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∞. If R and κ^-1 respectively denote the typical radius of curvature of the particle's surface and the usual Debye-Htickel screening length we assume that R ≫ κ^-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.