Interaction between two spheres under a uniform electric field in a porous medium

We present a systematic procedure to analyze the interaction between two spheres under a uniform electric field in a porous medium. We solve Laplace's equation in bispherical coordinates to obtain electric potential distribution. Such electric potential is utilized to obtain the slip velocities on the two spheres and the flow field around them is solved based on stream function. The solution is solved semi-analytically by considering geometric and electric parameters. The detailed flow field in the vicinity of the two spheres is investigated and our results reveal that the sphere interaction is dependent on the separation distance, sphere radii, zeta potential and normalized radius with respect to permeability. The increase of normalized radius with respect to permeability reduces the interaction between the two spheres. This is particularly prominent when normalized radius with respect to permeability is relatively small (alpha a < 50). (C) 2020 Elsevier Ltd. All rights reserved.

Automated summary

This study presents a systematic procedure to analyze the interaction between two spheres in a porous medium under a uniform electric field. The results show that the sphere interaction is dependent on parameters such as separation distance, sphere radii, zeta potential, and normalized radius with respect to permeability. An increase in the normalized radius with respect to permeability reduces the interaction between the two spheres, especially when the normalized radius is relatively small (αa < 50).