Chemical and Biological Engineering, Missouri University of Science and Technology, Rolla, MO 65409-1230, USA.
J Phys Condens Matter. 2010 Oct 20;22(41):415102. doi: 10.1088/0953-8984/22/41/415102. Epub 2010 Sep 13.
When a thin liquid film on a solid surface has a thickness corresponding to a particular part the spinodal region of the disjoining pressure versus thickness isotherm, the film breaks down. One of the patterns that emerges on the breakdown has been referred to as wavy instability. It is compared here to the labyrinthine instability seen in magnetic films. The system is modeled following the procedure used in magnetic systems, and the pattern of wavy instability is broken down into a curved thick-thin film in equilibrium with a flat thin-thin film of constant thickness. Minimization of free energy leads to expressions for various length scales that characterize the system. Comparisons with published experimental results on nematic liquid crystals for a number of very different features are satisfactory. They include film thicknesses in the bulk at equilibrium where the capillary pressure is not zero, and is determined as a part of the solution, as well as film thicknesses in the ledge where the capillary pressure is zero. Stability analysis shows that the system is unstable in both directions with some qualifiers. A model is proposed in the form of a tiled structure to explain the labyrinthine form.
当固体表面上的薄液膜厚度对应于推斥压力与厚度等温线的特定部分的旋节区时，液膜会破裂。在破裂过程中出现的一种模式被称为波纹不稳定性。在这里将其与磁膜中出现的迷宫不稳定性进行了比较。该系统是按照在磁体系统中使用的程序进行建模的，将波纹不稳定性的模式分解为与具有恒定厚度的平坦薄液膜处于平衡状态的弯曲厚-薄液膜。自由能最小化导致了用于描述系统的各种长度尺度的表达式。与关于向列液晶的许多非常不同的特征的已发表实验结果进行了比较，结果令人满意。它们包括平衡时在毛细压力不为零的体相中以及作为解的一部分确定的膜厚度，以及毛细压力为零的壁架处的膜厚度。稳定性分析表明，系统在两个方向上都是不稳定的，存在一些限定条件。提出了一种以平铺结构形式的模型来解释迷宫形式。
