Nonlinear electrophoresis of a charged polarizable liquid droplet

Abstract

A numerical study on the electrophoresis of a liquid droplet in an aqueous medium is made by considering the full set of governing equations based on the conservation principle. The surface of the droplet is considered to be charged, and the liquid filling the droplet is nonconducting. The dielectric polarization of the nonconducting droplet is also addressed in the present study. The impact of the surface conduction, double layer polarization, and relaxation effects creates a retardation on the electrophoresis. The occurrence of slip velocity at the droplet surface creates the surface conduction important even at weak electric field and a thin Debye layer for which the double layer polarization and relaxation may become small. The role of the surface conduction, which is measured through the Dukhin number, on the electrophoretic propulsion of the droplet is analyzed. Our numerical solutions for low charge density and thinner Debye length agree well with the existing simplified model and asymptotic analysis. However, a large discrepancy in mobility from these existing results occurs when the droplet size is bigger or droplet viscosity is lower than the suspended liquid medium. The variation of the electrophoretic mobility of a perfectly dielectric droplet as a function of the droplet viscosity, droplet size, and other electrokinetic parameters is analyzed. The dielectric polarization of the droplet and its impact on the electrophoresis are considered in the present work. The drag and the strength of the internal circulation are obtained.