Flow of an anisotropic dielectric liquid in a diverging channel

Steady plane flows of an electrically anisotropic polarizable liquid in a diverging metallic channel are studied. One of the channel walls is grounded while the other is kept at a high electric potential. The electrical anisotropy of the liquid is described by a unit vector whose direction is determined by a nonequilibrium relaxation equation. A dependence of the dielectric polarization on the electric field strength and anisotropy vector is determined by an equilibrium relationship. Such a model may correspond to a suspension of polarizable fibers in a dielectric liquid. The exact self-similar solution to the formulated governing equations is obtained. Distributions of the liquid velocity, pressure, polarization, anisotropy vector, and electric field in the channel are found and examined. As with the vanishing electric field, there is a critical value of the Reynolds number at which the reverse flow starts at the channel walls. The dependence of the critical Reynolds number on the liquid properties and channel characteristics is found. In particular, the presence of a sufficiently strong electric field between the channel walls leads to a rise in the critical Reynolds number. Thus, the flow of anisotropic dielectric liquid in a diverging channel can be controlled by electrical means.