Sellier, A. A note on the electrophoresis of a uniformly charged particle. (English) Zbl 1026.78007 Q. J. Mech. Appl. Math. 55, No. 4, 561-572 (2002). Summary: We examine the electrophoretic motion of a uniformly charged particle embedded in a varying electric field \(\mathbb{E}_\infty\). If \(R\) and \(\kappa^{-1}\) respectively denote the typical radius of curvature of the particle’s surface and the usual Debye-Hückel screening length we assume that \(R\gg\kappa^{-1}\) and allow variations of \(\mathbb{E}_\infty\) 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. Cited in 1 Document MSC: 78A35 Motion of charged particles 82C70 Transport processes in time-dependent statistical mechanics Keywords:electrolyte; Smoluchowski solution PDFBibTeX XMLCite \textit{A. Sellier}, Q. J. Mech. Appl. Math. 55, No. 4, 561--572 (2002; Zbl 1026.78007) Full Text: DOI