The influence of hydrodynamic slip on the electrophoretic mobility of a spherical colloidal particle

Abstract

Recent theoretical studies have suggested a significant enhancement in electro-osmotic flows over hydrodynamically slipping surfaces, and experiments have indeed measured O(1) enhancements. In this paper, we investigate whether an equivalent effect occurs in the electrophoretic motion of a colloidal particle whose surface exhibits hydrodynamic slip. To this end, we compute the electrophoretic mobility of a uniformly charged spherical particle with slip length λ as a function of the zeta (or surface) potential of the particle ζ and diffuse-layer thickness κ−1. In the case of a thick diffuse layer, κa⪡1 (where a is the particle size), simple arguments show that slip does lead to an O(1) enhancement in the mobility, owing to the reduced viscous drag on the particle. On the other hand, for a thin-diffuse layer κa⪢1, the situation is more complicated. A detailed asymptotic analysis, following the method of O’Brien [J. Colloid Interface Sci. 92, 204 (1983)], reveals that an O(κλ) increase in the mobility occurs at low-to-moderate zeta potentials (with ζ measured on the scale of thermal voltage kBT/e≈25 mV). However, as ζ is further increased, the mobility decreases and ultimately becomes independent of the slip length—the enhancement is lost—which is due to the importance of nonuniform surface conduction within the thin-diffuse layer, at large ζ and large, but finite, κa. Our asymptotic calculations for thick and thin-diffuse layers are corroborated and bridged by computation of the mobility from the numerical solution of the full electrokinetic equations (using the method of O’Brien and White [J. Chem. Soc., Faraday Trans. 2 74, 1607 (1978)]). In summary, then, we demonstrate that hydrodynamic slip can indeed produce an enhancement in the electrophoretic mobility; however, such enhancements will not be as dramatic as the previously studied κa→∞ limit would suggest. Importantly, this conclusion applies not only to electrophoresis but also to electro-osmosis over highly charged surfaces, wherein any inhomogeneities (e.g., due to curvature, roughness, charge patterning, or a variation in slip length) will drive nonuniform surface conduction, which prevents the significant slip-driven flow enhancements predicted for a uniform highly charged surface.