A note on the electrophoresis of a uniformly charged particle

We examine the electrophoretic motion of a uniformly charged particle embedded in a varying electric field E-infinity. If R and kappa(-1) respectively denote the typical radius of curvature of the particle's surface and the usual Debye-Huckel screening length we assume that R >> kappa(-1) and allow variations of E-infinity 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.