Transient electrophoresis of a conducting spherical particle embedded in an electrolyte-saturated Brinkman medium

In this study, the time-dependent electrophoretic motion of a conducting spherical particle embedded in an arbitrary electrolyte solution saturated porous medium is investigated. The porous medium is uniformly charged and the embedded hard particle is charged with constant $$ -potential or constant surface charge density. The unsteady modified Brinkman equation with an electric force term, which governs the fluid velocity field, is used to model the porous medium and is solved by Laplace's transform technique. An analytical expression for the electrophoretic velocity of the spherical particle is obtained in Laplace transform domain as a function of the relevant parameters, and its inversion is obtained through numerical techniques. Also, in this study, the steady-state electrophoretic velocity is obtained analytically as linear functions of  $$ -potential (or surface density charge) and the fixed charge density. The steady-state electrophoretic velocity is displayed graphically for various relevant parameters and compered with the available data in the literature. Also, the numerical values of the transient electrophoretic velocity are plotted versus the nondimensional elapsed time and discussed for different values of the Debye length parameter, density ratio, permeability of the porous medium, and for high and nonconducting particles.