Thermal instability in a sample of nematic liquid crystal contained in a rotating annulus

Abstract

Continuum theory is employed to investigate the stability of a sample of nematic liquid crystal contained between two long, concentric, circular cylinders, rotating with constant angular velocity about the cylindrical axis, when subjected to a radial thermal gradient. We consider the arrangement in which the anisotropic axis of the material is initially uniformly aligned parallel to the axis of the cylinders. Using Galerkin and ortho-normalization methods, both positive and negative thermal gradient thresholds are predicted at which the onset of a convective instability is possible. The effects of angular velocity and the strength of an applied magnetic field are also examined. These theoretical results suggest an experimental possibility of observing the small wavenumber instability predicted by Velarde and Zuniga [1] in the Rayleigh-Bénard problem for nematics