Faraday waves on nematic liquid crystals: effect of Marangoni flow and thermal phase transition

The parametric instability in nematic liquid crystal layers has been studied using linear stability theory. Using material parameters of typical nematics, the neutral stability curve and dispersion relation of a system that presents critical subharmonic waves is obtained. The critical acceleration and wave number of the unstable stationary waves are discontinuous at the nematic-isotropic transition temperature and conform to similar sharp changes experienced by the viscosities and surface tension as a function of temperature. Due to Marangoni flow the curve of the critical acceleration as a function of excitation frequency exhibits a minimum. If the Marangoni flow is neglected and the dynamical viscosity is increased, a monotonously increasing dependence of the acceleration in terms of oscillation frequency is observed. A bicritical instability is reached for a layer thickness of a few millimeters. A well-defined subharmonic wave is attained when the thickness of the layer is further increased. The dispersion relation of these waves displays a discontinuous shift at high frequencies due to alternating secondary thresholds of Faraday waves. At negligible external forcing we determined the dispersion relationship of thermal surface waves.