Electrokinetic Effects with Small Drops and Bubbles

Electrokinetic effects with drops and bubbles are studied. We first examine the electrophoresis of drops and bubbles, computing the electrophoretic mobility as a function of the zeta-potential and several other parameters. We find drops and bubbles to be electrophoretically distinct from particles; e.g., conducting drops do not always migrate in the direction that would be anticipated from the sign of their surface charge. The analysis shows the sense of the migration is dictated by the net electrochemical stress acting along the interface and the zeta-potential alone is not sufficient to characterize the surface. For similar reasons, large inviscid spheres tend to remain stationary at modest zeta-potentials and, in contrast to rigid particles, their mobility is actually enhanced by polarization of the double layer. Further, we have uncovered conditions for which the mobility of nonconducting drops is insensitive to the interior viscosity. Next we examine the influence of partial dissociation of ionogenic solutes on electrophoresis, with a view toward understanding, how, and under what conditions, dissociation -association alters the electrokinetics. We find generally that mass-action resists polarization of the diffuse ion cloud and, so, is quantitatively important where double layer polarization and relaxation would otherwise prevail. Mass -action can reduce the mobility of a conducting drop by an order of magnitude, and sizeable decreases (50% and more) in drop mobility are even found at zeta -potentials below 50 mV. Rigid particles are affected less dramatically and quantitative effects rarely exceed 10%; particles are indifferent to partial ionization unless the zeta-potential is high (above ca. 100mV) and akappa > 1. Finally the influence of diffuse charge layers on electrically-induced drop deformations is investigated by revisiting the archetypal problem in electrohydrodynamics: the circulation produced in a drop by an electric field. Singular perturbation methods are employed to constuct a coherent physicochemical description of the regions proximal to the drop surface, including the space charge distribution. The electrokinetic model employed yields predictions of drop deformation consistent with the lumped parameter theory known as the 'leaky dielectric.' Previously it had been thought the leaky dielectric failed to account for the effects of diffuse charge layers on electrohydrodynamic flows.