We employ the moderate-P´eclet-number macroscale model developed in part 2 of this sequence
(Schnitzer, Frankel & Yariv, 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 upon the pertinent limit
of near-contact configurations, where use of lubrication approximations provides closedform
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.