(271j) Nonlinear Electrophoretic Velocity of a Spherical Colloidal Particle

Electrophoresis is the motion of a charged colloidal particle in an electrolyte under the influence of an applied electric field. The electrophoretic velocity of a spherical particle depends on the dimensionless electric field strength, defined as the ratio of the product of the applied electric field magnitude and particle radius, to the thermal voltage. Traditionally, electrophoresis has been studied in the weak-field regime. Here, we develop a numerical scheme to compute the electrophoretic velocity of a spherical, rigid, dielectric particle, of fixed surface charge density over a wide range of applied fields. Our approach is based on a spectral element method algorithm and the Galerkin approximation to solve the full nonlinear electrokinetic equations. For moderately-charged particles, our results show that the electrophoretic velocity is linear in field strength at weak fields, and its dependence on the ratio of the Debye length to particle radius is in agreement with Henry’s formula. As the electric field strength increases, the nonlinear contribution to the electrophoretic velocity becomes prominent, and the onset of this behavior depends on the Debye length. However, at strong fields the electrophoretic velocity again becomes linear in field strength, approaching the Hückel limit of electrophoresis in a dielectric medium. For highly-charged particles, our computations are in good agreement with recent experimental results. Further, we confirm the transition of the nonlinear contribution to the electrophoretic mobility from retardation to enhancement as the electric field increases, as predicted by recent asymptotic analyses in the thin-Debye-layer limit.