薄膜沿倒置衬底流下的二维流动
Thin films flowing down inverted substrates: two dimensional flow
摘要：
本文在润滑近似的框架内研究了倒置基底上薄膜流动的自由表面不稳定性。我们允许前线和相关接触线的存在，并探讨它们在不稳定发展中所起的作用。据发现，接触线，建模常用的前体膜模型，导致自由表面不稳定性，没有任何额外的自然或激发扰动。单个参数D=（3Ca）^{1/3} \cot α $, where $ Ca $ is the capillary number and $ α $ is the inclination angle, is identified as a governing parameter in the problem. This parameter may be interpreted to reflect the combined effect of inclination angle, film thickness, Reynolds number and the fluid flux. Variation of $ D$导致不稳定性的波动性质的改变，使我们能够观察到行波行为、混合波和类似孤立波的波。
英文摘要：
We consider free surface instabilities of films flowing on inverted substrates within the framework of lubrication approximation. We allow for the presence of fronts and related contact lines, and explore the role which they play in instability development. It is found that a contact line, modeled by a commonly used precursor film model, leads to free surface instabilities without any additional natural or excited perturbations. A single parameter D=(3Ca)^{1/3}\cotα$, where $Ca$ is the capillary number and $α$ is the inclination angle, is identified as a governing parameter in the problem. This parameter may be interpreted to reflect the combined effect of inclination angle, film thickness, Reynolds number and the fluid flux. Variation of $D$ leads to change of the wave-like properties of the instabilities, allowing us to observe traveling wave behavior, mixed waves, and the waves resembling solitary ones.
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