Flow of an Anisotropic Dielectric Liquid in a Diverging Channel in a Strong Transverse Electric Field

Abstract

A steady plane flow of an anisotropically polarizable liquid in a channel with nonparallel walls was considered. One of the walls was grounded, and the other was under a high electric potential. The polarization anisotropy was described in terms of a unit vector whose direction was determined by a relaxation equation. The dependence of the polarization of the liquid on the strength of the electric field and the anisotropy vector was specified using an equilibrium relation. Such a model can describe, for example, a suspension of anisotropically polarizable particles in a highly insulating liquid. The velocity, pressure, polarization, anisotropy vector, and electric field distributions in the liquid were determined and investigated. It was shown that, at some critical Reynolds number, backflows are initiated near the channel walls. The dependence of the critical Reynolds number on the diverging angle of the channel and on the properties of a liquid in a strong electric field was determined. The applied electric field increases the critical Reynolds number, which provides a means of controlling the regime of the considered flow using electrical methods.