Multiscale modeling of colloidal dynamics in porous media including aggregation and deposition

- Effect of colloidal aggregation on the transport in porous media.
- Effective coefficients obtained through periodic homogenization.
- Effect of a nonlinear dynamic blocking function on the deposition.

We investigate the influence of aggregation and deposition on the colloidal dynamics in a saturated porous medium. On the pore scale, the aggregation of colloids is modeled by the Smoluchowski equation. Essentially, the colloidal mass splits into different size clusters and we treat clusters as different species involved in a diffusion-reaction mechanism. This modeling procedure allows for different material properties to be varied between the different species, specifically the diffusion rate, which changes due to size as described by the Stokes-Einstein relation, and the deposition rate. The periodic homogenization procedure is applied to obtain a macroscopic model. The resulting model is illustrated by numerical computations that capture the colloidal transport with and without aggregation.