Electrohydrodynamic wavelengths and response rates for a nematic liquid crystal

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Abstract
The two-dimensional boundary-value problem associated with hydrodynamic effects in a dc electric field has been solved under the assumption of dynamic distortions. The time-dependent terms included in the equations of motion are viscous forces and torques as well as displacement currents. Inertial effects are ignored so that the calculations are performed in the zero-Reynold's-number limit. It is found that above a critical voltage, there is a band of domain wavelengths which grow exponentially with time. The fastest growing solution is identified with the physical solution. The domain wavelength and rise rates are calculated as a function of voltage, thickness, and relevant material constants. In particular it is found that turn-on rates for the Williams-domain mode are bounded by the space-charge relaxation time. These calculations are in good agreement with experiment for methoxybenzilidene-butylaniline (MBBA). It is found that the difference between a domain mode and a field effect can be correctly predicted on the basis of the dynamic analysis.