Environ. Sci. Technol. 2003, 37, 2317-2322
Mechanistic Basis for Particle Detachment from Granular Media JOHN A. BERGENDAHL* Department of Civil and Environmental Engineering, Worcester Polytechnic Institute, Worcester, Massachusetts 01609 DOMENICO GRASSO Picker Engineering Program, Smith College, Northampton, Massachusetts, 01063
Colloids may become detached from surfaces in environmental systems as a result of chemical and physical conditions. Many researchers reporting on colloidal detachment in natural and model systems have stopped short of mechanistically and quantitatively describing their observations. In this work, a mathematical construct is presented that quantitatively determines the effect of thermodynamics and hydrodynamics on particle detachment from surfaces in granular media. Using the Buckingham π theorem, a mathematical model is structured based on governing dimensionless groupings. Determining dimensionless numbers elucidates conditions conducive for detachment in engineered and natural porous media. Published detachment data are compared to the mathematical model developed herein and provide support for its utility. Extensions of this technique have utility in many applications where fluid interaction with particulate-laden porous media is encountered.
Introduction Particle attachment to surfaces in granular media has received significant attention in the literature. The attachment process has been conceptually separated into transport (physical) and attachment (chemical) steps (1). However, the integration of these physical and chemical principles underlying particle detachment has received less attention. Particle detachment resulting from fluid flowing through granular material is of concern in many engineered systems such as filters. Groundwater flowing through an aquifer is a natural process of fluid transport through porous media that may also contain attached particles. Particles are ubiquitous in these systems and may become detached from surfaces if conditions are favorable. Particle detachment and subsequent mobilization may facilitate contaminant transport or otherwise result in permeability reductions, high turbidity, or analytical difficulties because of the presence of particles in sample aliquots. In engineered and natural systems that have been studied, colloidal mobilization observations have typically been qualitatively explained via classical particle stability theory (2, 3). The study of primary mechanisms and conditions promoting particle detachment from surfaces has significant practical importance to many fields. In the present work, a quantitative framework previously developed by the authors * Corresponding author telephone: (508)831-5772; fax: (508)8315808; e-mail:
[email protected]. 10.1021/es0209316 CCC: $25.00 Published on Web 04/18/2003
2003 American Chemical Society
(4-6) describing the relative impact of thermodynamic and hydrodynamic parameters for particle detachment is extended. The conceptually derived quantitative model of particle detachment in granular media is applied to data reported in the literature, illustrating the utility of the model.
Background Once steady-state conditions have been achieved in saturated porous media, a disturbance to the system is typically required for the majority of attached particles to become dislodged from the supporting substrate (4, 6). Many phenomenological studies focusing on colloid detachment have been insufficient to fully describe (a) the adhesion (thermodynamic) forces between surfaces and (b) the requisite hydrodynamics conditions for incipient detachment. The work presented herein presents an integrated and predictive approach using governing dimensionless numbers to describe detachment under various physicochemical and hydrodynamic conditions. Many investigators have studied detachment of particles from collectors in natural and model systems. Selected findings are summarized in Table 1. The majority of the data in the literature indicates that detachment occurs when solution pH increases, ionic strength decreases, or hydrodynamic shear increases. Batra et al. (7) investigated theoretically the removal of particles from a substrate when subject to hydrodynamic shear and surfactant solutions. In their study, a plate-plate configuration was assumed, and the effect of roughness on interaction energy was determined. Calculations accounted for the hydrodynamic lift force by reducing the total interaction energy. Plate surfaces with increasing asperity heights were calculated to have greater total interaction energies, and the hydrodynamic force required for detachment increased with increasing asperity height. McDowell-Boyer (2) reported mobilization of colloids in packed columns of sand to be very slow in the absence of physical or chemical perturbations. Reductions in ionic strength induced significant quantities of colloid release. One of McDowell-Boyer’s conclusions was that there is a critical need for advances in our quantitative understanding of colloid detachment. Ryan and Gschwend (8) looked at colloid mobilization from sand coated with iron oxides through solution chemistry changes. By quantifying the interfacial potential energy curve between the colloids and the sand surface, they were able to determine that dissolution of the iron sand coating was not the mechanism of release. Rather, colloid release rate was correlated to detachment energy. Despite these reports on particle detachment in porous media (Table 1), a predictive detachment model is not yet available. While colloid attachment in packed beds has been predicted with various filtration models (1, 9, 10), detachment of colloids has yet to be accurately and quantitatively predicted. Ryan and Elimelech (11) provided an excellent review on the mobilization of colloids in groundwater that included description of fundamental detachment concepts. Yet, particle detachment is still primarily qualitatively described. In this work, an extended colloid stability model, hydrodynamics, and solid mechanics are employed to quantitatively describe circumstances for incipient colloid detachment in granular media.
Theoretical Development To determine the thermodynamic basis for interaction between surfaces, a total interaction energy curve can be VOL. 37, NO. 10, 2003 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
9
2317
up to 30% particles mobilized, max removal at pH 12 up to 15% particles mobilized, max removal at pH 10.9 saline water to freshwater, permeability dropped ∼2 orders of magnitude 23-95% particles mobilized with lower ionic strength
% mobilized increased with increasing flow rate near-complete detachment for quartz grains as pH increased, approximately 60% released from Fe-coated quartz as pH increased
as I decreased, fraction released increased (only ∼33% released) significant particle (and plutonium) mobilization
pH pH ionic strength ionic strength
flow rate pH
ionic strength hydrodynamic shear with rainfall pH pH
developed as illustrated in Figure 1. The total interaction energy is a function of separation distance and is the sum of four components: electrostatic (∆GEL), van der Waals (∆GVDW), Born repulsion (∆GBorn), and Lewis acid-base (∆GAB) interaction energies (12, 13):
78-100% recovered with pH increase >100% recovered with pH increase
observations
∆GΣ ) ∆GEL + ∆GVDW + ∆GBorn + ∆GAB
(1)
The value for each of the components can be predicted from various relationships derived in the literature (14, 15). Referring to Figure 1, ∆Gmin is the depth of the primary energy minimum between surfaces, and ∆Gmax is the primary energy maximum that an attaching or detaching particle must transcend. Detachment of particles may occur because of the following mechanisms: (i) Thermodynamic Perturbations. A change in surface interactions that results in a net repulsive surface energy will detach particles. The relation between the number of particles detached (Ndetached) in the fluid domain and the number of particles attached (Nattached) can be conceptualized with a model based on chemical kinetics (16): kattachment
Ndetached {\ } Nattached k
(2)
detachment
2318
9
Following Ruckenstein and Prieve’s (17) approach, Arrheniustype kinetics can be derived to describe this phenomenon:
[
[
A more comprehensive list can be found in Bergendahl (5).
kdetachment ∝ exp -
a
iron oxide-coated sand iron oxide-coated sand
kattachment ∝ exp -
35 PRD1 bacteriophage 35 silica colloids
33 PRD1 bacteriophage, 62 nm diameter quartz grains and ferric oxyhydroxide-coated quartz, 210-297 µm diameter 23 0.468 µm diameter PS latex glass beads, 0.40-0.52 mm diameter 34 natural particles unsaturated plutonium-contaminated soil
stainless steel, 74-105 µm diameter stainless steel, 44-62 µm diameter sandstone sand (predominantly quartz & feldspar grains), 350-500 µm diameter 0.17 µm diameter hematite 0.19 µm diameter hematite clay 1.46 µm diameter polystyrene latex
30 31 32 2
media particles ref
TABLE 1. Selected Particle Release Experiments in Natural and Model Systemsa
{
perturbation
FIGURE 1. Total energy of interaction between two surfaces in aqueous solution.
ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 37, NO. 10, 2003
]
∆Gmax kT
(3)
]
∆Gmax - ∆Gmin kT
(4)
where k is Boltzmann’s constant (J K-1) and T is temperature (K). Equilibrium particle partitioning occurs when
Nattached kattachment ) ∝ Ndetached kdetachmemnt
[
]
∆Gmax kT ∝ ∆Gmax - ∆Gmin exp kT ∆Gmin exp (5) kT exp -
[
[
]
]
Clearly, if ∆Gmin is negative, an attractive interaction exists and particles will be predominantly attached to the supporting substrate (Nattached/Ndetached . 1). If ∆Gmin is positive, a repulsive interaction dominates and particles will be be poised toward detachment from the supporting surface and mobilized (Nattached/Ndetached , 1). The magnitude of ∆Gmin is a function of the nature of the interacting surfaces and the chemistry of the suspending solution (4). (ii) Hydrodynamic Perturbations. An increase in hydrodynamic shear acting on attached particles may physically detach particles attached to surfaces. van de Ven (18) hypothesized that shear reduces the effective energy mini-
another (see refs 21 and 22) and was calculated from refs 6 and 22:
Kinteraction ≡
4 1 - κ21 1 - κ22 3π + πE1 πE2
(
)
(7)
where κ is Poisson’s ratio, E is Young’s modulus of elasticity (N m-2), and subscripts 1 and 2 denote materials 1 and 2, respectively. For flow through porous media, eq 6 can be modified:
[
∆Gmin ) 1157NRe
( )( )(
)]
4/3 8/3 1/3 µ2 1 do acolloidKinteraction F d2 β g
3/4
(8)
where is porosity, dg is grain diameter (m), and
NRe )
FIGURE 2. Conceptual basis for hydrodynamic detachment model. The arrows indicate relative fluid velocity in the pore. mum (∆Gmin). To quantify the effect of hydrodynamics on attached particles, a conceptual view of porous media must be assumed. Flow through porous media may be modeled as flow through closely and periodically spaced tubes that are constricted (19). The parabolically shaped constricted tube model shown in Figure 2 is thought to adequately represent the void space in a packed bed (6). The shape of the constricted tubes with laminar flow produces a parabolic velocity flow profile that varies along the pore length (the z-axis in Figure 2). To determine conditions resulting in incipient detachment of attached particles, all quantitatively significant forces and moments must be described (i.e., hydrodynamic shear and the thermodynamics of interaction, ∆Gmin). Through a force and moment balance applied to attached particles, the value of hydrodynamic shear for incipient motion has been derived (6): 4/3 β∆Gmin 1 ∂v ) ∂r 12.381 d4/3π2µa8/3 K1/3 o
(6)
colloid interaction
where µ is the fluid absolute viscosity (Pa s), and acolloid is the colloid or particle radius (m). The distance of closest approach, do (m), is the separation distance between the colloid surface and the media surface when attached in the primary energy minimum and has been reported to be 0.158 × 10-9 m by van Oss (15). This value for do was used for all calculations and is consistent with other published values (20). The hysteresis loss factor (β) is a parameter that describes rolling energy loss and is described elsewhere (21). Kinteraction is the elastic interaction constant (N m-2) that accounts for the deformation experienced by a body in contact with
Fvsuperficialdg µ
where vsuperficial is the superficial fluid velocity (m s-1), and F is the fluid density (g L-1). Terms have been grouped on the right side of eq 8 to include a constant, Reynolds number (NRe) relating fluid viscosity and inertial forces, a term composed of fluid properties, a term composed of suspending media properties, and a final term describing particle properties. Equations 6 and 8 can be used to predict hydrodynamic forces required to overcome primary energy minima of attached particles. Performing dimensional analysis of the variables in eq 6 with the Buckingham π theorem provides the dimensionless groups shown in Table 2. Rearranging eq 6 by grouping variables into these dimensionless parameters yields
β3/4NTFT ) (1898π6)1/4(d*)(NDEF)1/4
(9)
This equation composed of dimensionless numbers provides a convenient quantitative technique to assess the potential for particle detachment. The left side of eq 9 is a particularly important dimensionless group, in that if the 3 thermofluid tension is large (∆Gmin . µacolloid ∂v/∂r), the primary energy minimum is sufficient to inhibit detachment for the fluid shear stress conditions imposed. When conditions result in a lower (β3/4NTFT) than that calculated by eq 9, detachment is realized. Data extracted from literature sources were used to calculate values for NDEF, and values for (β3/4NTFT) were determined from eq 9 for a range of expected Kinteraction, ∂v/ ∂r, and colloid radii. Ordinate values were then plotted for representative colloid diameters of 100 nm, 1 µm, 10 µm, and 100 µm (Figure 3) and domains of instability, where detachment is expected, delineated for various colloid sizes. If the point of intersection of (β3/4NTFT) and NDEF, for a given colloid size, lies below the stability line for that size, then detachment is expected. For all cases studied, the model predicted accurately.
Results and Discussion The results of studies summarized in Table 3 have been plotted in Figure 3. If not provided in the literature source, hydrodynamic shear (∂v/∂r) was estimated from the information provided regarding the flow system configuration, and Kinteraction estimated from the descriptions of materials. Except where noted, the colloids were considered to be detached when >50% of the attached colloids were removed. Bergendahl and Grasso (6) detached 1 µm polystyrene latex microspheres from glass beads in packed column experiments. The polystyrene colloids were found to be VOL. 37, NO. 10, 2003 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
9
2319
TABLE 2. Dimensionless Groups Obtained from Buckingham π Theory dimensionless group
group name
definition
thermofluid tension number, NTFT
ratio of surface interaction energy to fluid shear stress (momentum)
Kinteraction ∂v µ ∂r
deformation number, NDEF
ratio of elastic energy to shear stress (momentum)
do acolloid
dimensionless length, d*
ratio of distance of closest approach to colloid radius
( (
∆Gmin
µa3colloid
( )
)
∂v ∂r
)
FIGURE 3. Incipient detachment as a function of the thermofluid tension number and the deformation number for various particle diameters.
TABLE 3. Particle Detachment Data Adapted from Published Sources and Plotted in Figure 3 particle material polystyrene latex polystyrene latex natural Lincoln sand colloids natural Otis sand colloids polystyrene latex polystyrene latex glass polystyrene latex polystyrene latex a
Taken from ref 6.
b
particle diameter (µm) 1.0 0.468 0.7b 0.3b 20 40 10 2 5
media glass beads glass beads Lincoln sand Otis sand flat glass flat glass flat glass glass beads glass beads
Roy and Dzombak (23) conducted experiments to detach 0.486 µm diameter polystyrene colloids from glass bead packed beds. The detachment of these colloids was induced with ionic strength reductions that produced a net repulsion between the colloid and media surfaces. The aqueous chemistry changes reportedly produced significant particle detachment from the media. Although the 50% detachment point could not be determined from the reported data, significant detachment was noted. The shear rate on the attached polystyrene colloids was calculated with equations presented in Bergendahl and Grasso (6), and Kinteraction was estimated for the polystyrene/glass system to be 4.0 × 109 N m-2. The value for (β3/4NTFT) calculated from eq 9 is well below the line indicating detachment for 1 µm colloids, so detachment was expected under these conditions. 9
Kinteraction (N m-2)
ref
100.6 4.93 1.235 0.563 1227 482 491 386 370
4.0 × 4.0 × 109 a 4.8 × 1010 4.8 × 1010 4.0 × 109 a 4.0 × 109 a 4.8 × 1010 a 4.0 × 109 a 4.0 × 109 a
4, 6 23 23 23 24 24 24 25 25
109 a
Mode of the number-averaged diameter.
readily detached with hydrodynamic perturbations. From eq 7, Kinteraction was estimated to be 4.0 × 109 N m-2 for polystyrene/glass interactions (Epolystyrene ) 0.28 × 1010 N m-2, Eglass ) 6.9 × 1010 N m-2, κpolystyrene ) 0.33, κglass ) 0.2). Values of NDEF and (β3/4NTFT) were calculated and plotted in Figure 3. The actual detachment of the 1 µm polystyrene colloids took place as predicted by Figure 3.
2320
Dv/Dr (s-1)
ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 37, NO. 10, 2003
Natural colloids were also detached from packed columns of Lincoln sand (d50 ) 250 µm) and Otis sand (d50 ) 550 µm) by Roy and Dzombak (23). Through energy-dispersive X-ray (EDX) analysis, the released natural colloids were found to be primarily quartz, aluminosilicates, and silica. The modes of the number-averaged diameters of the detached colloids were 0.7 µm for the Lincoln sand colloids and 0.3 µm for the Otis sand colloids. Kinteraction was taken as 4.8 × 1010 N m-2 for glass/glass from eq 7 (Eglass ) 6.9 × 1010 N m-2, κglass ) 0.2). The calculated (β3/4NTFT) values for both Lincoln and Otis sand colloids were well below the line indicating detachment for 1 µm colloids. So again detachment was predicted. Sharma et al. (24) performed detachment experiments with flat glass surfaces. Polystyrene latex microspheres (10, 20, and 40 µm diameter) and glass microspheres (10, 15, 30, and 40 µm diameter) were attached to flat glass plates under quiescent conditions and then detached with hydrodynamic shear. The fraction of particles remaining on the surfaces was determined as a function of hydrodynamic force exerted on the attached particles. The data obtained from flow cell experiments were in agreement with results from centrifugal detachments experiments. Sharma et al. (24)
concluded that rolling was the release mechanism. Converting the hydrodynamic force to hydrodynamic shear and using 4.0 × 109 N m-2 as Kinteraction for polystyrene/glass and 4.8 × 1010 N m-2 for glass/glass, the calculated value for (β3/4NTFT) was well below the line indicating detachment for 10 µm colloids. Detachment of particles from fluidized media was investigated by Amirtharajah and Raveendran (25). Polystyrene microspheres, 2 and 5 µm in diameter, were attached to packed beds of 0.5 mm glass spheres and subsequently detached by increasing the flow rate through the bed into the transitional flow region fluidizing the bed. Hydrodynamic forces on the attached particles were calculated with an equation that accounted for Boussinesq’s eddy viscosities between 0 and 3 N s m-2. The reported hydrodynamic drag force was converted to hydrodynamic shear (6) using a Boussinesq’s eddy viscosity of 0 N s m-2. Letting Kinteraction ) 4.0 × 109 N m-2, the calculated values for (β3/4NTFT) were again below the line indicating detachment for the 1 µm colloids. So detachment was predicted for these particles with this quantitative model. Figure 3 indicates the relative insensitivity of (β3/4NTFT) to changes in the value of the deformation number (NDEF). The deformation number is the ratio of the elastic interaction energy constant to the fluid shear stress. Highly deformable material, such as organically coated particles, should have greater deformation numbers than more rigid material (e.g., silica or iron oxide particles). A 7 order of magnitude increase in NDEF produced only a 1 order of magnitude increase in (β3/4NTFT). While smaller deformation numbers would result from more elastic materials (with lower E), this relative insensitivity of detachment to the deformation number predicted by the model renders the material properties (i.e., E, κ) of low importance for predicting detachment. While the model predictions and data shown in Figure 3 indicate the insensitivity of material properties on detachment, other colloidal systems may possess properties that are not completely captured by this model (e.g., bacteria in biofilms, clay platelets). The delineation between attachment and detachment occurs at much greater values of (β3/4NTFT) for smaller colloid diameters due to larger d* values. At a NDEF value of 1011, 1 µm diameter colloids are detached at (β3/4NTFT) values approximately 3 orders of magnitude lower than for 1 nm diameter colloids. The 3 orders of magnitude difference in colloid diameter results in a threshold ∆Gmin for detachment that is 6 orders of magnitude greater for a 1 µm colloid than a 1 nm diameter colloid. This means that larger colloids are easier to detach than smaller colloids. Shear stress can overcome greater values of ∆Gmin (for a given µ, ∂v/∂r, and Kinteraction) for larger colloids. A smaller colloid attached with the same ∆Gmin would require a greater hydrodynamic shear to effect detachment. In addition, this may be further exacerbated by the difficulty of detaching small colloids from real surfaces due to appreciable surface roughness, where areas may exist in which smaller colloids may encounter reduced hydrodynamic shear. This is analogous to the “shadow” effect that may hinder attachment (26). The roughness of real surfaces may also dramatically affect the energy of interaction between surfaces (27, 28) and therefore impact the magnitude of the thermofluid tension number. Bhattacharjee et al. (27) determined that the attachment energy barrier was reduced with surface asperities that replicated surface roughness. Tabor (28) also found that adhesion energy was reduced with increased roughness, while Batra et al. (7) reported that the hydrodynamic force for detachment theoretically increased as the surface asperity size approached the separation distance. The implications
of these findings for particle detachment are not entirely clear and require further exploration. Difficulty in hydrodynamically detaching smaller colloids has practical ramifications in the event the mobilization of small colloids is desired. While large and small particles may be detached from granular media through thermodynamic and hydrodynamic changes to the system, smaller colloids are less likely to be detached via hydrodynamics than large colloids. Chemical perturbations may be more effective at mobilizing smaller colloids. While it is predicted to be more difficult to hydrodynamically detach small colloids, mobilization due to chemical perturbation has somewhat of a size dependency as well due to the effect of chemistry on ∆Gmin (see Grasso et al. (29)). A recently developed (4-6), physicochemical-based, quantitative model was extended and successfully used to predict conditions for particle detachment in model and natural porous media. The model is based on first principles and was structured by grouping variables into governing dimensionless numbers: a thermofluid tension number and a deformation number. Model predictions defined domains of instability (detachment) for a wide range of system characteristics. Published experimental data were consistent with the predicted domains of instability, illustrating the utility of the model as a predictive tool.
Acknowledgments The authors appreciate the thorough review and helpful suggestions provided by anonymous reviewers. This work was funded in part through a DOD fellowship awarded to J.A.B. Note Added after ASAP Posting. Table 2 of this article, released ASAP on 4/18/2003, was slightly modified for clarity. The modified version was posted on 5/13/2003.
Literature Cited (1) Yao, K.; Habibian, M. T.; O’Melia, C. R. Environ. Sci. Technol. 1971, 5, 1105-1112. (2) McDowell-Boyer, L. M. Environ. Sci. Technol. 1992, 26, 586593. (3) Kia, S. F.; Fogler, H. S.; Reed, M. G. J. Colloid Interface Sci. 1987, 118, 158-168. (4) Bergendahl, J. A.; Grasso, D. AIChE J. 1999, 45, 475-484. (5) Bergendahl, J. A. Modeling the Mechanics of Colloid Detachment in Environmental Systems. Doctoral Dissertation, University of Connecticut, Storrs, CT, 1999. (6) Bergendahl, J. A.; Grasso, D. Chem. Eng. Sci. 2000, 55, 15231532. (7) Batra, A.; Paria, S.; Manohar, C.; Khilar, K. C. AIChE J. 2001, 47, 2557-2565. (8) Ryan, J. N.; Gschwend, P. M. Environ. Sci. Technol. 1994, 28, 1717-1726. (9) Logan, B. E.; Jewett, D. G.; Arnold, R. G.; Bouwer, E. J.; O’Melia, C. R. J. Environ. Eng. 1995, 121, 869-873. (10) Vaidyanathan, R.; Tien, C. Chem. Eng. Sci. 1988, 43, 289-302. (11) Ryan, J. N.; Elimelech, M. Colloids Surf. A: Physicochem. Eng. Aspects 1996, 107, 1-56. (12) Chheda, P.; Grasso, D. Langmuir 1994, 10, 1044-1053. (13) van Oss, C. J.; Chaudhury, M. K.; Good, R. J. Chem. Rev. 1988, 88, 927-941. (14) Elimelech, M.; Gregory, J.; Jia, X.; Williams, R. Particle Deposition and Aggregation, 1st ed.; Butterworth-Heinmann: Oxford, 1995. (15) van Oss, C. J. Interfacial Forces in Aqueous Media, 1st ed.; Marcel Dekker: New York, 1994. (16) Ryan, J. N.; Gschwend, P. M. J. Colloid Interface Sci. 1994, 164, 21-34. (17) Ruckenstein, E.; Prieve, D. C. AIChE J. 1976, 22, 276-283. (18) Van de Ven, T. G. M. Colloids Surf. A: Physicochem. Eng. Aspects 1998, 138, 207-216. (19) Payatakes, A. C.; Tien, C.; Turian, R. M. AIChE J. 1973, 19, 5866. (20) Israelachvili, J. N. Intermolecular and Surface Forces, 2nd ed.; Academic Press: London, 1992. VOL. 37, NO. 10, 2003 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
9
2321
(21) Johnson, K. L. Contact Mechanics, 1st ed.; Cambridge University Press: Cambridge, U.K., 1985. (22) Johnson, K. L.; Kendall, K.; Roberts, A. D. Proc. R. Soc. London A 1971, 324, 301-313. (23) Roy, S. B.; Dzombak, D. A. Colloids Surf. A: Physicochem. Eng. Aspects 1996, 107, 245-262. (24) Sharma, M. M.; Chamoun, H.; Sita Rama Sarma, D. S. H.; Schechter, R. S. J. Colloid Interface Sci. 1992, 149, 121-134. (25) Amirtharajah, A.; Raveendran, P. Colloids Surf. A: Physicochem. Eng. Aspects 1993, 73, 211-227. (26) Ko, C.; Elimelech, M. Environ. Sci. Technol. 2000, 34, 36813689. (27) Bhattacharjee, S.; Ko, C.; Elimelech, M. Langmuir 1998, 14, 33653375. (28) Tabor, D. J. Colloid Interface Sci. 1977, 58, 2-13. (29) Grasso, D.; Subramaniam, K.; Butkus, M.; Strevett, K.; Bergendahl, J. Rev. Environ. Sci. Bio/Technol. 2002, 1, 17-38.
2322
9
ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 37, NO. 10, 2003
(30) Kuo, R. J.; Matijevic, E. J. Colloid Interface Sci. 1980, 78, 407420. (31) Kallay, N.; Matijevic, E. J. Colloid Interface Sci. 1981, 83, 289300. (32) Khilar, K. C.; Fogler, H. S. J. Colloid Interface Sci. 1984, 101, 214-224. (33) Loveland, J. P.; Ryan, J. N.; Amy, G. L.; Harvey, R. W. Colloids Surf. A: Physicochem. Eng. Aspects 1996, 107, 205-221. (34) Ryan, J. N.; Illangasekare, T. H.; Litaor, M. I.; Shannon, R. Environ. Sci. Technol. 1998, 32, 476-482. (35) Ryan, J. N.; Elimelech, M.; Ard, R. A.; Harvey, R. W.; Johnson, P. R. Environ. Sci. Technol. 1999, 33, 63-73.
Received for review September 10, 2002. Revised manuscript received February 26, 2003. Accepted March 5, 2003. ES0209316
