Electro-osmotic flows over highly polarizable dielectric surfaces

A thin-Debye-layer macroscale model is developed and analyzed for electrokinetic flows about dielectric surfaces, wherein solid polarization modifies the zeta-potential distribution. The harmonic electric potential within the solid is governed by a nonlinear boundary condition, which constitutes a generalization of the linear Robin-type condition of Yossifon et al. [Phys. Fluids 19, 068105 (2007)] to voltages comparable with the thermal scale. The resulting polarization model is demonstrated in the classical context of spherical-particle electrophoresis, where the electrophoretic mobility—now a function of applied-field magnitude and solid permittivity—is evaluated using both eigenfunction series expansions and asymptotic approximations. For strong polarization, the mobility saturates at a field-dependent value which is lower than the comparable Smoluchowski slope. At strongly applied fields, the mobility diminishes at a rate that corresponds to a logarithmic increase of particle velocity with applied-field magnitude.