Computer Modeling of Liquid Crystal Hydrodynamics

Liquid crystals are highly anisotropic materials that can be described by a tensor which contains information on their average local orientation and the degree of ordering. The accurate modeling of liquid crystal devices, involves the consideration of the elastic interactions within the material, and between the liquid crystal and the walls of the containing cells, the influence of the electric fields governed by the Poisson equation, flexoelectric properties which link the electric fields and the elastic distortion, and flow, governed by the Navier-Stokes equations. All this constitutes a highly nonlinear system, involving the order tensor, the potential, pressure and velocity fields. We present here a finite element solution of this problem, adequate for the study of devices in three dimensions.