A Kinetic-Hydrodynamic Simulation of Liquid Crystalline Polymers Under Plane Shear Flow: 1+2 Dimensional Case

Abstract

We consider the extended Doi model for nematic liquid crystalline polymers in-planar shear flow, which is inhomogeneous in shear direction. We study the formation of microstructure and the dynamics of defects. We discretize the Fokker-Plank equation using the spherical harmonic spectral method. Five in-plane flow modes and eight out-of-plane flow modes are replicated in our simulations. In order to demonstrate the validity of our method in simulating liquid crystal dynamics, we replicated weak shear limit results and detected defects. We also demonstrate numerically that the Bingham closure model, which maintains energy dissipation, is a reliable closure model.