Numerical Investigation of Two-dimensional Flows of Nematic Liquid Crystals

We present a numerical method for solving two-dimensional nematic liquid crystal flows subject to a magnetic field. The dynamic equations of nematic liquid crystals are based on the Ericksen-Leslie dynamic theory. This theory accounts for fluid anisotropy and elastic stresses resulting from spatial distortion of the “director”, which is a vector field describing the local average molecular orientation. A numerical method for solving the governing equations for 2D flows has been formulated. The basic equations are solved by a finite difference technique based on the GENSMAC methodology introduced by Tomé and McKee (1994), Tomé et al. (2002). Channel flow was simulated and by using mesh refinement validated results are given. To demonstrate the capabilities of the numerical method, the flow of a nematic liquid crystal through a two-dimensional L-shaped channel was simulated. Results are presented for several values of the Reynolds and Ericksen numbers.