Te-Sheng Lin, Linda J. Cummings, Andrew J. Archer, Lou Kondic, Uwe Thiele
We discuss the long-wave hydrodynamic model for a thin film of nematic liquid crystal in the limit of strong anchoring at the free surface and at the substrate. Our aim is to clarify how the elastic energy enters the evolution equation for the film thickness; several models exist in the literature that result in qualitatively different behaviour. We consolidate the various approaches and show that the long-wave model derived through an asymptotic expansion of the full nemato-hydrodynamic equations with consistent boundary conditions agrees with the equation one obtains by employing a thermodynamically motivated gradient dynamics formulation based on an underlying free energy functional. As a result, we find that the elastic distortion energy is always stabilising in the case of strong anchoring. To support the discussion in the main part of the paper, an appendix gives the full derivation of the evolution equation for the film thickness via asymptotic expansion.
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http://arxiv.org/abs/1301.4110
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