Colloidal particles (e.g., humic substances, suspended clay particles, metal oxides, and microorganisms) are commonly found in subsurface environments [Kretzschmar et al., 1999]. Many contaminants can sorb onto colloids in suspension, thereby increasing their concentrations in solution beyond thermodynamic solubilities [Kim et al., 1992]. Experimental evidence now exists that many contaminants are transported not only in a dissolved state by water, but also sorbed to moving colloids. This colloid-facilitated transport has been illustrated in the literature for numerous contaminants, including heavy metals [Grolimund et al., 1996; Šimůnek et al., 2006], radionuclides [Von Gunten et al., 1988; Noell et al., 1998], pesticides [Vinten et al., 1983; Kan and Tomson, 1990; Lindqvist and Enfield, 1992], pharmaceuticals [Tolls, 2001; Thiele-Bruhn, 2003], hormones [Hanselman et al., 2003], and other contaminants [Magee et al., 1991; Mansfeldt et al., 2004]. Since mobile colloids often move at rates similar or faster as non-sorbing tracers, the potential of enhanced transport of colloid-associated contaminants can be very significant (e.g., McCarthy and Zachara, 1989). Failure to account for colloid-facilitated solute transport can severely underestimate the transport potential and risk assessment for these contaminants. Models that can accurately describe the various mechanisms controlling colloid and solute transport, and their mutual interactions and interactions with the solid phase, are essential for improving predictions of colloid-facilitated transport of solutes in variably saturated porous media.

The transport behavior of dissolved contaminant species has been studied for many years. By comparison, colloid transport and the many interactions among contaminants, colloids, and porous media are less well understood. While colloids are subject to similar subsurface fate and transport processes as chemical compounds, they are also subject to their own unique complexities [van Genuchten and Šimůnek, 2004; Flury and Qiu, 2008]. Since many colloids and microbes are negatively charged, they are electrostatically repelled by negatively-charged solid surfaces. This will lead to an anion exclusion process that can cause slightly enhanced transport relative to fluid flow. The advective transport of colloids may similarly be enhanced by size exclusion, which limits their presence to the larger pores [Bradford et al., 2003, 2006]. In addition to being subject to adsorption-desorption at solid surfaces, colloids are also affected by straining [Bradford et al., 2003, 2006] and may accumulate at air-water interfaces [Wan and Wilson, 1994; Thompson and Yates, 1999; Wan and Tokunaga, 2002; Crist et al., 2005; Torkzaban et al., 2008; Lazouskaya et al., 2011]. All of these complexities require colloid transport models to be more flexible than regular solute transport models.

Models that consider colloid-facilitated transport are based upon mass balance equations for all colloid and contaminant species. The various colloid-facilitated transport models that have appeared in the literature differ primarily in the manner which colloid transport and contaminant interactions are implemented. For example, Mills et al. [1991] and Dunnivant et al. [1992] assume that colloids are non-reactive with the solid phase, Corapcioglu and Jiang [1993] and Jiang and Corapcioglu [1993] consider a first-order kinetic attachment of colloids, Saiers and Hornberger [1996] assume irreversible nonlinear kinetic attachment of colloids, and van de Weerd and Leijnse [1997] describe colloid attachment kinetics using the Langmuir equation. All colloid-facilitated transport models account for interactions between the contaminants and colloids. Various equilibrium and kinetic models have been used for this purpose.

Although already relatively complex, no existing model for colloid-facilitated contaminant transport to our knowledge includes all of the major processes contributing to colloid and colloid-facilitated transport. For example, most models for colloid-facilitated transport consider flow and transport only in fully saturated groundwater systems, usually for steady-state flow, and thus do not account for colloid interactions with the air-water interface. Also, no colloid-facilitated transport model has considered straining and size exclusion as mechanisms of colloid retention and transport, respectively. These two processes, and especially straining, have recently received much attention since classical colloid transport models are often unable to describe simultaneously both breakthrough curves versus time and concentration profiles versus depth [Bradford et al., 2003, 2006; Li et al., 2004; Tufenkji and Elimelech, 2005].

Straining involves the entrapment of colloids in down-gradient pores that are too small to allow particle passage. The critical pore size for straining will depend on the size of the colloid and the pore-size distribution of the medium [McDowell-Boyer et al., 1986; Bradford et al., 2002, 2003]. Straining may have significant implications for colloid-facilitated solute transport, as illustrated by Bradford et al. [2006]. Considering average capillary pressure-saturation curves for the 12 major soil textural groups given by Carsel and Parrish [1988], they calculated that a 2 m colloid, which is the size of a clay particle, will be excluded or strained in 10 to 86% of the soil pore space for various soil textures [Bradford et al., 2006]. These percentages should significantly increase if a soil becomes unsaturated.

Size exclusion, a process closely related to straining, affects the mobility of colloids by constraining them to flow domains and pore networks that are physically accessible [Ryan and Elimelech, 1996; Ginn, 2002]. Electrostatic forces also play an important role in the distribution (and mobility) of colloids. Anionic colloids will be excluded from locations adjacent to negatively charged solid surfaces; similar to the much reported anion exclusion process for anionic solutes [Krupp et al., 1972; Gvirtzman and Gorelick, 1991; Ginn, 1995]. In case of size or anion exclusion, colloids will tend to reside in larger pores and in more conductive parts of the flow domain. As a result, colloids will be transported faster than a conservative solute tracer (Reimus, 1995; Cumbie and McKay, 1999; Harter et al., 2000; Bradford et al., 2004]. Differences in the dispersive flux for colloids and a conservative solute tracer are also anticipated as a result of exclusion [Scheibe and Wood, 2003]. Bradford et al. [2002] observed that the dispersivity of 3.2 m carboxyl latex colloids was up to 7 times greater than bromide in saturated aquifer sand. Conversely, Sinton et al. [2000] found in a field. microbial transport experiment that the apparent colloid dispersivity decreased with increasing particle size.

Colloid and colloid-facilitated contaminant transport in partially saturated porous media is even more complex than in water-saturated systems. In addition to all of the processes and difficulties discussed above, colloid transport in partially saturated porous media is further complicated by the presence of an air phase and thin water films, in addition to the solid and water phases present in saturated media. Wan and Wilson [1994] observed that colloidal particles deposit preferentially on the air-water interface via a capillary force acting on the particles, and that particle transport was tremendously retarded since the air-water interface acted as a strong sorption phase. Another physical restriction on colloid transport in unsaturated systems is imposed by thin water films; this process is often referred to as film straining [Wan and Tokunaga, 1997; Saiers and Lenhart, 2003]. Wan and Tokunaga [1997] proposed that colloid transport in unsaturated systems depends on the ratio of colloid size to water film thickness. Corapcioglu and Choi [1996] developed a mathematical model describing colloid transport in unsaturated porous media, and also studied the effects of colloids on volatile contaminant transport and air-water partitioning in unsaturated porous media.

Most current models for colloid-facilitated transport assume that the number of colloids with respect to the contaminant is large and that kinetic reactions coefficients are not dependent on the number of colloids in the system. Although this may be true for some systems, the number of colloids (or concentrations) is often highly variable, with colloids being mobilized (or immobilized) due to changing chemical or hydrological conditions. Thus the reaction coefficients need to be adjusted to the number of colloids in the system in different phases (i.e., mobile, immobile, attached to the air-water interface). This adjustment needs to be carried out also for numerical stability reasons. For example, if the number of colloids in the system decreases dramatically and the sorption constants for solute to colloids are assumed to be constant, this may lead to large sorbed concentrations, and hence numerical instabilities.

C-Ride is a two-dimensional numerical module that incorporates processes associated with colloid and colloid-facilitated solute transport in variably-saturated porous media. C-Ride (which refers to Colloids providing a ride for solutes) was developed specifically for the HYDRUS (2D/3D) software package [Šimůnek et al., 2011; Šejna et al., 2011]. The general conceptual basis of the module is discussed in a paper by Šimůnek et al. [2006], and restated here for multi-dimensional systems. The module accounts for both colloid and solute transport due to advection, diffusion and dispersion in variably-saturated media, as well as for solute movement facilitated by colloid transport. The colloid transport module additionally considers the processes of attachment/detachment to/from the solid phase, straining, and/or size exclusion. The module allows for different pore water velocities and dispersivities for the colloids and the solute. However, the module does not describe all of the processes discussed above, such as attachment/detachment to the air-water interface. These processes likely will be added in future versions of the module.

The C-Ride documentation focuses mostly only on the colloid and colloid-facilitated transport features of the C-Ride module. All processes related to variably-saturated water flow and heat transport are described in detail in the HYDRUS (2D/3D) documentation [Šimůnek et al., 2011], and will not be repeated here.

The C-Ride module may be used to analyze water and solute movement in unsaturated, partially saturated, or fully saturated porous media. C-Ride can handle flow domains delineated by irregular boundaries. The flow region itself may be composed of nonuniform soils having an arbitrary degree of local anisotropy. Flow and transport can occur in the vertical plane, the horizontal plane, or in a three-dimensional region exhibiting radial symmetry about a vertical axis. The water flow part of the model considers prescribed head and flux boundaries, as well as boundaries controlled by atmospheric conditions.

The governing flow and transport equations are solved numerically using standard Galerkin-type linear finite element schemes. The C-Ride module is fully supported by the HYDRUS (2D/3D) graphical user interface [Šejna et al., 2018]. Applications of the C-Ride module are demonstrated later in this report on several examples.

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