Electrohydrodynamic migration of charged droplets in an insulating fluid

Abstract

The motion of charged, conducting droplets present in an insulating fluid medium is analyzed under the action of an electric field, in microgravity. Previous analyses of this problem have considered the Maxwell stresses as the only driving force. In the present study, arguments from macroscopic thermodynamics and the molecular theory of surface tension are used to show that the surface tension gradients can be induced due to the variation of the electric potential on the interface. In the limit of Reynolds numbers small compared to unity, the terminal velocity of migration of the droplet is calculated under the combined action of the Maxwell stresses and the surface tension gradients. The results show that there are no surface tension gradients (i.e., no electric potential variation at the interface) in a case that is due to the convection of the surface charges, surface tension gradients do exist and tend to reduce the terminal velocity of the droplet. The shape of the droplet altered by the motion was also calculated, when the deformations from the speherical shape are small.