Transient behaviors of molecular orientation field of nematic liquid crystal under shear flows between concentric cylinders

Abstract

Transient behaviors of molecular orientation field of nematic liquid crystal (4-n-4’-octylcyanobiphenyl) under shear flows between concentric cylinders have been numerically investigated using the Leslie-Ericksen continuum theory in which the molecular orientation is represented with a unit vector, called the director. As well as the rotation speed of an inner cylinder, the director anchoring conditions at the inner and outer cylinders are chosen as simulation parameters to obtain four different cases of director initial profiles, which are homeotropic, hybrid, planar, and twist cases. After the imposition of the shear flow, the director start rotating within the shear plane, increasing the curvature energy of the director field. When the energy exceeds a certain critical value, the director start escaping from the shear plane, called the out-of-plane behavior. Because the escaping direction (i.e., either +z or -z directions) is the stochastic choice, the director field is randomly separated into the positive and negative out-of-plane regions. Then, the spatially distributed two out-of-plane regions are transformed into line defect structures. The spatial patterns of the out-of-plane regions and the line defect structures strongly depends on the director anchoring conditions, and no patterns are found for the twist case. The evolutions of torques of the inner cylinder is also estimated from the simulation results for four cases, and the oscillatory behavior of the torque is found for the homeotropic case.