Dipartimento di Matematica e Fisica "E. De Giorgi", Università del Salento, 73100 Lecce, Italy.
Dipartimento di Ingegneria, Università degli Studi di Perugia, 06125 Perugia, Italy.
Phys Rev E. 2018 May;97(5-1):052705. doi: 10.1103/PhysRevE.97.052705.
Nematic films are thin fluid structures, ideally two dimensional, endowed with an in-plane degenerate nematic order. In this paper we examine a generalization of the classical Plateau problem to an axisymmetric nematic film bounded by two coaxial parallel rings. At equilibrium, the shape of the nematic film results from the competition between surface tension, which favors the minimization of the area, and the nematic elasticity, which instead promotes the alignment of the molecules along a common direction. We find two classes of equilibrium solutions in which the molecules are uniformly aligned along the meridians or parallels. Depending on two dimensionless parameters, one related to the geometry of the film and the other to the constitutive moduli, the Gaussian curvature of the equilibrium shape may be everywhere negative, vanishing, or positive. The stability of these equilibrium configurations is investigated.
向列膜是薄的流体结构，理想情况下是二维的，具有面内简并向列序。在本文中，我们研究了经典的普拉托问题在轴对称向列膜中的推广，该向列膜由两个同轴平行环限定。在平衡状态下，向列膜的形状是由表面张力和向列弹性之间的竞争决定的，表面张力有利于最小化面积，而向列弹性则促进分子沿着共同方向排列。我们发现了两类平衡解，其中分子沿子午线或平行线均匀排列。根据两个无量纲参数，一个与膜的几何形状有关，另一个与本构模量有关，平衡形状的高斯曲率可能处处为负、为零或为正。我们研究了这些平衡构型的稳定性。
