Particle self-diffusiophoresis near solid walls and interfaces

Abstract

The purpose of this paper is to explore, from a theoretical viewpoint, the mechanisms whereby locomotion of low-Reynolds-number organisms and particles is affected by the presence of nearby no-slip surfaces and free capillary surfaces. First, we explore some simple models of the unsteady dynamics of low- Reynolds-number swimmers near a no-slip wall and driven by an arbitrarily imposed tangential surface slip. Next, the self-diffusiophoresis of a class of two-faced Janus particles propelled by the production of gradients in the concentration of a solute diffusing into a surrounding fluid at zero Reynolds and P´eclet numbers is studied, both in free space and near a no-slip wall. The added difficulty now is that the tangential slip is not arbitrarily chosen but is given by the solution of a separate boundary value problem for the solute concentration. Finally, an analysis of a model system is used to identify a mechanism whereby a non-self-propelling swimmer can harness the effects of surface tension and deformability of a nearby free surface to propel itself along it. The challenge here is that it is a free boundary problem requiring determination of the surface shape as part of the solution.