Electrophoretic Mobility of a Dilute, Highly Charged "Soft" Spherical Particle in a Charged Hydrogel

In this paper, numerical modeling studies are carried out on the electrophoretic mobility of a dilute, highly charged "soft" spherical particle in a hard hydrogel subjected to a weak, constant, external electric field. The particle contains a solid core with either a uniform charge density or "zeta" potential on its surface. Outside of this lies a charged gel layer of uniform thickness, composition, and charge density. The present work extends previous studies by accounting for the "relaxation effect", or distortion of the charge distribution in the vicinity of the model particle due to the imposition of an external electric and/or flow field. The particle gel layer and ambient hydrogel are modeled as porous Brinkman media. The (steady state) electrodynamic problem is solved at the level of the Poisson equation. Applications emphasize the influence of the relaxation effect and hydrogel charge density on the electrophoretic mobility.