Electrophoresis of a dielectric droplet with constant surface charge density

Electrophoresis of a dielectric fluid droplet with constant surface charge density is investigated theoretically in this study. A pseudo-spectral method based on Chebyshev polynomials is adopted to solve the governing electrokinetic equations. It is found, among other things, that the larger the electrolyte strength in the ambient solution is, the slower the droplet moves in general. This is due to the strong screening effect of the large amount of indifferent counterions in the neighborhood of the droplet, with no reinforcement of potential-determining ions adsorbing to the droplet surface. The droplet comes to a complete halt eventually. Critical points are discovered for highly charged droplets, at which the droplet surface becomes immobile and the interior fluid stops recirculating. The droplet moves like a rigid particle with constant mobility regardless of its viscosity, a situation referred to as the "solidification phenomenon." The deadlock between the spinning motions on the charged droplet surface induced by the electric driving force and the hydrodynamic driving force respectively is responsible for this peculiar phenomenon. This is also observed for a dielectric droplet with constant surface electric potential. We demonstrate here that it occurs in the constant surface charge density situation as well.