Note on the hydrodynamic description of thin nematic films: Strong anchoring model
Note on the hydrodynamic description of thin nematic films: Strong anchoring model
复制标题
DOI：
10.1063/1.4816508
复制
发表时间：
2013-01
影响因子：
4.6
通讯作者：
Te-Sheng Lin;L. Cummings;A. Archer;L. Kondic;U. Thiele
中科院分区：
文献类型：
--
作者：
Te-Sheng Lin;L. Cummings;A. Archer;L. Kondic;U. Thiele
讨论了向列液晶薄膜在自由面和衬底处的强锚固极限下的长波流体力学模型。我们严格澄清弹性能如何进入薄膜厚度的演化方程，以便为进一步研究提供坚实的基础：文献中存在几个相互冲突的模型，它们预测了定性不同的行为。我们整合了各种方法，并表明通过具有一致边界条件的完整线形-流体动力学方程的渐近展开得到的长波模型与采用基于底层自由能泛函的热力学驱动梯度动力学公式得到的模型一致。结果表明，在强锚固情况下，弹性变形能总是稳定的。为了支持本文主要部分的讨论，附录给出了薄膜厚度演化方程的渐近展开的完整推导。
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.