake increased with shear. Thus, based on the enrichment of smaller particles alone, cakes can be expected to have a higher specific resistance in the crossflow mode with increases in the shear rate. Hydrodynamic selection of smaller particles and cake reorganization result in cakes with a higher specific resistance during the crossflow filtration of polydisperse suspensions. Thus, increasing the wall shear stress beyond a critical value is expected to have a limited value in increasing permeate flux. Such behavior is evidenced in Figure 5 where relatively no change in the specific permeate flux is observed for a 4-fold increase in the shear rate. Similar observations have also been made during the turbulent crossflow filtration of mineral suspensions that formed compressible cakes (17). As the shear rate increases, progressively smaller particles in the feed are expected to be selectively deposited. Cakes formed at higher shear rates are also expected to be more compact. Therefore, for a given composition of the feed, cake specific resistance should increase with shear rate. Also, because initially deposited particles are less likely to be rearranged at higher permeation rates, cake specific resistance should be inversely related to Vwo for any given entrance shear rate. Experimental data from the P series experiments are consistent with these expectations as shown in Figure 7. Results reported in this paper suggest that bench- and/or pilot-scale studies may be necessary to identify particle size fractions that correspond to minimum back-transport conditions and higher potentials for membrane fouling before designing commercial membrane systems. Such studies can also be used to evaluate various pretreatment strategies aimed at adjusting the PSD of the feed water to reduce its fouling potential.

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Literature Cited (1) Jacangelo, J. G.; Laıˆne, J.-M.; Carns, K. E.; Cummings, E. W.; Mallevialle, J. J. Am. Water Works Assoc. 1991, 83 (9), 97-106. (2) Wiesner, M. R.; Hackney, J.; Sethi, S.; Jacangelo, J. G.; Laıˆne, J.-M. J. Am. Water Works. Assoc. 1994, 86, (12), 33-41. (3) Pickering, K. D.; Wiesner, M. R. J. Environ. Eng. Div. ASCE 1993, 119, 772-797. (4) Belfort, G.; Davis, R. H.; Zydney, A. L. J. Membr. Sci. 1994, 96, 1-58. (5) Fane, A. G. Prog. Filtr. Sep. 1986, 4, 101-179. (6) Chellam, S.; Wiesner, M. R. Environ. Sci. Technol. 1992, 26, 16111621. (7) Fischer, E.; Raasch, J. Model Tests of the Particle Deposition at the Filter Medium in Cross-flow Filtration. In Proceedings of the 4th World Filtration Congress; 1986; pp 11.11-11.17. (8) Lu, W. M.; Ju, S. C. Sep. Sci. Technol. 1989, 24, 517-540. (9) Davis, R. H.; Leighton, D. T. Chem. Eng. Sci. 1987, 42, 275-281. (10) Chellam, S. Laminar Fluid Flow, Particle Transport and Permeate Flux Behavior in Crossflow Membrane Filters. Ph.D. Dissertation, Rice University, Houston, TX, 1995.

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(11) Wiesner, M. R.; Clark, M. M.; Mallevialle, J. J. Environ. Eng. 1989, 115, 20-40. (12) Romero, C. A.; Davis, R. H. J. Membr. Sci. 1991, 62, 249-273. (13) Wakeman, R. J.; Tarleton, E. S. Desalination 1991, 83, 35-52. (14) Tanaka, T.; Abe, K.-I.; Asakawa, H.; Yoshida, H.; Nakanishi, K. J. Ferment. Bioeng. 1994, 78, 455-461. (15) Mackley, M. R.; Sherman, N. E. Chem. Eng. Sci. 1992, 47, 30673084. (16) Ogden, G. E.; Davis, R. H. Chem. Eng. Commun. 1990, 91, 1128. (17) Baker, R. J.; Fane, A. G.; Fell, C. J. D.; Yoo, B. H. Desalination 1985, 53, 81-93.

Received for review June 17, 1996. Revised manuscript received October 7, 1996. Accepted October 16, 1996.X ES9605228 X

Abstract published in Advance ACS Abstracts, January 1, 1997.