Spreading of a liquid over a plane rigid substrate in an electric field

Abstract

The influence of an electric field on spreading of a thin conducting liquid layer over a plane rigid substrate is investigated theoretically. The conductivity of the liquid is assumed to be so low that the effect of the magnetic field of the currents generated in the liquid under the action of the electric field can be neglected. The spreading is assumed to be so slow that the quasi-steady approximation can be used to calculate the electric field strength which can be considered to be equal to zero inside the liquid. Equations that describe variations in the layer shape are obtained in the lubrication theory approximation. The general formulation of the problem is considered. The solution of the problem is obtained in parametric form when the effect of the gravity force and the surface tension can be neglected. Variations in the layer thickness along the substrate are so smooth that the charge distribution over its surface can be assumed to be the same as that over the substrate surface in the absence of the liquid.