Director orientation in nematic liquid crystals under orthogonal magnetic and electric fields

The orientation of the director in nematic liquid crystals can be driven by an electric or a magnetic field or a crossed combination of both. The dynamic response of nematics to crossed fields has been studied experimentally by Faetti et al. [1] and others in an attempt to measure quantities such as the rotational viscosity coefficient. We investigate the director orientation of an incompressible nematic liquid crystal under the influence of tilted, mutually perpendicular, constant magnetic and electric fields. We assume that flow effects are negligible and employ an averaging method to derive an equation describing the dynamic response of the average molecular tilt angle. Travelling wave solutions are calculated and we discuss criteria for their stability. Finally, we investigate director response when both or either of the applied fields are turned off with a view to gaining information about the characteristic times of relaxation. These analytical characteristic times are shown to depend on the various material properties.