Numerical Simulations of Shear Flows of a Tumbling Liquid Crystal between Concentric Cylinders

Abstract

Numerical simulations of shear flows of a tumbling-type nematic liquid crystal (4-Octyl-4'-cyanobiphenyl) between concentric cylinders have been performed using the Leslie-Ericksen continuum theory. The shear flow is imposed on the liquid crystal by rotating the inner cylinder. In the Leslie-Ericksen theory, the local averaged orientation of the rodlike liquid crystalline molecules is represented with a unit vector called the director, and small perturbations are added on the initial director field to obtain the director escape from the shear plane. Depending on the curvature of the flow geometry and the shear rate and also on the perturbations, four kinds of director behaviors emerge, which are the in-plane, non-twisted out-of-plane, 2π-twisted out-of-plane, and periodic director behaviors. Finally, we discuss the probability of the emergence of the director behaviors.