A Kinetic-Hydrodynamic Simulation of Liquid Crystalline Polymers Under Plane Shear Flow: 1+2 Dimensional Case (Communications in Computational Physics, 2008)
We consider the extended Doi model for nematic liquid crystalline polymersin-planar shear flow, which is inhomogeneous in shear direction. We study the formation of microstructure and the dynamics of defects. We discretize the Fokker-Plankequation using the spherical harmonic spectral method. Five in-plane flow modes andeight 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 replicatedweak shear limit results and detected defects. We also demonstrate numerically thatthe Bingham closure model, which maintains energy dissipation, is a reliable closuremodel.