Dynamic Electrophoresis of an Oil Drop

We present a theoretical framework describing how the electrophoretic mobility of a weakly charged oil droplet in an aqueous electrolyte varies with frequency when the system is subjected to an oscillatory electric field. The surface charge of the droplet arises from the adsorption of electrolyte ions. Our analysis is based on a simplified form of the Baygents-Saville model, in which the interior of the droplet is assumed to contain no dissolved ions. In this approach, variations in interfacial tensions along the droplet surface, generated by the Marangoni effect, are explicitly included. From the formulation, we derive a general expression for the dynamic electrophoretic mobility of a charged spherical droplet, and, in addition, obtain concise analytical formulas applicable in the limit of small zeta potentials.