Dielectric Response of a Charged Prolate Spheroid in an Electrolyte Solution

We derived the so-called standard set of electrokinetic equations in prolate spheroidal coordinates for all ionic strengths, zeta potentials, and applied electric field frequencies, with the assumption, however, that the particle's electrophoretic mobility is small. We subsequently solved these equations using finite differences methods. We show that the dipolar coefficient of a prolate spheroid reduces to that of a sphere in the corresponding limit, but deviates strongly from it when the eccentricity of the spheroid is large, for the same particle volume. We also verified that a previously published analytical theory (Chassagne and Bedeaux, J. Colloid Interface Sci., 326:240, 2008) is in good agreement with the numerical results for a large range of zeta potentials, ionic strengths, and frequencies.