Zhenlu Cui*, Jianbing Su and Xiaoming Zeng Pages 349 - 353 ( 5 )
Background: Extensive theoretical efforts in active nematics have been carried out in the past decade, but the effects of initial and boundary conditions are scarcely studied. Most studies only consider either tangential or normal anchoring boundary conditions. However, it is well known that boundary effects and confinement can play a very important role in the formation of self-organized patterns. We consider an oblique anchoring boundary conditions extending the previous studies from tangential and normal boundary conditions to neither of them in both shear and Poiseuille flows. Methods: Mathematical modeling, analysis and numerical simulations.Results: We have established the asymptotic formulas of the steady boundary-value problem subject to a steady weak shear and plane Poiseuille flows. We have also found remarkable dualities of active nematics in the systems. Conclusion: The director anchoring boundary condition plays a very important role in the hydrodynamics and stability of active nematic systems. The Leslie’s angle is the boundary for the stability region.
Active nematics, asymptotic expansions, hydrodynamics, instability, liquid crystals, shear flow.
Department of Mathematics, and Computer Science, Fayetteville State University, NC, School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, 221116, School of Mathematical Sciences, Xiamen University, Xiamen, 361005