Modeling and Experimental Validation of Aggregating Nanoparticle Transport with Nonlinear Attachment

A conceptual mathematical model was designed to simulate the transport behavior of migrating nanoparticles in homogeneous, water-saturated, one-dimensional porous media. The model accounts for nanoparticle collisions that lead to aggregation and considers nanoparticles as either reversibly or irreversibly attached to the solid matrix of the porous medium or suspended in the aqueous phase. These attached particles can influence further deposition by promoting or hindering it, leading to either ripening or blocking phenomena. The aggregation process is described using the Smoluchowski Population Balance Equation (PBE), which is coupled with the advection-dispersion-attachment equation (ADA), resulting in a system of partial differential equations governing nanoparticle migration in porous media. An efficient finite volume solver was utilized to solve the PBE, optimizing computational efficiency by reducing the number of equations while maintaining accuracy. The model was validated against experimental nanoparticle transport data available in the literature and successfully simulated experimental data exhibiting nonlinear attachment behaviors, such as ripening and blocking, demonstrating its ability to capture the multiple physical mechanisms governing nanoparticle transport