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
Keywords: Active nematics, asymptotic expansions, hydrodynamics, instability, liquid crystals, shear flow.
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