A theoretical investigation of Benard-Couette instabilities in nematic liquid crystals

Abstract

Employing continuum theory, this paper investigates the onset of homogeneous and roll instabilities in Couette flow of a nematic liquid crystal when a radial temperature gradient is present. The arrangement considered is that in which the anisotropic axis of the liquid crystal is initially aligned parallel to the axis of the circular cylinders. Using an orthonormalisation method, the authors present accurate numerical results for the shear rate thresholds as a function of the applied thermal gradient. It is shown that a positive thermal gradient reduces the roll threshold but that a thermal gradient of either sign has no effect on the homogeneous threshold. They therefore predict a value phi T for the radial temperature gradient at which there is a transition from a homogeneous to a roll-type instability. In addition they demonstrate the important effect rotation has through the centrifugal force.