Colloidal Hydrodynamics and Interfacial Effects

Abstract

Interfaces and boundaries play an important role in numerous soft matter and biological systems. Apart from direct interactions, the boundaries interact with suspended microparticles by altering the solvent flow field in their vicinity. Hydrodynamic interactions with walls and liquid interfaces may lead to a significant change in the particle dynamics in (partially) confined geometry. In these lecture notes we review the basic concepts related to colloidal hydrodynamics and discuss in more detail the effects of geometric confinement and the hydrodynamic boundary conditions which an interface imposes on a suspension of microparticles. We start with considering the general characteristic features of low-Reynolds-number flows, which are an inherent part of any colloidal system, and discuss the appropriate boundary conditions for various types of interfaces. We then proceed to develop a proper theoretical description of the friction-dominated, inertia-free dynamics of colloidal particles. To this end, we introduce the concept of hydrodynamic mobility, and analyse the solutions of the Stokes equations for a single spherical particle in the bulk and in the presence of a planar solid-fluid, and fluid-fluid interfaces. Both forced and phoretic motions are considered, with a particular emphasis on the principles of electrophoresis and the associated fluid flows. Moreover, we discuss the hydrodynamic interactions of self-propelling microswimmers, and the peculiar motion of bacteria attracted to slip and no-slip walls.