We study the evolution of unstable liquid films via numerical solutions of the thin-film equation. The film is placed on a coated substrate with disorder. This is modeled by a random spatial variation of the relative value of the Hamaker constants for the substrate and coating. The free energy consists of (a) the van der Waals term for the substrate/coating interactions with the film and (b) a term due to gravity. This free energy admits a Maxwell double-tangent construction with two coexisting phases, i.e., "thin" and "thick" phases. In the absence of disorder, the film dewets by true morphological phase separation (MPS), i.e., the elimination of domain walls between the coexisting phases. The introduction of disorder may result in the trapping of these domain walls, with a drastic slowdown in growth kinetics. We present detailed numerical results in D=2 and D=3 to understand this slow coarsening, where D is the dimensionality of the liquid-film system.

中文翻译：

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在无序基材上的重力作用下，不稳定液膜中的缓慢粗化。

我们通过薄膜方程的数值解研究了不稳定液膜的演化。将该膜无序放置在涂覆的基材上。这通过基材和涂层的Hamaker常数的相对值的随机空间变化来建模。自由能由（a）范德华（van der Waals）项表示与膜的底物/涂层相互作用，以及（b）重力引起的项。这种自由能允许麦克斯韦双切线结构具有两个共存的相，即“薄”相和“厚”相。在无紊乱的情况下，薄膜会通过真正的形态相分离（MPS）（即消除共存相之间的畴壁）进行润湿。无序性的引入可能导致这些畴壁的陷获，并且生长动力学急剧减慢。