Band instability under shear in polymer liquid crystals

Abstract
We study a shear flow instability in a liquid crystal aligned by the initial flow. A periodic distortion of the director and the velocity field in the plane perpendicular to the flow and the velocity gradient is investigated. We obtain the critical shear rate and the value of the critical wave vector at threshold. We discuss the instability in the case of a conventional liquid crystal and a polymer liquid crystal. Good qualitative agreement with experiment is found and the theory clarifies the observation of banded textures created in many polymer liquid crystals by shear flow.