Magnetohydrodynamic Instabilities in Nematic Liquid Crystals

Abstract

This paper discusses two problems in which surface alignment, shear flow and a magnetic field normal to the plane of shear compete to produce instabilities in a nematic. The first is that described by Pieranski and Guyon,^1,2 where the anisotropic axis is initially everywhere normal to the shear plane, and the flow causes a change of orientation at a critical shear rate. In the second, the anisotropic axis is at first in the plane of shear, and the magnetic field induces the instability at a critical field strength. Solutions of the continuum equations for infinitesimal, homogeneous perturbations to the initial flow are given, the analysis proving to berather similar in both cases. Of interest is the possibility of a transition from one homogeneous instability to another, the change being accompanied by the appearance of a net transverse flux of fluid.