Electrokinetic Lift of a Sphere Moving in Slow Shear Flow Parallel to a Wall: II. Theory

Abstract

Any flow in the counterion cloud next to a charged interface causes convection of charge. Conservation of charge requires a streaming potential which exerts an electrical stress on the interface. For a sphere moving near a plane wall, the net electrokinetic force that is produced can be significant at separations equal to many Debye lengths and is always repulsive, regardless of the relative sign of charge on each of the two surfaces. The electrokinetic lift on a sphere, freely rotating and translating in linear shear flow along a plane wall, was calculated numericaly assuming that the zeta potentials of the sphere and the plate are equal and that the Debye length is sufficiently small that the space charge density is not perturbed by flow. Compared to earlier models [S. G. Bike and D. C. Prieve, J. Colloid Interface Sci. 136, 95 (1990)], we have relaxed the lubrication approximation and have accounted more fully for the hydrodynamics, including rotation as well as translation. Although the predictions are in qualitative agreement with all of the experimental observations in Part I, the magnitude of the predictions is too weak to produce the effects observed. We suspect that the Debye length in our experiments is not small enough to allow the perturbation of the counterion cloud caused by flow to be neglected.