Analysis of thermal instabilities in a layer of nematic liquid crystal with oblique orientation at the boundaries

Utilises continuum theory to investigate the occurrence of thermal instabilities when a vertical temperature gradient is applied across a sample of nematic liquid crystal confined between two horizontal flat plates, the molecules being uniformly aligned obliquely with respect to the plates. Two distinct types of roll solution are examined, one being independent of the direction perpendicular to the vertical planes containing the molecules initially and the other independent of the horizontal direction in these planes. Both a Fourier series method and an orthonormalisation method are employed to obtain the critical values of the temperature gradient at which the initial configuration becomes unstable. It is shown that the type of roll instability likely to occur depends on whether heating is from above or below. The variation of the critical temperature gradient with the boundary orientation of the molecules is also investigated.