Note on the hydrodynamic description of thin nematic films: strong anchoring model
journal contributionposted on 07.10.2014 by Te-Sheng Lin, Linda J. Cummings, Andrew Archer, Lou Kondic, Uwe Thiele
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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. We rigorously clarify how the elastic energy enters the evolution equation for the film thickness in order to provide a solid basis for further investigation: several conflicting models exist in the literature that predict 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 model one obtains by employing a thermodynamically motivated gradient dynamics formulation based on an underlying free energy functional. As a result, we find that in the case of strong anchoring the elastic distortion energy is always stabilising. 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.
T.L. and U.T. acknowledge support from the European Union (EU) under Grant No. MRTN-CT-2004-005728 (MULTIFLOW). U.T. would like to thank Günter Grün for an invitation to Bonn in October 2004 where they did a derivation similar to that in the appendix and discussed the sign of the elasticity term in the resulting evolution equation. L.J.C. and L.K. acknowledge support from the National Science Foundation (NSF) under Award Nos. DMS-0908158 and DMS-1211713, and L.J.C. also acknowledges support from KAUST under Award No. KUK-C1-013-04.
- Mathematical Sciences