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A note on the electrophoresis of a uniformly charged particle. (English) Zbl 1026.78007

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.

MSC:

78A35 Motion of charged particles
82C70 Transport processes in time-dependent statistical mechanics
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