Interaction between two spheres under a uniform electric field in a porous medium - Yao, Xin (2022)
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 (αa<50).