The structure of the flow induced by the van der Waals destabilization of a nonwetting liquid film placed on a solid substrate is studied by means of theory and numerical simulations of the Stokes equations. Our analysis reveals that lubrication theory, which yields $h_{\text{min}}\propto {\tau }^{1/5}$, where $h_{\text{min}}$ is the minimum film thickness and $\tau$ is the time until breakup, cannot be used to describe the local flow close to rupture. Instead, the slender lubrication solution is shown to experience a crossover to a universal self-similar solution of the Stokes equations that yields $h_{\text{min}}\propto {\tau }^{1/3}$, with an opening angle of ${37}^{\circ }$ off the solid.

中文翻译：

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薄膜破裂的斯托克斯理论

通过理论和Stokes方程的数值模拟，研究了由放置在固体基质上的非润湿性液膜的范德华力失稳引起的流动结构。我们的分析表明，润滑理论可以得出$H_{\text{分}}\propto {\tau }^{\mathrm{1个}/5}$，在哪里 $H_{\text{分}}$ 是最小薄膜厚度， $\tau$是直到破裂的时间，不能用来描述接近破裂的局部流动。取而代之的是，细长的润滑解决方案显示出与Stokes方程的通用自相似解相交，从而产生$H_{\text{分}}\propto {\tau }^{\mathrm{1个}/3}$，打开角度为 ${37}^{\circ }$ 掉固体。