We report on the stability of thin liquid films overflowing single microstructures with sharp corners. The microstructures were of rectangular and triangular shape. Their heights and widths were 0.25, 0.5, and 0.75 times the Nusselt film thickness. To observe steady, wavy, and very unstable films we performed simulations with Reynolds numbers ranging from 10 to 70. The dynamics of the liquid film and the overflowing gas phase were described by the coupling between the Cahn-Hilliard and the Navier-Stokes equations. The resulting model forms a very tightly coupled and nonlinear system of equations. Therefore we carefully selected the solution strategy to enable efficient and accurate large-scale simulations. Our results showed that the formation of waves was shifted to higher Reynolds numbers compared to the film on a smooth surface. If waves were finally formed, the microstructures led to irregular waves. Our results indicate a great influence of the microstructure's shape and dimension on the stability of the overflowing liquid film.

中文翻译：

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重力驱动的液膜溢出具有尖角的微结构的稳定性

我们报告了具有尖角的单个微观结构溢出的薄液膜的稳定性。微观结构为矩形和三角形。它们的高度和宽度分别是Nusselt膜厚度的0.25、0.5和0.75倍。为了观察稳定，波浪状和非常不稳定的薄膜，我们进行了雷诺数从10到70的模拟。通过Cahn-Hilliard和Navier-Stokes方程之间的耦合来描述液膜和溢流气相的动力学。结果模型形成了一个紧密耦合的非线性方程组。因此，我们精心选择了解决方案策略，以实现高效，准确的大规模仿真。我们的结果表明，与光滑表面上的膜相比，波的形成向更高的雷诺数转移。如果最终形成波，则微结构导致不规则波。我们的结果表明，微观结构的形状和尺寸对溢流的液膜的稳定性有很大的影响。