Electrophoresis of dumbbell-like colloidal particles

Abstract

A theoretical analysis of the dynamics of dumbbell-like colloidal particles moving by electrophoresis is presented. The dumbbell consists of two rigid spheres of arbitrary radii connected by an infinitesimally thin, rigid rod. Each sphere has a uniform but arbitrary zeta potential and is surrounded by a thin electrical double layer, as defined in the Helmholtz limit. The analysis utilizes the linearity of the governing electrokinetic equations to reduce the problem to subproblems for which the solutions already exist or are easily derived. Translational and angular velocities of the nonuniformly charged dumbbell are obtained by utilizing rigid-body mechanics, solutions for the electrophoresis of two freely suspended spheres and solutions for the components of the grand resistance matrix for two spheres translating and rotating with arbitrary velocities. The results, which depend linearly on the zeta potentials of the spheres, are presented in the form of four dimensionless functions, two to describe the translation, one to describe the rotation and one to locate the ”center“ of the dumbbell. These four functions depend only on the spheres' radii and the distance between the centers of the spheres. Sample calculations are presented to illustrate features of the electrophoretic motion of doublets that could be formed by heterocoagulation or bridging mechanisms. Estimates of angular velocities indicate that only modest fields might be required to align a suspension of doublets, even when the suspension undergoes shear flow.