Transport of aggregating nanoparticle in porous media: Novel Mathematical Modeling

The migration of aggregating nanoparticles in water-saturated, homogeneous porous media with one-dimensional uniform flow was conceptualized through a novel numerical model. Nanoparticles were assumed to be found suspended in the aqueous phase or attached reversibly and/or irreversibly to the solid matrix. The Smoluchowski population balance equation was used to model the process of particle aggregation and was coupled with the advection-dispersion-attachment equation to form a nonlinear transport model. Employing an efficient and precise solver for the population balance equation, coupled with an iterative solver for linear or nonlinear attachment equations, significantly reduced computational time, while maintaining its accuracy. The new numerical model was successfully applied to nanoparticle transport experimental data available in the literature. Conventional colloid transport models may prove to be inadequate in scenarios of high ionic strength where aggregation becomes a dominant process. The proposed model demonstrated exceptional performance under high ionic strength conditions, capturing various physical processes related to nanoparticle transport, including the particle-size-dependent dispersion. Neglecting the aggregation process and relying solely on conventional colloidal transport models, could potentially yield inaccurate results.