### Abstract

- Top of page
- Abstract
- 1. Introduction
- 2. Experimental Methods
- 3. Model for Mobilization, Transport, and Deposition
- 4. Model Application Procedures
- 5. Experimental Results
- 6. Quantification of Deposition and Mobilization Rates: Application of the Model
- 7. Discussion
- Acknowledgments
- References

[1] We report results on the effects of porewater pH and transients in porewater flow on the deposition and mobilization of colloid-sized clay particles within unsaturated sand columns. The deposition rates of illite under steady-flow conditions were essentially independent of pH, while the deposition rates of kaolinite nearly doubled as the pH decreased from 7.4 to 4.6. Mobilization of kaolinite colloids was slow or negligible under steady-flow conditions; however, transients in porewater flow induced rapid colloid release. A model that accounts for rate-limited deposition reactions and that links colloid mobilization to variations in moisture content and porewater velocity describes the effluent colloid concentrations measured during the steady-flow and transient-flow stages of the column experiments. On the basis of these results we infer that the effects of pH on clay-colloid deposition depend on the mineralogy of the clay colloids and that perturbations in flow are critical in mobilizing clay colloids within the vadose zone.

### 1. Introduction

- Top of page
- Abstract
- 1. Introduction
- 2. Experimental Methods
- 3. Model for Mobilization, Transport, and Deposition
- 4. Model Application Procedures
- 5. Experimental Results
- 6. Quantification of Deposition and Mobilization Rates: Application of the Model
- 7. Discussion
- Acknowledgments
- References

[2] Vadose zone environments typically contain colloid-sized clay particles in great abundance [*Denovio et al.*, 2004]. These clay colloids can adsorb a variety of contaminants and, if mobilized, may carry contaminants across the water table and into groundwater aquifers [*Ryan et al.*, 1998; *Sprague et al.*, 2000]. Colloid mobilization occurs during infiltration events that are characterized by spatiotemporal changes in porewater flow rate, moisture content, and porewater chemistry [*Pilgrim and Huff*, 1983; *El-Farhan et al.*, 2000; *Saiers et al.*, 2003; *Rousseau et al.*, 2004]. Once mobilized, colloids travel by advection and dispersion and can be removed from the porewater by reactions that take place at solid-water and air-water interfaces [*Wan and Wilson*, 1994; *Gamerdinger and Kaplan*, 2001; *Cherrey et al.*, 2003]. The rates of the deposition reactions vary broadly and depend on the physicochemical properties of the soil-water-colloid system [*Wan and Tokunaga*, 1997; *Lenhart and Saiers*, 2002; *Saiers and Lenhart*, 2003].

[3] In this work, we describe results from column experiments and model simulations that are designed to address four questions related to the controls on clay-colloid movement through unsaturated porous media: (1) How do the deposition kinetics of clay colloids respond to variations in porewater pH? (2) Does the relationship between pH and deposition rates vary as a function of clay-colloid mineralogy? (3) How does clay-colloid retention differ between saturated media, where colloid deposition occurs only at solid-water interfaces, and unsaturated media, where colloids collect at both solid-water and air-water interfaces? (4) What effects do perturbations in volumetric moisture content have on the mobilization of clay colloids? To our knowledge, these questions have not been addressed before in the context of clay-colloid transport in unsaturated porous media. The answers to these questions should illuminate how key variables that characterize the vadose zone affect the movement of clay colloids and should improve conceptual and theoretical descriptions of the processes of colloid-facilitated contaminant transport and soil-profile development.

### 3. Model for Mobilization, Transport, and Deposition

- Top of page
- Abstract
- 1. Introduction
- 2. Experimental Methods
- 3. Model for Mobilization, Transport, and Deposition
- 4. Model Application Procedures
- 5. Experimental Results
- 6. Quantification of Deposition and Mobilization Rates: Application of the Model
- 7. Discussion
- Acknowledgments
- References

[10] Here we summarize a published model [*Saiers and Lenhart*, 2002] that can be used as a diagnostic tool to quantify the rates of colloid deposition in the experiments and to test expectations about relationships between porewater flow transients and colloid mobilization. The model solves the advection-dispersion equation for the transport of the clay colloids:

where *C* is the porewater colloid concentration, Γ_{STR} is the concentration of colloids immobilized by straining (colloid mass per sand mass), Γ_{TIR} is the sum of the concentrations of colloids immobilized by air-water interface capture and sand grain attachment (colloid mass per volume of air and sand), ρ_{b} is the bulk density, Θ is the volumetric moisture content, *D* is the dispersion coefficient, *q* is the specific discharge, *t* is time, and *z* is the coordinate parallel to flow. Variations in *q* and Θ, which were induced in our experiments through adjustment of the column inflow and outflow rates, are specified on the basis of the numerical solution to the Richards equation. Equation (1) is coupled with equations for the rate-limited transfer of colloids between mobile and immobile phases.

[11] Immobilization by straining occurs within porewater conduits that are too narrow to permit the colloids to pass [*Wan and Tokunaga*, 1997]. The submicrometer clay colloids are too small to be strained within the water-saturated pore spaces of our sand pack, but may become trapped at the three-phase contacts of pore-corner menisci, within adsorbed water films, and at the termini of discontinuous porewater ducts. The release of strained colloids is negligible during steady porewater flow; however, increases in Θ promote expansion of porewater conduits, which leads to mobilization. Observations on the mobilization of strained silica colloids during porous medium imbibition (wetting) reveal that the fraction of colloids eligible for release increases with increasing Θ [*Saiers and Lenhart*, 2002]. This finding suggests that dimensions of the porewater conduits exhibit a distributed response to changes in measured Θ, which spreads colloid release over a range of Θ.

[12] A phenomenological way to distribute colloid mobilization during the imbibition process is to divide the population of strained colloids into a series of compartments that release colloids at different moisture contents [*Saiers and Lenhart*, 2002]. We assume that a first-order rate law describes the temporal change in the concentration of strained colloids within the ith compartment, such that

while the temporal variation in the total concentration of strained colloids is

where *N*_{C} is the number of compartments, *k*_{STR} is the straining-rate coefficient, and *k*_{Ri} is the mobilization rate coefficient for the ith compartment. We assume *k*_{STR} does not vary between compartments and account for the dependence of *k*_{STR} on Θ and *v* with an empirical function reported by *Lenhart and Saiers* [2002]:

where Θ_{r} is the residual moisture content, *n* is porosity, and *N*_{1} is a constant. Values of *k*_{Ri} vary between compartments according to the relationship between Θ (calculated by solving the Richards equation) and a compartment's characteristic value of critical moisture content:

where *N*_{2} is a constant and Θ_{CRi} is the critical moisture content for compartment i. According to equations (4a) and (4b), colloid mobilization from the ith compartment occurs only if Θ exceeds the value of the critical moisture content assigned to that compartment, in which case *k*_{Ri} varies directly with *v*. We treat Θ_{CR} as a continuously distributed variable that can assume any value between Θ_{dep} and *n*, where Θ_{dep} is the steady state Θ under which colloids were applied to the column (Θ_{dep} = 0.12 in our study). A piecewise linear density function describes the distribution in Θ_{CR} [see *Saiers and Lenhart*, 2002].

[13] Clay colloids traveling through water-filled pores or relatively large porewater conduits of partially saturated pores are not susceptible to straining, but may diffuse to solid-water or air-water interfaces and be retained by electrostatic forces. We use the terms air-water interface capture and mineral-grain attachment to describe colloid immobilization in cases where electrostatic forces govern colloid adhesion at interfaces. Because the contributions of air-water interface capture and mineral-grain attachment to colloid immobilization cannot be separately resolved (without ambiguity) from analysis of column experiments, we adopt a simple, lumped parameter approach and account for both mechanisms with a single second-order kinetics expression:

where k_{TIR} is the rate coefficient for attachment and *X*_{TIR} is the colloid-retention capacity of the interfaces, which expresses the maximum attainable mass of interface-attached colloids per volume of air and solid. Equation (5) describes an irreversible reaction. Rate laws for irreversible reactions provide a reasonable approximation of air-water interface capture and mineral-grain attachment for conditions of steady porewater flow and chemistry [*Saiers and Lenhart*, 2003]. During transient-flow, colloids may be mobilized through destruction of air-water interfaces or mobilized from solid-water interfaces by increases in shear or by moving air-water interfaces that scour colloids from the sand-grain surfaces. Equation (5) does not account for these mobilization mechanisms and thus the model presented here will approximate breakthrough concentrations measured during the transient-flow stage of the kaolinite experiments only if the release of strained kaolinite (as described by equations (2a)–(4b)) dominates the mobilization response.

[14] Equations (1)–(5) govern the transport, deposition, and mobilization of colloids in unsaturated and saturated media. These equations for colloid transport and mass transfer, together with the equations for porewater flow (i.e., the Richards equation), were solved numerically by finite differences [*Saiers and Lenhart*, 2002]. In order to accommodate numerical solution and to be compatible with equations (2a) and (2b), the continuous density for Θ_{CR} must be discretized into *N*_{C} compartments. As *N*_{C} increases, the discretized form of the Θ_{CR} function converges to the true, continuous form of the density function, which we approximated by setting *N*_{C} = 60.

### 4. Model Application Procedures

- Top of page
- Abstract
- 1. Introduction
- 2. Experimental Methods
- 3. Model for Mobilization, Transport, and Deposition
- 4. Model Application Procedures
- 5. Experimental Results
- 6. Quantification of Deposition and Mobilization Rates: Application of the Model
- 7. Discussion
- Acknowledgments
- References

[15] We quantified colloid deposition in the illite experiments and during the steady-flow stage of the kaolinite experiments by identifying values of *k*_{STR}, *k*_{TIR}, and *X*_{TIR} that minimized the differences between modeled and measured breakthrough concentrations. The straining rate coefficient (*k*_{STR}) was set to zero in simulations of clay-colloid transport in saturated sand. Because *k*_{STR} depends on physical properties, but is independent of porewater chemistry, we used the *k*_{STR} values estimated from the unsaturated experiments at pH 7.4 to describe straining at pH 6.0 and 4.6.

[16] We quantified mobilization during the transient-flow stage of the kaolinite experiments by adjusting values of *N*_{2} and the shape of the cumulative density for Θ_{CR} in order to obtain a best fit between measured and modeled kaolinite concentrations. The shape of the Θ_{CR} density is governed by the number and position of “anchor” critical moisture contents that separate the straight line segments of the distribution [see *Saiers and Lenhart*, 2002, Figure 1]. The cumulative densities at the anchors, are found by optimization and the entire distribution is defined through linear interpolation between anchors. We employed the methods described by *Saiers and Lenhart* [2002] to determine the optimal number of anchors and to estimate the cumulative density associated with each anchor.

[17] Colloids mobilized by the transients in Θ and *v* were susceptible to redeposition deeper within the column. Variations in *k*_{STR} with Θ and *v* were described by equation (3). This involved computing *N*_{1} in equation (3) from values of *k*_{STR} estimated from the steady-flow stage of the experiments and then reapplying the parameterized form of equation (3) to compute *k*_{STR} variations during transient flow. The parameters *k*_{TIR} and *X*_{TIR} likely depend on Θ and *v*, too, but data are unavailable to define these dependencies. Therefore we used the values of *k*_{TIR} and *X*_{TIR} estimated from the steady state stage of the unsaturated experiments to quantify the combined effects of mineral-grain attachment and air-water interface capture on kaolinite immobilization during periods of transient flow. This simplifying assumption should not jeopardize the model descriptions provided that mobilization rates substantially exceed redeposition rates during the transient-flow stage.

### 7. Discussion

- Top of page
- Abstract
- 1. Introduction
- 2. Experimental Methods
- 3. Model for Mobilization, Transport, and Deposition
- 4. Model Application Procedures
- 5. Experimental Results
- 6. Quantification of Deposition and Mobilization Rates: Application of the Model
- 7. Discussion
- Acknowledgments
- References

[27] We find that initial adhesion rates of illite to air-water and solid-water interfaces (as quantified by *k*_{TIR}) and the maximum interfacial coverages (as quantified by *X*_{TIR}) of illite vary weakly with pH. Values of *k*_{TIR} and *X*_{TIR} for kaolinite are roughly the same as those for illite at pH 6.0 and 7.4, but are substantially greater at pH 4.6. *Wan and Tokunaga* [2002] measured clay-colloid partitioning in a bubble column and similarly observed that kaolinite partitioning to air-water interfaces was more sensitive to pH changes than that of illite. Kaolinite adhesion to negatively charged air-water and solid-water interfaces is sensitive to pH because it has edge sites that become more protonated (and positively charged) as pH decreases [*Langmuir*, 1997]. Illite also has edge sites with pH-dependent charge, but compared to kaolinite, it has a higher permanent charge, higher aspect ratio, fewer planar edge sites, and a lower zero point of charge [*Wan and Tokunaga*, 2002]. These characteristics dampen the influence of pH on illite adhesion.

[28] The variation in the response of clay-colloid mobility to changes in Θ is attributable to differences in colloid affinities for the air-water and solid-water interfaces. Examination of the best fit values of *X*_{TIR} estimated from the saturated and unsaturated experiments indicates that the air-water and solid-water interfaces had a relatively low capacity for binding illite at pH 4.6–7.4 and kaolinite at pH 6.0 and 7.4. For these combinations of pH and colloids, straining in partially saturated pores represented the main contributor to immobilization in unsaturated media, and a decrease in Θ from 0.34 to 0.12 led to only a modest (15 mg L^{−1}) decline in peak breakthrough concentrations. Both solid-water and air-water interfaces were more effective in retaining kaolinite at pH 4.6, and calculations based on estimates of *X*_{TIR} taken from both the saturated and unsaturated experiments reveal that a unit volume of air was capable of immobilizing nearly 9 times more kaolinite than a unit volume of sand at pH 4.6. Because of the high capacity of air-water interfaces to retain kaolinite at pH 4.6, kaolinite mobility declined precipitously with the transition from saturated to unsaturated conditions.

[29] Transients in flow mobilized kaolinite colloids that were retained within the column under steady-flow conditions. A parametrically simple model that links mobilization to moisture content changes and flow velocity describes the kaolinite concentrations measured during the transient-flow stage with reasonably good success. The largest model data discrepancy occurs in the pH-4.6 experiment where the model underestimates peak effluent concentrations (Figure 2f). Our model accounts only for the release of strained colloids, but the destruction of air-water interfaces during sand-pack imbibition probably contributed significantly to mobilization at pH 4.6, as these interfaces served as efficient collectors of kaolinite during the steady-flow stage of this experiment.

[30] The flow transients succeeded in mobilizing from 25 to 47% of the colloid mass retained within the columns. Maximum moisture contents measured during the transient stage equaled 0.2, which are well below the sand-pack porosity (0.34). Further increases in Θ would have undoubtedly mobilized more colloids, but such increases would have required exceedingly high flow rates. In natural vadose zone environments, clay-colloid mobilization is likely enhanced by perturbations in chemistry (e.g., reduction in ionic strength, increases in pH) that occur concomitantly with transients in flow. In an additional experiment, we found that 56% of kaolinite colloids trapped within a column under steady-flow conditions were mobilized during displacement of a pH-4.6 solution with a pH-7.4 solution. Although preliminary, these data suggest that chemical perturbations may, under some conditions, be of equal or of greater importance than flow perturbations in mobilizing clay colloids within the vadose zone.