Domain structure of a nematic-liquid-crystal layer in low-frequency Couette flow

The spatially periodic structure arising in a homeotropic nematic-liquid-crystal (NLC) layer in low-frequency Couette flow is described theoretically. The analysis of this phenomenon is based on the hydrodynamic equations for NLCs, from which a self-consistent system of equations is selected for perturbations of hydrodynamic variables: the steady-state angle of the molecule rotation, the liquid flow, and the velocity of oscillating vortex flows. The formation of the periodic structure is explained by the phase delay of the velocities of the vortex oscillating flows forming in the deformed structure with respect to the shear velocity in the Couette flow. It is shown that at low frequencies this difference in the velocities is caused by the orientational waves near the layer boundaries. In the case of fixed orientation of molecules at the boundaries, the dependence of the threshold shear amplitude on the frequency and layer thickness is given by the relation u_th ～ (ωh²)^?1/4. The influence of the conditions for the molecule orientation at the layer boundaries on the above phenomenon is analyzed.