Abstract

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.

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