Dielectric-solid polarization at strong fields: Breakdown of Smoluchowski's electrophoresis formula

Abstract

We investigate the thin-double-layer electrophoretic drift of a uniformly charged dielectric particle, driven by an intense electric field comparable to the transverse Debye-layer field. Under these circumstances, solid polarization affects the leading-order electrokinetic transport in the fluid by inducing a nonuniform zeta-potential distribution. The resulting expression for the particle velocity is accordingly nonlinear in the applied field. The electrophoretic “mobility”—the ratio of this velocity and the applied field—depends upon two parameters, the first quantifying the surface-charge density, and the second constituting the product of the solid-to-liquid permittivity ratio and the scaled applied-field magnitude. At weak values of this product, solid polarization results in field-cubed deviations from Smoluchowski's velocity; at large values of it, the particle velocity is a slowly increasing function of the applied field, essentially varying with its logarithm. The transition between these two limits features a shift from zeta-potential proportionality to a charge-density proportionality. For all values of the two governing parameters solid polarization acts so as to reduce the electrophoretic velocity relative to the Smoluchowski limit.