A Note on the Electrophoresis of a Uniformly Charged Particle

Abstract

We examine the electrophoretic motion of a uniformly charged particle embedded in a varying electric field E . If R and -1 respectively denote the typical radius of curvature of the particle's surface and the usual Debye-Hckel screening length we assume that R -1 and allow variations of E over lengths of order at least R. Under these assumptions, this paper shows that it is unnecessary to calculate the total electric field in the electrolyte when determining the rigid-body motion of the particle. The well-known Smoluchowski solution is thereafter readily recovered. Finally, we pay special attention to orthotropic and uniformly charged particles and detail the case of a solid ellipsoid.