Numerical Simulation of Torsional Shear Flow between Concentric Parallel Disks of Nematic Liquid Crystals

Abstract

Numerical simulation of nematic liquid crystalline flow between rotating parallel disks has been performed using the Leslie-Ericksen continuum theory. It is assumed that the director lies in the shear plane and that the velocity profile is linear in the gap direction of the two disks. For a tumbling-type liquid crystal both the two-dimensional analysis and the Carlsson and Skarp model, in which molecular field elasticity in the radial direction is ignored, can predict step-like changes of the director orientation angles in the radial direction at high Ericksen numbers. The orientation angles are predicted to be discontinuous at tumbling regions for the Carlsson and Skarp model, whereas they are continuous for the two-dimensional analysis. A peculiar behavior observed in a light intensity experiment reported by Carlsson et al. That dark rings move from the disk periphery to its center is satisfactorily simulated by the two-dimensional analysis.