Langmuirian Blocking of Irreversible Colloid Retention: Analytical Solution, Moments, and Setback Distance.

Soil and aquifer materials have a finite capacity for colloid retention. Blocking of the limited number of available retention sites further decreases the rate of retention with time and enhances risks (e.g., pathogens or colloid-associated contaminants) or benefits (e.g., remediation by microorganisms or nanoparticles) of colloid migration. Our objective was to use a straightforward procedure, based on variable transformation and Laplace transform, to solve the problem of advective colloid transport with irreversible retention and Langmuirian blocking for a pulse-type condition. Formulas for the mean breakthrough time and retardation factor were obtained using zero- and first-order time moments of the breakthrough curves. Equations for the time and position (setback distance) for a particular colloid concentration were obtained from this information. D21 g breakthrough curves and retention profiles in fine sand at four ionic strengths were well described by the model when parameters were optimized. Illustrative simulations demonstrated that blocking becomes more important for smaller retention capacity () and for larger retention rate coefficient (), input concentration (), and pulse duration. Blocking tended to delay colloid arrival time at a particular location relative to a conservative tracer, and produced larger setback distances for smaller and /.

Analytic solutions for colloid transport with time- and depth-dependent retention in porous media.

Elucidating and quantifying the transport of industrial nanoparticles (e.g. silver, carbon nanotubes, and graphene oxide) and other colloid-size particles such as viruses and bacteria is important to safeguard and manage the quality of the subsurface environment. Analytic solutions were derived for aqueous and solid phase colloid concentrations in a porous medium where colloids were subject to advective transport and reversible time and/or depth-dependent retention. Time-dependent blocking and ripening retention were described using a Langmuir-type equation with a rate coefficient that respectively decreased and increased linearly with the retained concentration. Depth-dependent retention was described using a rate coefficient that is a power-law function of distance. The stream tube modeling concept was employed to extend these analytic solutions to transport scenarios with two different partitioning processes (i.e., two types of retention sites). The sensitivity of concentrations was illustrated for the various time- and/or depth-dependent retention model parameters. The developed analytical models were subsequently used to describe breakthrough curves and, in some cases, retention profiles from several published column studies that employed nanoparticle or pathogenic microorganisms. Simulations results provided valuable insights on causes for many observed complexities associated with colloid transport and retention, including: increasing or decreasing effluent concentrations with continued colloid application, delayed breakthrough, low concentration tailing, and retention profiles that are hyper-exponential, exponential, linear, or non-monotonic with distance.

Combined physical and chemical nonequilibrium transport model for solution conduits.

Solute transport in karst aquifers is primarily constrained to relatively complex and inaccessible solution conduits where transport is often rapid, turbulent, and at times constrictive. Breakthrough curves generated from tracer tests in solution conduits are typically positively-skewed with long tails evident. Physical nonequilibrium models to fit breakthrough curves for tracer tests in solution conduits are now routinely employed. Chemical nonequilibrium processes are likely important interactions, however. In addition to partitioning between different flow domains, there may also be equilibrium and nonequilibrium partitioning between the aqueous and solid phases. A combined physical and chemical nonequilibrium (PCNE) model was developed for an instantaneous release similar to that developed by Leij and Bradford (2009) for a pulse release. The PCNE model allows for partitioning open space in solution conduits into mobile and immobile flow regions with first-order mass transfer between the two regions to represent physical nonequilibrium in the conduit. Partitioning between the aqueous and solid phases proceeds either as an equilibrium process or as a first-order process and represents chemical nonequilibrium for both the mobile and immobile regions. Application of the model to three example breakthrough curves demonstrates the applicability of the combined physical and chemical nonequilibrium model to tracer tests conducted in karst aquifers, with exceptionally good model fits to the data. The three models, each from a different state in the United States, exhibit very different velocities, dispersions, and other transport properties with most of the transport occurring via the fraction of mobile water. Fitting the model suggests the potentially important interaction of physical and chemical nonequilibrium processes.

Colloid transport in dual-permeability media.

It has been widely reported that colloids can travel faster and over longer distances in natural structured porous media than in uniform structureless media used in laboratory studies. The presence of preferential pathways for colloids in the subsurface environment is of concern because of the increased risks for disease caused by microorganisms and colloid-associated contaminants. This study presents a model for colloid transport in dual-permeability media that includes reversible and irreversible retention of colloids and first-order exchange between the aqueous phases of the two regions. The model may also be used to describe transport of other reactive solutes in dual-permeability media. Analytical solutions for colloid concentrations in aqueous and solid phases were obtained using Laplace transformation and matrix decomposition. The solutions proved convenient to assess the effect of model parameters on the colloid distribution. The analytical model was used to describe effluent concentrations for a bromide tracer and 3.2- or 1-µm-colloids that were observed after transport through a composite 10-cm long porous medium made up of a cylindrical lens or core of sand and a surrounding matrix with sand of a different grain size. The tracer data were described very well and realistic estimates were obtained for the pore-water velocity in the two flow domains. An accurate description was also achieved for most colloid breakthrough curves. Dispersivity and retention parameters were typically greater for the larger 3.2-µm-colloids while both reversible and irreversible retention rates tended to be higher for the finer sands than the coarser sand. The relatively small sample size and the complex flow pattern in the composite medium made it difficult to reach definitive conclusions regarding transport parameters for colloid transport.

Numerical investigation of the impact of ethanol on flow in the vadose zone.

There is a need to elucidate the impact of ethanol on the subsurface environment because of the application of ethanol as automotive fuel. This study quantifies the effects of changes in surface tension, viscosity, and density induced by ethanol on the transmission and retention of water in the vadose zone. The HYDRUS-1D model was modified to simulate two different scenarios of flow in a sandy loam involving ponding (constant head) or spillage with a subsequent rainfall event (constant flux). Solutions containing different amounts of the highly miscible ethanol (10, 50, and 100% by weight) as well as pristine water were considered. During ponding, ethanol reduced the amount of fluid entering the soil and slowed down the advancement of the wetting front. Viscosity effects were predominant for this scenario, reducing the average depth of the infiltrating liquid up to 44%. The total amount of pure ethanol that entered the soil was 11.38 vs. 17.64 cm for pure water. For the spillage scenario, the results suggest that density has little impact on the liquid movement. Surface tension effects are predominant in the upper portion of the soil. The changes in hydraulic conductivity due to ethanol-induced modifications of solution viscosity are responsible for the slower advancement of the moisture front. The 10% ethanol solution moved 43.1% faster than pure ethanol during the first 2 d because of viscosity and surface tension effects.

Combined physical and chemical nonequilibrium transport model: analytical solution, moments, and application to colloids.

The transport of solutes and colloids in porous media is influenced by a variety of physical and chemical nonequilibrium processes. A combined physical-chemical nonequilibrium (PCNE) model was therefore used to describe general mass transport. The model partitions the pore space into "mobile" and "immobile" flow regions with first-order mass transfer between these two regions (i.e, "physical" nonequilibrium or PNE). Partitioning between the aqueous and solid phases can either proceed as an equilibrium or a first-order process (i.e, "chemical" nonequilibrium or CNE) for both the mobile and immobile regions. An analytical solution for the PCNE model is obtained using iterated Laplace transforms. This solution complements earlier semi-analytical and numerical approaches to model solute transport with the PCNE model. The impact of selected model parameters on solute breakthrough curves is illustrated. As is well known, nonequilibrium results in earlier solute breakthrough with increased tailing. The PCNE model allows greater flexibility to describe this trend; for example, a closer resemblance between solute input and effluent pulse. Expressions for moments and transfer functions are presented to facilitate the analytical use of the PCNE model. Contours of mean breakthrough time, variance, and spread of the colloid breakthrough curves as a function of PNE and CNE parameters demonstrate the utility of a model that accounts for both physical and chemical nonequilibrium processes. The model is applied to describe representative colloid breakthrough curves in Ottawa sands reported by Bradford et al. (2002). An equilibrium model provided a good description of breakthrough curves for the bromide tracer but could not adequately describe the colloid data. A considerably better description was provide by the simple CNE model but the best description, especially for the larger 3.2-microm colloids, was provided by the PCNE model.