Electrophoresis of a soft charged particle in a sparsely packed bed

In this study, the migration of a single charged spherical hydrogel (polyelectrolyte) micro/nanoparticle is considered in an electrolyte solvent medium where several identical micro/nanoparticles are suspended. Each particle can be modeled as a charged linearly elastic fibrous spherical solid saturated with a Newtonian electrolyte. In this study, a new analytical approach is proposed for finding the steady response of the soft charged hydrogel sphere to a DC electric field using the perturbation method. It is possible to obtain a closed form for the electrophoretic mobility of a single sphere within a sparsely packed sphere bed for a wide range of electric double layer thickness. The response of each hydrogel sphere toward the external fields includes both the particle translation and infinitesimal deformation in the polymeric skeleton of a hydrogel sphere. The hydrodynamics inside a sphere and the corresponding strain of the solid phase are studied by adopting field equations from the theory of biphasic mixtures. This study highlights that factors like fixed charge density, dielectric constants, elasticity coeffcients of polymer skeleton influence the mobility and deformation of the particle. This study has a close relevance to an electric field induced drug delivery in biological media.