Numerical simulation of deep bed filtration in electrically charged porous media

We study the inertial capture of fine particles in laminar flow through a granular filter by means of computational fluid dynamics with consideration of electrostatic interactions. During their flow through the filter, the suspended particles are subjected to an attractive electrostatic interaction with the filter grains, which is modeled by means of the Yukawa potential, while gravity is neglected in the simulations. We find that the fraction of uncaptured particles reaching the end of the filter undergoes a phase transition at a porosity-dependent critical Stokes number Stc∼ϵ−β, where β=4.880 ± 0.015. Above this critical Stokes number, nearly all particles are captured. Moreover, we find that the amount of suspended particles in the medium decays exponentially with downstream flow distance in the filter and propose a phase diagram for the filter efficiency. Our results indicate that, in the presence of the Yukawa potential, the filter efficiency decreases with the intensity of the electrostatic interaction, A. This result is consistent with the observed decrease in the penetration length of the particles with increasing A and opens applications for improving filter efficiency through the design of electrically charged filter structures.