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a Department of Civil, Environmental, and Architectural Engineering, University of Colorado at Boulder, 428 UCB, Boulder, CO 80309-0428
b School of Forestry and Environmental Studies, Yale Univ., Sage Hall, 205 Prospect Street, New Haven, CT 06511
* Corresponding author (joseph.ryan{at}colorado.edu).
Received 22 January 2004.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONCOLLOID MOVEMENT IN IDEAL...COLLOID MOVEMENT IN NONIDEAL...FUTURE DIRECTIONSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONCOLLOID MOVEMENT IN IDEAL...COLLOID MOVEMENT IN NONIDEAL...FUTURE DIRECTIONSREFERENCES |
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How do these colloids become suspended in porewater? Are they readily transported through the vadose zone? How rapidly are these colloids deposited back onto soil surfaces? These questions can be addressed, in part, by examining processes of colloid deposition and mobilization in saturated porous media (McDowell-Boyer et al., 1986; Ryan and Elimelech, 1996), but in this review, we focus on what is known about these processes in unsaturated porous media.
Three key features of the vadose zone play a critical role in colloid movement: (i) the presence of air–water interfaces, (ii) transients in flow and chemistry, and (iii) soil structure and heterogeneity (Fig. 1) . First, the unsaturated nature of the vadose zone introduces a third phase, air, which affects colloid partitioning between water and soil. Colloids of many types associate with the air–water interface (Wan and Wilson, 1994b; Sirivithayapakorn and Keller, 2003), and the movement of these colloids is affected by the movement of air bubbles (Gomez-Suarez et al., 1999; Gomez-Suarez et al., 2001; Saiers et al., 2003). Second, porewater flow and chemistry are highly transient in unsaturated porous media. Flow transients, generated by rainfall and snowmelt events interspersed by drying periods, can promote very rapid colloid mobilization (El-Farhan et al., 2000). Chemical transients, often produced by the introduction of low ionic-strength rainwater into the vadose zone, result in destabilization of colloidal aggregates in soils and mobilization of colloids (e.g., Kaplan et al., 1993; Ryan et al., 1998). Third, the soils of the vadose zone are usually structured or physically heterogeneous to some extent. For example, macropores promote preferential flow that has the potential to augment colloid mobilization and reduce colloid deposition. Soil layering often inhibits colloid movement by enhancing deposition of colloids mobilized in the upper soil horizons (Bond, 1986).
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COLLOID MOVEMENT IN IDEAL POROUS MEDIA |
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TOPABSTRACTINTRODUCTIONCOLLOID MOVEMENT IN IDEAL...COLLOID MOVEMENT IN NONIDEAL...FUTURE DIRECTIONSREFERENCES |
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The kinetics of colloid deposition on mineral grains depends on the rate of colloid transport from the bulk fluid to the grain surface and on the probability that a colloid collision with the mineral grain will succeed in attachment. Colloids are transported from the bulk fluid to the mineral grains by Brownian diffusion, interception, and sedimentation (Yao et al., 1971). The transport rates due to these three mechanisms can be calculated for water-saturated media as functions of the physical properties of the porous medium–water–colloid system, including colloid diameter and density, grain size, and flow velocity (Yao et al., 1971; Rajagopalan and Tien, 1976; Logan et al., 1995; Tufenkji and Elimelech, 2004). An analogous theory for water-unsaturated media is unavailable. Its development relies on improvements in models for air–water configuration in variably saturated porous media and, for natural systems, on consideration of the effects of irregularities in the shapes of the mineral grains and colloids.
Attachment of colloids that strike the mineral grains is determined from the net-interaction potential, which can be calculated from DLVO theory as the sum of the electrostatic double-layer force, the van der Waals force, and short-range solvation or steric forces (Derjaguin and Landau, 1941; Verwey and Overbeek, 1948; McDowell-Boyer et al., 1986; Ryan and Elimelech, 1996). The magnitude and direction of these forces depend on the chemical and physical characteristics of the colloid and soil-grain surfaces and, for the electrical double-layer force, the chemical composition of the porewater. At low ionic strength and for similarly charged colloids and soil grains, the net-interaction potential exhibits a repulsive maximum that hinders the attachment of colloids that approach the mineral-grain surface. With increasing ionic strength, the repulsive barrier decreases in magnitude, which increases the probability that a colloid-grain collision will succeed in colloid attachment. The repulsive barrier is absent for oppositely charge colloids and soil grains, in which case the deposition rate is controlled by the rate at which colloids are transported from the pore fluid to the mineral-grain surface.
Predictions of colloid deposition that are based on DLVO theory have not been published for water-unsaturated systems, but DLVO theory has been tested against measurements of colloid deposition in water-saturated porous media. These evaluations show that theoretically determined deposition rates substantially underestimate corresponding measured values when repulsive barriers exist between the colloids and mineral grains (Elimelech et al., 1995). Agreement between DLVO-based and laboratory-measured deposition rates has been improved through recent modifications to theory that account for complexities associated with surface-charge heterogeneity, grain-scaled surface roughness, and deposition within the secondary minimum of the net-interaction energy profile (Bhattacharjee et al., 1998; Hahn and O'Melia, 2004). These modifications, although designed to improve descriptions of colloid deposition in water-saturated media, should also be applicable for quantifying colloid deposition reactions on mineral-grain surfaces present within unsaturated porous media.
Like the soil surfaces, air–water interfaces present within unsaturated porous media can serve as collectors of colloidal particles (Fig. 1 and 2) . Colloids that are transported to the air–water interface are retained by either capillary or electrostatic forces; therefore, colloid capture at air–water interfaces depends on pH, ionic strength, and colloid surface properties. Increases in ionic strength reduce the magnitude of the repulsive energy barrier between the negatively charged air–water interface and like-charged mineral colloids, leading to progressively more favorable conditions for attachment and faster rates of air–water interface capture (Wan and Wilson, 1994a; Saiers and Lenhart, 2003a). Hydrophobic colloids, such as certain bacteria, exhibit a greater affinity for air–water interfaces than mineral colloids, which have comparatively hydrophilic surfaces (Wan and Wilson, 1994b; Schäfer et al., 1998; Lenhart and Saiers, 2002). Among clay-mineral colloids, the affinity for the air–water interfaces depends on the colloid shape and surface-charge distribution and varies inversely with colloid cation-exchange capacity. Kaolinite partitions more strongly to the air–water interface than illite, while bentonite and montmorillonite exhibit negligible partitioning (Wan and Tokunaga, 2002).
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The relative importance of soil-grain attachment, air–water interface capture, and film straining to colloid deposition is not constant, but varies as a function of porewater chemistry, moisture content, and colloid characteristics. The work of Wan and Tokunaga (1997) and Lenhart and Saiers (2002) suggests that film straining represents the most important deposition mechanism for hydrophilic colloids under conditions of low ionic strength (<10–3 M) and low to intermediate moisture content. As moisture content and ionic strength increase, the leading colloid deposition mechanism may transition from film straining to air–water interface capture or soil grain attachment, depending on the surface characteristics of the colloids and mineral grains (Saiers and Lenhart, 2003a).
Modeling Colloid Transport and Deposition
The observations reviewed above have been instrumental in guiding the development of mathematical models for colloid transport and deposition within homogeneous granular materials. Most of these transport and deposition models are based on the assumption of steady porewater flow and conceptualize the unsaturated porous medium as a three-component system consisting of air, water, and mineral grains (e.g., Sim and Chrysikopoulos, 2000). Colloids are transmitted through the water-filled sections of the porous medium by advection and dispersion and are removed from the porewater by straining, air–water interface capture, and deposition onto soil–water interfaces. Film straining and air–water interface capture are treated as irreversible mass-transfer processes, a suitable approximation provided that flow and porewater chemistry remain steady (Corapcioglu and Choi, 1996; Wan and Tokunaga, 1997). Colloid release from soil–water interfaces is often accommodated in unsaturated transport models, but is generally slow in the absence of hydrologic and chemical perturbations (Schäfer et al., 1998; Chu et al., 2001).
The advection–dispersion equation describes the movement of porewater colloids. The one-dimensional form of this equation is given by
 | [1] |
STR, AWI, and SWI are immobile-phase colloid concentrations for removal by film straining (STR) air–water interface capture (AWI), and soil–water interface deposition (SWI); t is time; 
c is the ratio of colloid mass to its effective cross-sectional area; Sw is water saturation; fair is the air–water interfacial area per unit void volume; fsoil is the soil–water interfacial area per unit void volume; AL is the longitudinal dispersivity; v is the average porewater velocity; and z is the coordinate parallel to flow. The concentration of strained colloids (STR) is expressed in terms of colloid mass per volume of porewater, while AWI and SWI are expressed in terms of normalized surface coverages (i.e., area of attached colloids per area of interface). Solution of Eq. [1] requires specification of the kinetics expressions for film straining, air–water interface capture, and deposition onto soil–water interfaces.
Wan and Tokunaga (1997) quantified colloid straining inside thin films with a first-order kinetics expression:
 | [2] |
 | [3] |
In Eq. [3], P(
) is the probability of pendular ring discontinuity (expressed as a function matric potential, ), d is the colloid diameter, set w is the film thickness. h, N, and ß are empirical parameters. Wan and Tokunaga (1997) employed Eq. [2] and [3] to describe film straining rates in a suite of column experiments that were conducted at matric potentials ranging from –0.05 to –0.5 m and with microspheres ranging in diameter from 0.014 to 0.97 µm.
Colloids traveling within relatively large water channels (e.g., interconnected pendular rings) are not affected by film straining, but they may diffuse to the air–water interface where electrostatic or capillary forces retain them. A second-order kinetics expression has been invoked to describe the attachment of microspheres, bacteria, viruses, and mineral colloids at air–water interfaces present within porous media (Corapcioglu and Choi, 1996; Schäfer et al., 1998; Chu et al., 2001). The formulation of this rate law varies slightly depending on whether the captured colloid mass is normalized by the volume of air or by air–water interfacial area. For the case of normalization by interfacial area, the rate law is expressed by
 | [4a] |
AWI is a blocking function. The blocking function declines linearly as AWI increases:
 | [4b] |
AWI is an excluded area parameter equivalent to the ratio of blocked air–water interfacial area to the projected cross-sectional area of the colloid. Inspection of Eq. [4a] and [4b] shows that colloid capture rates vary linearly with C and decline as colloids accumulate on the air–water interface.
The magnitude of kAWI depends on the rate of colloid transport from the bulk fluid phase to the air–water interface and on the probability that a colloid collision with the interface will result in attachment. While neither the transport rate nor the attachment probability can be accurately determined on a theoretical basis, discernible trends between the magnitude of kAWI and some system properties have been identified. In particular, values of kAWI that quantify silica-colloid attachment vary proportionately with the one-third power of the porewater velocity (kAWI 
v1/3) (Lenhart and Saiers, 2002) and increase linearly with porewater ionic strength (Saiers and Lenhart, 2003a).
The reciprocal of AWI (AWI–1) defines the maximum attainable surface coverage at the air–water interface. Estimates of AWI–1 increase with ionic strength because of a reduction in repulsive electrical double layer forces between colloids. Even at elevated ionic strengths, maximum surface coverages for both biocolloids and mineral colloids are low. For example, Abdel-Fattah and El-Genk (1998) reported AWI–1 values for hydrophobic microsphere ranging from 0.012 to 0.08 for ionic strengths between 0.001 and 1 M, while Saiers and Lenhart (2003a) reported AWI–1 values for silica colloids ranging from 0.001 to 0.03 for ionic strengths between 2 x 10–4 and 0.2 M. The parameter AWI–1 likely depends on hydrodynamic forces in addition to forces between colloids (Ko and Elimelech, 2000). Because hydrodynamic forces vary with position along the air–water interface, colloid surface coverages are undoubtedly nonuniform, with some areas of the air–water interface completely devoid of colloids (even at maximum surface coverages), while other areas collect colloids in high concentrations. Estimates of AWI–1, then, should be regarded as a spatial average over the entire air–water interface.
Methods for quantifying soil–water interface reactions in unsaturated media are largely based on approaches derived from studies conducted in water-saturated systems. Several investigators have adopted a second-order reversible rate law to describe colloid mass-transfer reactions with the solid phase (Corapcioglu and Choi, 1996; Schäfer et al., 1998; Chu et al., 2001):
 | [5a] |
 | [5b] |
SWI is an excluded area parameter. Application of this kinetics formulation to data on microsphere, virus, and bacteria transport indicate that kR is small or zero, at least for conditions of constant flow and porewater chemistry. Like their air–water interface counterparts, kSWI and SWI are sensitive to porewater chemistry, soil composition, and colloid type (Corapcioglu and Choi, 1996; Schäfer et al., 1998; Chu et al., 2001). The deposition rate coefficient (kSWI) should exhibit an additional dependence on volumetric moisture content because changes in air–water configuration that accompany variation in moisture content will affect colloid trajectories around (and the transport rate to) the mineral-grain surfaces.
bEquations [1], [2], and [4a] to [5b] with unknowns C, STR, AWI, and SWI are suitable for simulating colloid transport, film straining, air–water interface capture, and mineral-grain attachment in unsaturated, homogeneous porous media. Published models that incorporate one or more of these three mass-transfer mechanisms have successfully reproduced data from laboratory experiments on the transport of both inorganic and organic colloids in ideal porous media. Though very encouraging, these results should not be taken as evidence that the colloid-transport problem has been solved. The published simulations rely on adjustment of model parameters that cannot be determined on a theoretical basis and hence the favorable model-data agreement should not be considered definitive proof of positive identification of the mechanisms that govern colloid mass transfer. Alternative interpretations of the experimental observations are possible.
Colloid Mobilization
Few experimental or theoretical studies on colloid mobilization within ideal unsaturated media are available. On the basis of studies with saturated porous media, we anticipate that perturbations in porewater chemistry will promote colloid release (Fig. 1). Ionic-strength reductions and pH increases are the most common chemical perturbations that mobilize colloids in saturated systems (McDowell-Boyer, 1992; Ryan and Gschwend, 1994; Grolimund and Borkovec, 1999) and are likely to play an important role in colloid mobilization within unsaturated systems.
Physical perturbations in flow that characterize typical infiltration events also drive colloid mobilization. Several mechanisms for this flow-induced mobilization have been proposed (Fig. 1). Colloids trapped in narrow porewater conduits (by straining) may be released into the pore fluid when these flow paths expand during soil imbibition (Fig. 3 ; Saiers and Lenhart, 2003b). Moving air–water interfaces associated with wetting and drying fronts may scavenge colloids from mineral-grain surfaces and facilitate their transport through the porous medium (Gomez-Suarez et al., 1999, 2001; Saiers et al., 2003). Increases in shear stress that accompany porewater-velocity increases may cause colloids to roll along the surface to which they are attached, and these colloids may be released into the porewater upon encountering surface roughness that reduces the DLVO adhesion force (Hubbe, 1985).
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COLLOID MOVEMENT IN NONIDEAL POROUS MEDIA |
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TOPABSTRACTINTRODUCTIONCOLLOID MOVEMENT IN IDEAL...COLLOID MOVEMENT IN NONIDEAL...FUTURE DIRECTIONSREFERENCES |
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Experimental Findings
Colloid movement through nonideal porous media has been measured in small-scale field experiments and in laboratory experiments with intact soil cores. These experiments most often involve applying water to the surface of the soil and measuring the concentrations of colloids in water samples collected in lysimeters installed within the soil profile (for field experiments) or at the base of the core (for laboratory experiments). Results of these studies have been instrumental in improving our understanding of factors that control the mobilization of naturally occurring soil colloids.
A salient characteristic of these field and intact soil laboratory experiments is the consistent occurrence of a pulse of colloids at the beginning, and sometimes at the end, of a rainfall event with an interlude of relatively steady colloid mobilization (e.g., Kaplan et al., 1993; Jacobsen et al., 1997; Ryan et al., 1998; El-Farhan et al., 2000). The colloid pulses during imbibition and draining can be attributed to the effect of flow transients on colloid mobilization. The relatively steady colloid mobilization during the rainfall event can be attributed to the gradual propagation of chemical (and perhaps some physical) perturbations through the soil column.
The best example of colloid mobilization pulses coinciding with the beginning and end of a simulated rainfall event is provided by the field experiments conducted by El-Farhan et al. (2000). Infiltrating water was applied as water ponded on the soil surface. Peak colloid concentrations (up to 265 mg L–1) were recorded in the first few and last few samples of water taken from zero-tension lysimeters at 25-cm depths (Fig. 4) . These peak concentrations were attributed to the passage of colloid-scavenging air–water interfaces during imbibition and draining. The experiments conducted by Saiers et al. (2003) in ideal porous media reinforce this interpretation for the draining. In addition, some of the pulse of colloid mobilization that occurs at the beginning of a rainfall event can be attributed to the release of colloids into expanding of water films (Saiers and Lenhart, 2003b).
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In nonideal porous media, there are indications that the detachment step is promoted by various chemical and physical perturbations (e.g., decreasing ionic strength, increasing pH, shear stress), with the addition of another chemical perturbation, the detachment of colloids by dissolution of mineral cements that bind together various soil constituents (e.g., Harris et al., 1987; Weisbrod et al., 2002). Despite these indications, experiments in nonideal porous media have not yielded much insight into detachment mechanisms because it is highly unlikely that the detachment kinetics would be the rate-limiting step in an experiment in which a measurable amount of colloids were mobilized. Instead, most of these experiments show that kinetics of colloid mobilization during steady infiltration appears to be limited by the diffusion step (Jacobsen et al., 1997; Lægdsmand et al., 1999; Schelde et al., 2002).
The key experimental result that supports an interpretation of diffusion-limited kinetics for colloid mobilization is a linear relationship between the cumulative mass of mobilized colloids and the square root of time (Fig. 5)
following
 | [6] |
is the total mass of colloids that can be mobilized in a sheet of thickness l, and Dc is the diffusion coefficient of the colloid (Crank, 1975). Such linear relationships were observed by Jacobsen et al. (1997), Lægdsmand et al. (1999), and Schelde et al. (2002) for intact soils in laboratory columns.
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Modeling Colloid Mobilization in Nonideal Media
Efforts are just beginning to build a modeling framework appropriate for describing the mobilization and transport of colloids in nonideal, unsaturated porous media (Jarvis et al., 1999; Schelde et al., 2002). These colloid-transport models, like those developed for ideal systems, ignore the effects of biological processes (e.g., growth, decay, predation, and inactivation) and thus are most appropriately applied to the movement of inorganic colloids.
Schelde et al. (2002) developed a model capable of simulating the mobilization and transport of natural mineral colloids within macroporous soils cores (Fig. 6) . This model is similar in form to dual-porosity, mobile–immobile models for solute transport in structured and aggregated porous media (Coats and Smith, 1964; van Genucthen and Cleary, 1979; Nkedi-Kizza et al., 1984). It accounts for an equivalent macropore that approximates the average behavior of the actual macropore network. Water in the partially saturated macropore is assumed to occur as a thin film with mobile- and immobile-water portions. Colloids are generated from a "crust layer" near the macropore edge. These colloids presumably diffuse across the stagnant portion of the water film and enter its mobile-water portion, where flow is steady and the colloids are transported by advection and dispersion. Although Schelde et al. (2002) developed this model in the context of macroporous soils, it could be applied to describe colloid transport and mass transfer in aggregated soils by conceptualizing the water in the aggregates as immobile water and the water in the interaggregate pore spaces as the mobile water.
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While progress has been made toward developing a capability to simulate the unsaturated transport of colloids in nonideal systems characterized by porous-medium heterogeneity, there is clearly a long way to go. Available models are very simple and incorporate only a subset of the mass-transfer processes that combine to influence colloid mobility in the vadose zone. Additional testing of models over a broader range of experimental conditions is needed. These model-data evaluations will lead to model refinement by illuminating gaps in our understanding of processes and will help to define quantitative relationships between model parameters and measurable system properties.
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FUTURE DIRECTIONS |
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TOPABSTRACTINTRODUCTIONCOLLOID MOVEMENT IN IDEAL...COLLOID MOVEMENT IN NONIDEAL...FUTURE DIRECTIONSREFERENCES |
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Using tools like light transmission through transparent micro- and meso-models (Wan and Wilson, 1994a; Sirivithayapakorn and Keller, 2003), magnetic resonance imaging, and X-ray computed tomography, efforts are underway to improve our understanding of flow and colloid transport in the unsaturated zone (Darnault et al., 2002; Nestle et al., 2002; Wildenschild et al., 2002; Weisbrod et al., 2003). As the resolution and capabilities of these visualization systems improve, it will be possible to test hypotheses regarding proposed mechanisms of colloid mobilization and deposition, as well as to identify new mechanisms that cannot readily be inferred from analysis of column experiments. Visualization experiments that permit air–water interface reactions to be unambiguously distinguished from solid–water interface reactions should be particularly useful in guiding the development of mechanistic models for colloid deposition and mobilization.
Transients in flow conditions—the wetting and drying cycles of soils—have recently been identified in field and laboratory experiments as key factors governing the mobilization of soil colloids (El-Farhan et al., 2000; Saiers and Lenhart, 2003b; Saiers et al., 2003). This transient flow–induced mobilization is particularly complex because it is governed by multiple mechanisms, including (but not limited to) thin-film expansion, air–water interface scour, and fluid shear. Additional field and laboratory studies on bulk soils, combined with better visualization techniques, are needed to evaluate the responses of these mechanisms for the range of physical and chemical conditions encountered in real vadose-zone environments. These observations are required to advance theory appropriate for quantifying colloid mobilization in near-surface soils, where transient-flow regimes predominate.
Soil structure (i.e., preferential flow paths, aggregates) plays an important role in infiltration processes and thus in the mobilization and transport of colloid-sized particles. Disintegration of soil aggregates leads to the release of clay particles. Although observations of this phenomenon are available (Rengasamy et al., 1984; Pojasok and Kay, 1990; Brubaker et al., 1992; Oades, 1993; Le Bissonnais, 1996), additional research is needed to examine the relationship between colloid dispersion in the typical batch system and in intact soils. A recent step in this direction is the work of Kjaergaard et al. (in press), who observed a correlation between the amount of clay released from soils taken from a hill slope sequence with a wide range of clay content and the amount of clay released by a "low-energy" water-dispersible colloid batch experiment. Their low-energy test used soils at field moisture contents and less vigorous shaking. Experiments with intact cores suggest that preferential flow paths (e.g., macropores) affect colloid transport and filtration (Jacobsen et al., 1997; Ryan et al., 1998; Lægdsmand et al., 1999; Schelde et al., 2002), but evaluating these processes in laboratory experiments with the goal of defining mechanisms is difficult. One of the fundamental issues that remain unresolved is identification of the conditions under which macropore flow is initiated, a problem common to all aspects of flow and transport in the vadose zone. To improve our understanding of the influences of preferential flow paths on colloid transport, we must better characterize the nature of these flow paths in natural soils and develop ways of reproducing them in model soil systems.
The effects of pore straining on the removal of larger colloids in saturated porous media is receiving renewed attention owing to concern about the transport of protozoan cysts during riverbank filtration (Bradford et al., 2002, 2003). The removal of colloids by film straining has been incorporated into models of colloid transport in the vadose zone, but pore straining has not. Pore straining of colloids will strongly affect soil permeability and may lead to irreversible clogging, an important concern for wastewater reclamation and soil aquifer treatment.
The importance of transients in porewater chemistry more drastic than the infiltration of rainwater of low ionic strength must also be evaluated. To assess colloid-facilitated contaminant migration at sites of improper disposal of hazardous and radioactive waste, we must examine colloid transport and mass-transfer processes at a broad range of porewater pH, porewater compositions, and temperatures (e.g., Gschwend et al., 1990; Flury et al., 2002; Blume et al., 2002). In addition, the formation of porewater colloids by precipitation of supersaturated mineral phases, which has been observed in both surface and groundwaters (e.g., Gschwend and Reynolds, 1987; Liang et al., 1993; Schemel et al., 2000), must be assessed in vadose zones subject to these hazardous-waste environments.
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ACKNOWLEDGMENTS |
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TOPABSTRACTINTRODUCTIONCOLLOID MOVEMENT IN IDEAL...COLLOID MOVEMENT IN NONIDEAL...FUTURE DIRECTIONSREFERENCES |
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), specific conductance (SC), isoelectric point (pHiep), electrophoretic mobility (EM), and zeta potential (
).
