Advanced Mathematical Model for the Transport of Aggregating Nanoparticles in Water Saturated Porous Media: Nonlinear Attachment and Particle Size‐Dependent Dispersion

Abstract A conceptual mathematical model was developed to describe the migration of aggregating nanoparticles in water saturated, homogeneous porous media with one‐dimensional uniform flow. Nanoparticles can be found suspended in the aqueous phase or attached reversibly and/or irreversibly onto the solid matrix. The Smoluchowski population balance equation (PBE) was used to model the process of particle aggregation and was coupled with the advection‐dispersion‐attachment equation to form a nonlinear transport model. Furthermore, an efficient and accurate solver for the PBE, and an iterative solver for the linear or nonlinear attachment equations were employed. The new numerical model was applied to nanoparticle transport experimental data available in the literature. Although, conventional transport models can be used to describe nanoparticle migration at low ionic strength conditions, such models might not be applicable for high ionic strength conditions, where aggregation becomes a dominant process. Aggregation is significantly affecting the transport characteristics of nanoparticles. Under high ionic strength conditions, the mass retention in the solid matrix of the porous medium increases, and a nonlinear particle attachment behavior may be observed. The proposed model performed remarkably well, successfully capturing numerous physical processes associated with nanoparticle transport, including particle‐size‐dependent dispersion. Ignoring the aggregation process and using conventional colloidal transport models to model nanoparticle transport may lead to erroneous results.