Modeling the Transport of Aggregating Nanoparticles in Porous Media

A novel mathematical model was developed to describe the transport of nanoparticles in
water saturated, homogeneous porous media with uniform flow. The model accounts for the simultaneous
migration and aggregation of nanoparticles. The nanoparticles are assumed to be found suspended in
the aqueous phase or attached reversibly or irreversibly onto the solid matrix. The Derjaguin-Landau-
Verwey-Overbeek theory was used to account for possible repulsive interactions between aggregates.
Nanoparticle aggregation was represented by the Smoluchowski population balance equation (PBE). Both
reaction-limited aggregation and diffusion-limited aggregation were considered. Particle-size dependent
dispersivity was accounted for. In order to overcome the substantial difficulties introduced by the PBE,
the governing coupled partial differential equations were solved by employing adaptive operator splitting
methods, which decoupled the reactive transport and aggregation into distinct physical processes. The
results from various model simulations showed that the transport of nanoparticles in porous media is
substantially different than the transport of conventional biocolloids. In particular, aggregation was
shown to either decrease or increase nanoparticle attachment onto the solid matrix, depending on
particle size, and to yield early or late breakthrough, respectively. Finally, useful conclusions were drawn
regarding possible erroneous results generated when aggregation, particle-size dependent dispersivity or
nanoparticle surface charges are neglected.