Aggregating nanoparticle transport with nonlinear attachment: Modeling and experimental validation

A conceptual mathematical model was developed to simulate the transport of migrating nanoparticles in homogeneous, water saturated, 1-dimensional porous media. The model assumes that nanoparticles can collide with each other and aggregate. Nanoparticles can be found attached reversibly and/or irreversibly onto the solid matrix of the aquifer or suspended in aqueous phase. Attached particles may either contribute to the acceleration of subsequent particle deposition or hinder it, leading to the ripening or blocking process, respectively. The aggregation process was simulated based on the Smoluchowski Population Balance Equation (PBE) and was coupled with the advection-dispersion-attachment equation (ADA) to form a family of partial differential equations that govern the migration of nanoparticles in porous media. For the solution of the PBE, an efficient finite volume solver was employed that significantly accelerated computation times, by reducing the number of participating equations, while maintaining the required accuracy. The developed model was applied to nanoparticle transport experimental data available in literature. The model successfully matched the breakthrough concentration curves, and estimated the corresponding nanoparticle diameter, proving its ability to capture the physical processes participating in nanoparticle transport.