Influence of Surface Charge Distributions and Particle Size

Feb 26, 2008 - Engineering, The University of Texas at Austin,. C1786 Austin, Texas 78712 .... zero charge (PZC) of Min-U-Sil 5 is approximately pH 2...
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Environ. Sci. Technol. 2008, 42, 2557–2562

Influence of Surface Charge Distributions and Particle Size Distributions on Particle Attachment in Granular Media Filtration J I N K E U N K I M , †,‡ J E F F R E Y A . N A S O N , †,§ A N D D E S M O N D F . L A W L E R * ,† Department of Civil, Architectural, and Environmental Engineering, The University of Texas at Austin, C1786 Austin, Texas 78712

Received September 23, 2007. Revised manuscript received December 13, 2007. Accepted January 8, 2008.

Filtration experiments were performed with a laboratoryscale filter using spherical glass beads with 0.55 mm diameter as collectors. Suspensions were made with Min-U-Sil 5 particles, and two different methods (pH control and polymer dosing)wereusedfordestabilization.InthepHcontrolexperiments, all particles had negative surface charge, and those with lower (absolute value) charge were selectively attached to the collectors, especially during the early stage of filtration. This selective attachment of the lower charged particles caused the zeta potential distribution (ZPD) of the effluent to move to a more negative range. However, the ZPD of the effluent did not continue moving to more negative values during the later stages of filtration, and this result was attributed to two reasons: ripening effects and detachment of flocs. In the polymer experiments, substantial differences were found between experiments performed with negatively charged particles (underdosing) and those with positively charged particles (overdosing). With under-dosing, the results were similar to the pH control experiments (which also had negatively charged particles), but with overdosing, the effluent’s ZPDs in the early stages did not overlap with those of the influent and more highly charged particles were removed more efficiently than lesser-charged particles. It is hypothesized that, despite a substantial period of pre-equilibration of media and coagulant, this equilibrium shifted when particles were also added. It was assumed that coagulant molecules previously adsorbed to the particles desorbed and subsequently attached to the filter media because of surface area differences in the particle and filter media.

including microorganisms, in granular media filters. Even at low turbidity (i.e., less than 0.1 NTU), the water can contain hundreds of particles per milliliter (1). With proper pretreatment, most particles are removed in granular media filters, but some particles pass through the filters or detach after being captured. The primary objective of this research was to determine why some particles have a higher probability of attachment to the media and previously captured particles than others as they flow through the filter under various chemical conditions. The granular media filtration process can be viewed as having two steps: transport and attachment (2). Transport involves the long-range forces or mechanisms that bring a particle near the surface of the collector (media grain) or previously retained particles. The principal mechanisms of transport of particles to a single filter grain are interception, sedimentation, and Brownian motion (diffusion). On the other hand, the fundamental theories of attachment are based on consideration of the DLVO (3, 4) forces (van der Waals (VDW) force and the electric double layer (EDL) interaction) acting on a particle with a collector of defined geometry (5, 6). Chemical pretreatment before filtration is normally employed to ensure that the EDL interactions are not repulsive, or at least are minimally so (2, 7). Of primary interest in this research was the effect of surface charge (expressed by zeta potential) and particle size on the ability to retain particles in a filter. Results from laboratory scale column experiments (e.g., Tufenkji et al. (8), and references therein) suggest that heterogeneity in interactions between individual colloids and collectors results in nonuniform deposition profiles where more “sticky” colloids are preferentially removed. Tong and Johnson (9) attribute deviations from classical filtration theory to heterogeneities in the properties of the colloids themselves (size, surface charge, and hydrophobicity). In a previous paper (10), the fact that most suspensions exhibit a distribution of zeta potentials, and not just a single mean value, was delineated; a hypothesis of this research was that this distribution would help explain why some particles are retained (captured) in a filter while others are not. In engineered systems for particle removal, the EDL interactions are often changed by adding chemicals to destabilize the particles. These chemicals change the zeta potential distribution (ZPD) of particles (10) and thereby change the filtration efficiency. Nevertheless, few reports on the influence of ZPDs (as distinct from mean ZP values) on filtration exist. In WTPs, filters are operated at near-optimal conditions of chemical pretreatment (or ZPD); in this research, several experiments were performed at nonoptimal conditions to help elucidate the effects of ZPD on particle retention.

Experimental Methods Introduction Granular media filtration is used almost universally as the last particle removal process in conventional water treatment plants (WTPs). The increased concern for the safety of drinking water has increased the need to remove particles, * Corresponding author e-mail: [email protected]. † The University of Texas at Austin. ‡ Current address: Kwater Academy, Kwater (Korea Water Resources Corporation), Daejeon 306-711, Korea. § Current address: School of Chemical, Biological, and Environmental Engineering; Oregon State University, 103 Gleeson Hall, Corvallis, OR 97331. 10.1021/es7023934 CCC: $40.75

Published on Web 02/26/2008

 2008 American Chemical Society

Filtration Experiments. Granular media filtration experiments were performed in a down-flow column with an inner diameter of 3.8 cm, as shown in Figure 1. A short bed of 10 cm was used to ensure that some particles escaped capture and would be found in the effluent. All experiments were performed for 4 h at a filtration velocity of 5 m/h. The relatively short filtration run time reflects the interest in this research in the early stages of filtration associated with ripening. Solid glass spheres (Potters Industries, Inc., New Jersey) in a size range of 0.5-0.6 mm were chosen for filter media, and scanning electron microscopy (SEM) (Jeol T330A, Jeol USA Inc., Peabody, Massachusetts) measurements confirmed their sphericity. Extensive cleaning of the media with acid and VOL. 42, NO. 7, 2008 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 1. Schematic of the experimental filtration system. base washings (6) removed any surface impurities and avoided surface chemical heterogeneities other than those intrinsic to silica glass; others have shown that mixtures of different surfaces create heterogeneity that drastically effects particle capture (11). Separate pumps were provided for the water and the highconcentration suspension (i.e., 800 mg/L); after they were blended in-line to yield a solids concentration of 20 mg/L, a syringe pump injected the destabilizing chemical immediately prior to the filter influent, thereby ensuring that little change of the size distribution occurred by flocculation prior to the filter. To establish equilibrium between the solution and media in terms of surface charge, a particlefree solution with identical chemistry as in the subsequent experiment was pumped through the filter for at least 60 min before time zero. After time zero, all three pumps operated continuously throughout the experiment. A more detailed explanation of the filter system can be found elsewhere (12). Particles. Min-U-Sil 5 (U.S. Silica Company, Berkeley Springs, West Virginia) particles were used throughout this research. These particles are white, natural crystalline silica powder with virtually all particles below 5.0 µm in size (diameter); the majority of particles (88.4%) have diameters in the range 0.8-2.5 µm (-0.1 < log dp < 0.4). SEM images reveal that these particles are quite angular. The point of zero charge (PZC) of Min-U-Sil 5 is approximately pH 2.0 (10). During the experiments, the particle concentration of the effluent was measured in two ways. Spectrophotometric absorbance at 500 nm wavelength was converted to suspended solids concentration via a calibration curve. Particle size distributions (PSDs) were quantitatively measured with a Coulter Multisizer III (Coulter Electronics) fitted with 30 and 100 µm apertures. Zeta Potential. ZPDs were obtained from electrophoretic mobility measurements made with a Zetaphoremeter IV (CAD, France), a microscopic electrophoresis instrument equipped with an automatic tracking function using digital image processing. In this instrument, the electrodes are arranged so that the stationary plane is vertical; therefore, gravity does not pull particles out of the stationary layer. The number of tracked particles (i.e., electrophoretic mobility measurements) for each chemical condition was between 80 and 120 to ensure statistically significant distributions. 2558

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Particle shape can influence electrophoretic mobility and the translation to zeta potential. The angularity of Min-U-Sil 5 particles could cause a variation of as much as 6% in the measured electrophoretic mobility (and therefore calculated zeta potential) (13). Such variations could account for a portion of the standard deviations in the ZPDs reported in this paper. Chemical Conditions. To investigate ZPD changes of particles in media filtration under various chemical conditions, two different methods of particle destabilization (pH control and polymer destabilization) were used. For each method, three different conditions were chosen, one of which was expected to have much better particle removal than the others based on surface charge considerations. For the destabilization by pH control, experiments were performed at a constant ionic strength (10-2 M) and at pH values of 3.0, 4.0, and 5.0, all above the pHPZC, which is approximately pH 2.0. The pH was controlled by adding HCl, and the ionic strength was bolstered as necessary by KCl. At these low pH values, no other buffering was provided. The pH was occasionally measured on influent and effluent samples throughout the experiments; these measurements indicated that the pH did not change more than 0.1 unit either with time or through the filter. Another set of chemical conditions investigated surface charge effects using a synthetic organic polymer. Several types of polymers are widely used in particle removal processes at WTPs, depending on the purpose of polymer addition (e.g., primary coagulant, coagulant aid, or filter aid). A cationic polymer with high charge density and relatively low molecular weight is often used as a primary coagulant because of its potential for charge neutralization, whereas nonionic, anionic, or low charge density cationic polymers with high molecular weight are usually used as a coagulant or filtration aid because of their bridging capabilities (14). Because accomplishing destabilization by charge neutralization was desired in this research, high charge density cationic polymers such as poly-DADMAC and polyamine were considered as possible coagulants. On the basis of preliminary experiments, a polyamine (Superfloc C-572, Cytec Industries Inc., Indiana, dimethyl amine polymerized with epichlorohydrin) was chosen. To choose polymer doses for the subsequent filtration experiments, standard 1 L jar-tests in 11.5 cm square vessels were performed: 1 min of rapid mixing (150 rpm, with the velocity gradient G estimated as 230 s-1 based on previously documented calibration curves (15)), 20 min of slow mixing (50 rpm, G ) 47 s-1), and 20 min of settling. Polymer was added via digital pipet into the vortex formed by the paddle stirrer from a stock solution. Based on ZPD measurements on the supernatant particles after the jar tests, doses to yield negative, near zero, and positive particle surface charges were chosen. To supply alkalinity that was reasonably consistent with conditions in water treatment, Min-U-Sil 5 particles were dispersed in 2 × 10-3 M NaHCO3 throughout the polymer experiments while pH was set to 5.2. Stock solutions were made by diluting the liquid product as obtained from the manufacturer on a volume basis, so doses are reported in ppmv.

Experimental Results and Discussion pH Control. Based on the zeta potential measurements at different pH values, three different pH conditions (pH ) 3.0, 4.0, and 5.0) were chosen at a constant ionic strength (10-2 M). The mean zeta potentials ((1 standard deviation) at pH 3.0, 4.0, and 5.0 were -26.4 ( 7.1, -38.7 ( 9.2, and -54.7 ( 9.3 mV, respectively. Detailed test results on the zeta potential of Min-U-Sil 5 at these pH values can be found elsewhere (10), but these three conditions led to increasingly negative values of the mean ZPD with increasing pH, as expected.

FIGURE 2. ZPDs of Min-U-Sil 5 at pH 4.0 during the initial stage (A) and later stage (B). During the pH control experiments, chemical conditions of the glass beads were assumed to be the same as or at least similar to those of Min-U-Sil 5, because the main component of both materials is silica. The ZPDs of Min-U-Sil 5 particles during the early stage of filtration at pH 4.0 are shown in Figure 2A; the results indicate that the ZPD of the effluent was more negative than the influent and shifted to an even more negative surface charge during these first few minutes. This movement of the ZPD can be attributed to the fact that more destabilized (less negative) particles are selectively attached to the collectors, whereas less destabilized particles appear in the effluent at the beginning of filtration. Similar results were found in independent research performed at low filtration velocities of 4–8 m/d; Tong and Johnson (9) found that the mean electrophoretic mobility of colloids in filter effluent was more negative than those in the influent and noted that even small changes in surface charge could result in dramatic changes in the deposition rates. These results agree with the research hypothesis. The ZPDs during later stages of filtration are presented in Figure 2B. The ZPDs of the effluent moved from more negative to less negative, that is, closer to that of the influent. Two factors apparently combine to influence the small decrease (absolute value) of the zeta potential during the later filtration stage. First, there was an influence of particle accumulation, that is, the ripening effect. The surface area of the collector is increased by the solids accumulation, which leads to an improvement of transport efficiency. That is, as time progressed and media grains were increasingly covered with particles of various charges, the surface heterogeneity, both physical (roughness) and chemical (charges), increased, leading to a more random capture of particles and, therefore, no systematic change between the influent and effluent ZPD. Second, some flocs could possibly breakoff from the filter media. Flocs that were once attached to the filter media but were detached can be assumed to have less negative surface charge than particles in the suspension that were never caught (nonattachment particles). Therefore, detachment of flocs can cause the mean zeta potential to become less negative. The effluent concentration (not shown) decreased gradually throughout the period between 10 and 120 min. A t-test confirmed that the three mean zeta potential values in Figure 2A are statistically different with a 95% confidence level and that the 10 min value is different from both the influent and the 4 min sample. The increase of the mean effluent zeta potential (absolute value), expressed as a percent of the mean influent value, is shown as a function of the cumulative hydraulic loading (CHL) at all three pH values in Figure 3. The CHL is the cumulative volume throughput per cross-sectional filter area (the product of the constant filtration velocity and time) and allows direct comparisons with experiments run in different ways. During the initial stage, the absolute value of the mean

FIGURE 3. Relative increase of mean zeta potential (absolute value) of Min-U-Sil 5 from the mean influent value: effect of CHL and pH.

FIGURE 4. Effects of ripening: fractional solids concentration remaining in the effluent (C/Co) and mean zeta potential values of Min-U-Sil 5 as a function of CHL at pH 3.0. (Error bars indicate one standard deviation.) zeta potential rapidly increased (i.e., became more negative) at all three pH values, meaning that less negative particles were well-attached during this stage. The magnitude of the zeta potential increase was greater when the absolute value of influent zeta potential was small (i.e., pH 3). The maximum changes of the effluent mean zeta potential from that of the influent were 9.4 mV (pH 3.0), 8.2 mV (pH 4.0), and 5.2 mV (pH 5.0). In the latter part of all three experiments, the mean zeta potential values stayed relatively constant, although their absolute values remained higher than the influent zeta potential values. The values of solids concentration remaining (C/Co, that is, the effluent concentration divided by the influent concentration) and mean zeta potential changes at pH 3.0 are shown in Figure 4 as a function of CHL. The entire experiment is quite short and can be considered to be in the ripening stage of a full-scale filter operation. The solids concentration VOL. 42, NO. 7, 2008 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 5. Fractional solids concentration remaining in the effluent (C/Co) at different pH values during the initial stage (A) and overall stage (B).

FIGURE 6. Fractional particle number concentration remaining in the effluent (N/No) vs CHL at pH 3.0 (A) and 4.0 (B). in the effluent increased during the very early stage of filtration (as the particle-laden influent replaced the particlefree water in the filter prior to time zero) and then continually decreased due to the ripening effect being more dominant than detachment of the flocs. The mean zeta potential values of the effluent moved quickly from less negative to more negative values during the clean bed removal stage and early ripening stage. It can be assumed that, during the initial stage of filtration, particle retention in the filter and, therefore, the shape of effluent ZPDs are influenced mainly by surface charge interactions between particles and collectors. On the other hand, particle retention during the later stage of this filtration run, that is, after approximately 0.83 m3/m2 CHL, was likely determined by charge interactions not only between particles and collectors but also between particles in suspension and previously collected particles. Less negative surface charge (more destabilized chemical conditions) resulted in better solids removal during the clean bed removal period, as shown in Figure 5A; that is, the results at pH 3.0 have the lowest fraction remaining. On the other hand, the results in Figure 5B suggest that better clean bed removal does not necessarily mean better overall particle removal; the filters operated at pH 4.0 and pH 5.0 achieved better solids removal than at pH 3.0 after a certain amount of CHL. The fractional particle number concentration remaining (N/No) at pH 3.0 for different particle size ranges is presented in Figure 6A. At the beginning of the run, bigger particles were better attached to the collectors than smaller particles, due to the better transport efficiency of larger particles. Particle removal efficiency improved for smaller particles after 6 min (0.5 m3/m2 CHL) but not for larger particles (4.0–5.0 µm). The poorer removal of larger particles after the first few minutes was most likely caused by the detachment of flocs; that is, some of the 4.0–5.0 µm particles in the effluent at the later stages were flocs of smaller particles that individually attached earlier but broke off together as a floc. Such 2560

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detachment of flocs in this size range was documented in previous work (16). The particle number remaining at pH 4.0 is shown in Figure 6B. When these results were compared to those of pH 3, the 1.0–2.0 µm particles continuously improved; the 2.0–3.0 µm particles improved for a while and then remained constant in both cases. However, unlike the PSD at pH 3.0, at the beginning of the filtration, better particle removal efficiency was noticed for the larger size particles (e.g., 4.0–5.0 µm), and the particle removal efficiency improved from 0.33 to 5.0 m3/m2 CHL for all particle size ranges. These results are consistent with those in Figure 5B, indicating that, after ripening, removal was greater at pH 4.0 than at pH 3.0, contrary to expectations. Apparently, physical aspects of the buildup of captured particles can have a substantial role in filter ripening. Here, it seems that the accumulation of larger particles can accelerate the ripening process; Kau and Lawler. (17) reported similar results. Polymer Destabilization. In the jar tests described earlier, zeta potential measurements were performed on the supernatant suspension after settling. The mean zeta potential of 20 mg/L Min-U-Sil 5 suspensions continuously increased (i.e., from negative to positive) with an increase of polymer dose. Based on these jar-tests, three polymer doses were chosen to make negative, near zero, and positive particle surface charges. Those three doses were 0.001 ppmv (belowoptimum dose), 0.01 ppmv (optimum dose), and 0.1 ppmv (above-optimum dose), and the corresponding mean zeta potentials ((1 standard deviation) were -53.3 ( 13.1, 1.0 ( 18.1, and 50.9 ( 7.9 mV. A polymer dose of 0.001 ppmv was assumed to maintain negative surface charges on collectors as well as on particles. The ZPDs of particles during the early stage of filtration at a polymer dose of 0.001 ppmv are shown in Figure 7A, and as in pH control experiments, the same trend of movement to a more negative ZPD was observed. The ZPDs of the effluent moved from a less negative to a more negative region,

FIGURE 7. ZPDs of Min-U-Sil 5 at a polymer dose of 0.001 ppmv during the initial stage (A) and later stage (B).

FIGURE 8. ZPDs of Min-U-Sil 5 at polymer dose of 0.1 ppmv during the initial stage (A) and later stage (B). meaning that during this stage, better destabilized (less negative) particles were well attached to the filter media. The ZPDs of particles at the later stage of filtration are shown in Figure 7B. The ZPDs of the effluent were still less than that of the influent, and they remained relatively constant over this period. The ZPD movement was considerably different between polymer destabilization at this dose and pH control at 5.0 (graph not shown here), even though the influent particle surface charges were similar in both cases (i.e., mean zeta potentials of Min-U-Sil 5 were -54.7 mV for pH 5.0 and -53.3 mV for a polymer dose of 0.001 ppmv). Under pH 5.0 conditions, ZPD moved from more to less negative (i.e., toward that of influent) with time. At the polymer dose of 0.001 ppmv, however, no significant movement occurred at the later stage of filtration. From this difference, it is thought that the particle detachment was more substantial at the pH 5.0 conditions. This finding can be related to the floc strength; under polymer destabilization, the floc strength can be assumed to be stronger than that of pH control. Therefore, the magnitude of particle detachment during the later stage of filtration was more severe at pH 5.0, which in turn leads to movement of the ZPDs from more to less negative direction during the later stage of filtration (12). The ZPDs of effluent during the filtration at a polymer dose of 0.1 ppmv are shown in Figure 8. At this dose, all particles had a positive surface charge because the polymer feed exceeded the optimum dose. The effluent ZPD at 2 min had shifted to less positive values (to the left on the figure) in comparison to the influent. But at later times, the ZPD moved to the right. The effluent ZPD gradually moved toward that of the influent ZPD but remained less positive than that of the influent. Two things can be inferred from these graphs. First, ZPDs of the effluent at the initial stage of filtration moved from a more highly charged region to a lesser charged region but soon afterward reversed that trend. This result means that more highly charged particles were well-removed during the

initial stage of filtration. This finding is quite different from the results that were previously noticed during the polymer dose of 0.001 ppmv and pH control experiments. Second, the effluent ZPD at the start of the experiment did not overlap well with that of the influent, which means that the ZPD of the suspension was changed for some reason. Several ideas might explain this phenomenon. One likely possibility is that the surface charge of the glass beads was not similar to that of Min-U-Sil 5, despite the precoating of the filter grains accomplished by the one-hour period of feed with particle-free but polymer-dosed water. When polymer is used for destabilization by charge neutralization, the mean zeta potential of particles is a function of both polymer dose and particle concentration. The amount of coagulant required for charge neutralization is proportional to the total surface area of particles in the suspension (14). In granular media filtration, where the surface area includes the particles in suspension and the media, the surface charge of particles entering the filter might change if adsorbed polymers desorb and subsequently attach to the media. That is, the difference between the surface area concentration available in the suspension prior to entering a filter and in the filter itself could lead to changes in mean zeta potential of particles within the filter and thereby affect the attachment efficiency of particles to filter grains or previously captured particles. During a filter run, destabilizing chemicals (e.g., coagulants) and destabilized particles coat the filter media, causing the surface charge of the media to shift toward those of the destabilized particles (12). Other possible explanations for the discrepancy between surface charge ranges of influent and effluent ZPDs were considered, such as not establishing equilibrium before the filtration. To check this possibility, an equilibration period of 3 h was compared to the standard 1 h period; no significant difference in the results was found, meaning that equilibrium duration was not a problem during this experiment. VOL. 42, NO. 7, 2008 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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Comparison of the three ZPDs in Figure 8B from the later parts of the run shows that the total range of the three distributions was relatively well overlapped (although the mean of the 20 min sample was statistically different from the influent at the 0.05 level); this overlap means that transfer of charged molecules was minimal after a certain amount of CHL (e.g., 0.83 m3/m2). On the other hand, profound desorption/adsorption of polymers might have happened in the early part of the run (Figure 8A) because of a disequilibrium between the particle suspension and the solution water. However, as deposited particles gradually covered the glass beads, this disequilibrium was decreased, so the possibility of polymer transfer from particles in suspension to the media or particles already on the media decreases with the increase of CHL. Particle behavior in the early stages of granular media filtration is more complex than heretofore realized. Generally, in the very early stages of a filter run, larger particles and particles with lower surface charge were captured to a greater extent than smaller particles and those with greater charge, as expected from theory, but very soon thereafter, particle capture was strongly influenced by the previously retained particles, and in several cases, the trends of particle removal were contrary to those expected based on size and charge. Nevertheless, ripening (improved removal with increasing cumulative hydraulic loading) occurred under most conditions tested.

Literature Cited (1) McTigue, N. E.; LeChevallier, M.; Arora, H.; Clancy, J. National Assessment of Particle Removal by Filtration. AWWARF and AWWA: Denver, Colorado, 1998. (2) O’Melia, C. R.; Stumm, W. Theory of water filtration. J. Amer. Water Works Assoc. 1967, 59 (11), 1393–1412. (3) Derjaguin, B. V.; Landau, L. Theory of stability of strongly charged lyophobic sols and coalescence of strongly charged particles in solutions of electrolytes. Acta Physicochim. URSS 1941, 14, 633– 662.

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(4) Verwey, E. J. W.; Overbeek, J. Th. G. Theory of the Stability of Lyophobic Colloids. Elsevier, Amsterdam, 1948. (5) Elimelech, M. Effect of particle size on the kinetics of particle deposition under attractive double layer interactions. J. Colloid Interface Sci. 1994, 164, 190–199. (6) Tobiason, J. E.; O’Melia, C. R. Physicochemical aspects of particle removal in depth filtration. J. Amer. Water Works Assoc. 1988, 80 (12), 54–64. (7) Elimelech, M.; Gregory, J.; Jia, X.; Williams, R. Particle Deposition and Aggregation; Butterworth Heinemann: Oxford, United Kingdom, 1995. (8) Tufenkji, N.; Redman, J. A.; Elimelech, M. Interpreting deposition patterns of microbial particles in laboratory-scale column experiments. Environ. Sci. Technol. 2003, 37 (3), 616–623. (9) Tong, M.; Johnson, W. P. Colloid population heterogeneity drives hyperexponential deviation from classic filtration theory. Environ. Sci. Technol. 2007, 41 (2), 493–499. (10) Kim, J.; Nason, J. A.; Lawler, D. F. Zeta potential distributions in particle treatment processes. J. Wat. Supply: Res. Tech.-Aqua 2006, 55 (7–8), 461–470. (11) Elimelech, M.; Nagai, M.; Ko, C.; Ryan, J. N. Relative insignificance of mineral grain zeta potential to colloid transport in geochemically heterogeneous porous media. Environ. Sci. Technol. 2000, 34 (11), 2134–2148. (12) Kim, J. Physicochemical Aspects of Particle Breakthrough in Granular Media Filtration. Ph.D. Dissertation, The University of Texas at Austin, 2004. (13) Kim, J. Y.; Yoon, B. J. Electrophoretic motion of a slightly deformed sphere with a nonuniform zeta potential distribution. J. Colloid Interface Sci. 2002, 251, 318–330. (14) Letterman, R. D.; Amirtharajah, A.; O’Melia, C. R. Coagulation and Flocculation. In Water Quality and Treatment, 5th ed.; Letterman, R. D., Ed.; McGraw-Hill, Inc.: New York, 1999, 6.1– 6.43.. (15) Cornwell, D. A.; Bishop, M. M. Determining velocity gradients in laboratory and full-scale systems. J. Amer. Water Works Assoc. 1983, 75 (9), 470–475. (16) Moran, M.; Moran, D.; Cushing, R.; Lawler, D. Particle behavior in deep bed filtration part 2: Particle detachment. J. Amer. Water Works Assoc. 1993, 85 (12), 82–93. (17) Kau, S. M.; Lawler, D. F. Dynamics of Deep-Bed Filtration: Velocity, Depth, and Media. J. Environ. Eng., ASCE 1995, 121 (12), 850–859.

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