Commun. Comput. Phys.,
A Kinetic-Hydrodynamic Simulation of Liquid Crystalline Polymers Under Plane Shear Flow: 1+2 Dimensional Case
Guanghua Ji 1, Haijun Yu 2, Pingwen Zhang 3*1 Laboratory of Mathematics and Complex Systems, Ministry of Education and School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China.
2 School of Mathematical Sciences and CCSE, Peking University, Beijing 100871, China.
3 LMAM, School of Mathematical Sciences and CCSE, Peking University, Beijing 100871, China.
Received 4 March 2008; Accepted (in revised version) 20 July 2008
Available online 9 September 2008
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.
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PACS: 61.30.Dk, 61.30.Jf, 64.70.mf
Key words: Non-local potential, anchoring condition, spherical harmonic, kinetic-hydrodynamic, defects, Bingham closure.
Email: email@example.com (G. Ji), firstname.lastname@example.org (P. Zhang)