Unsteady electrophoresis of a dielectric cylindrical particle suspended in porous medium

Abstract

The starting electrophoresis of a dielectric cylindrical particle in an electrolyte solution saturated in a charged porous medium after the sudden application of an external electric field is investigated semi-theoretically. For the case of a thin electric double layer, the apparent slip velocity caused by the time-dependent electroosmotic flow of the electrolyte solution in the Brinkman medium along a charged plane is used as the boundary condition at the particle surface to drive the dynamic electrophoretic motion. Analytical formulas, for the time-dependent electrophoretic velocity of the cylindrical particle in the Laplace transform, have been obtained for both axially and transversely when the uniform electric fields are imposed. They can also be linearly superimposed for an arbitrarily oriented relative to the electric field. Results for the electrophoresis mobility and acceleration are presented as functions of the dimensionless elapsed time, the particle-to-medium density ratio, the electrokinetic particle radius, and the permeability parameter of the porous medium. In general, the electrophoretic velocity with the dimensionless time for a cylindrical particle is weaker than for a spherical one due to its smaller specific surface area. The growth of the electrophoretic mobility with the time scale is more slower for high permeability, and the effect of the relaxation time for unsteady electrophoresis is found to be negligible, regardless of the thickness of the double layer, the relative mass density or the permeability of the medium.