Streaming-potential phenomena in the thin-Debye-layer limit. Part 3. Shear-induced electroviscous repulsion

Abstract

We employ the moderate-Péclet-number macroscale model developed in part 2 of this sequence (Schnitzer et al., J. Fluid Mech., vol. 704, 2012, pp. 109–136) towards the calculation of electroviscous forces on charged solid particles engendered by an imposed relative motion between these particles and the electrolyte solution in which they are suspended. In particular, we are interested in the kinematic irreversibility of these forces, stemming from the diffusio-osmotic slip which accompanies the salt-concentration polarisation induced by that imposed motion. We illustrate the electroviscous irreversibility using two prototypic problems, one involving side-by-side sedimentation of two spherical particles, and the other involving a force-free spherical particle suspended in the vicinity of a planar wall and exposed to a simple shear flow. We focus on the pertinent limit of near-contact configurations, where use of lubrication approximations provides closed-form expressions for the leading-order lateral repulsion. In this approximation scheme, the need to solve the advection–diffusion equation governing the salt-concentration polarisation is circumvented.