The prediction of electrokinetic phenomena within multiparticle systems. I. Electrophoresis and electroosmosis

Henry's classic theory for the electrophoresis of a single isolated sphere is extended analytically to cover the more practical problem of the electrophoresis of a swarm of identical, dielectric, spherical particles. The effects of interaction of the individual particles and their associated electric fields are taken into explicit account by employing a fundamental cell-model representation which is known to provide good predictions for the motion of a swarm of spheres within a fluid in the absence of electrical effects. For thin double layers, the electrophoretic velocity of (or the electroosmotic velocity within) a swarm of identical dielectric spheres is shown to be invariant, practically speaking, with respect to the void fraction of the swarm. However, as the double layer thickness increases the electrophoretic (electroosmotic) velocity decreases sharply and becomes strongly dependent on the void fraction. The computed results provide theoretical justification for Smoluchowski's widely quoted approximate result for electroosmotic flow within porous media of arbitrary pore geometry.