Nonlinear interactions in electrophoresis of ideally polarizable particles

Abstract

In the classical analysis of electrophoresis, particle motion is a consequence of the interfacial fluid slip that arises inside the ionic charge cloud (or Debye screening layer) surrounding the particle surface when an external field is applied. Under the assumptions of thin Debye layers, weak applied fields, and zero polarizability, it can be shown that the electrophoretic velocity of a collection of particles with identical zeta potential is the same as that of an isolated particle, unchanged by interactions [L. D. Reed and F. A. Morrison, “Hydrodynamic interaction in electrophoresis,” J. Colloid Interface Sci. 54, 117 (1976)]. When some of these assumptions are relaxed, nonlinear effects may also arise and result in relative motions. First, the perturbation of the external field around the particles creates field gradients, which may result in nonzero dielectrophoretic forces due to Maxwell stresses in the fluid. In addition, if the particles are able to polarize, they can acquire a nonuniform surface charge, and the action of the field on the dipolar charge clouds surrounding them drives disturbance flows in the fluid, causing relative motions by induced-charge electrophoresis. These two nonlinear effects are analyzed in detail in the prototypical case of two equal-sized ideally polarizable spheres carrying no net charge, using accurate boundary-element simulations, along with asymptotic calculations by the method of twin multipole expansions and the method of reflections. It is found that both types of interactions result in significant relative motions and can be either attractive or repulsive depending on the configuration of the spheres.