Thermal instabilities in nematic liquid crystals

Continuum theory is employed to investigate the onset of a certain type of thermal instability when a sample of nematic liquid crystal confined between two horizontal flat plates is in the presence of a vertical temperature gradient. Two particularly simple experimental situations are examined, in one a parallel orientation is obtained at the plates and in the other the boundary orientation is perpendicular to the plates. Using a Fourier series method, an expression for determining the critical temperature gradient at which instability sets in is derived. In both cases, the analysis allows for the presence of an applied magnetic field.