The prediction of electrokinetic phenomena within multiparticle systems: II. Sedimentation potential

Abstract

A geometric cell model for a concentrated suspension in aqueous electrolyte of identical charged dielectric colloidal spheres was employed in an earlier paper in a theory of electrophoresis and electroosmosis. The same model is used here to study the related phenomenon of the sedimentation of such a suspension. The theory is restricted to small surface potentials (in the linear Debye-Huckel range) and to values of κ a ≳ 10, where a is the particle radius and 1/κ is the double layer thickness. The distortion from spherical symmetry in the diffuse layer charge density within a cell (the relaxation effect) due to the sedimentation is described by a simple approximation. A steady state “streaming potential” condition of zero net current flow through a cell and also Henry's condition of zero normal component of current flow at a particle surface are used to calculate the induced dipole moment, the induced sedimentation electric field and the sedimentation velocity. For very dilute suspensions and thin double layers, these calculated quantities tend towards the classic results of Smoluchowski, as required. In the limiting case of a single particle the value obtained for the sedimentation velocity lies between those calculated by Smoluchowski and by Booth. The predictions for the sedimentation velocity in concentrated suspensions are consistent with the rather limited experimental data available in the literature.