Modeling the Transport and Retention of Nanoparticles in a Single Partially Saturated Pore in Soil

Pore-network models are powerful tools for studying particle transport in complex porous media, and investigating the role of interfaces in their fate. The first step in simulating particle transport using pore-network models is to quantitatively describe particle transport in a single pore, and obtain relationships between pore-averaged deposition rate coefficients and various pore-scale parameters. So, in this study, a three-dimensional (3D) mathematical model is developed to simulate the transport and retention of nanoparticles within a single partially saturated pore with an angular cross-section. The model accounts for particle deposition at solid-water interfaces (SWIs), air-water interfaces (AWIs), and air-water-solid (AWS) contact regions. We provide a novel formulation for particle diffusive transport from AWI to AWS, where particles are assumed to be retained irreversibly by capillary forces. The model involves 12 dimensionless parameters representing various physicochemical conditions. The 3D model results are averaged over the pore cross-section and then fitted to breakthrough curves from one-dimensional (1D) advection-dispersion-sorption equations with three-site kinetics to estimate 1D-averaged deposition rate coefficients at interfaces. We find that half-corner angle, particle size, radius of curvature of AWI, and mean flow velocity have a significant effect on those coefficients. In contrast, chemical parameters such as ionic strength and surface potentials of particles and interfaces have negligible effects. AWS is found to be the major retention site for particles, especially for hydrophobic particles. We develop algebraic relationships between 1D-averaged deposition rate coefficients at interfaces vis-a-vis various pore-scale parameters. These relationships are needed for pore-network models to upscale nanoparticle transport to continuum scale.