Problem of a free liquid film vertically bounded by solid walls and being under the influence of gravity and thermocapillary forces in a thin-layer approximation is considered. A solution in which the film thickness is constant and temperature is a linear function of the longitudinal coordinate is investigated for stability analytically using the method of matched asymptotic expansions and numerically using the orthogonalization method for various values of acceleration of gravity. The results obtained analytically and numerically are in good agreement. It is shown that the solution is unstable, but the increment of perturbations is small even under terrestrial gravity.

中文翻译：

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重力场中自由非等温液膜稳定性的研究

考虑了由固体壁垂直约束并在薄层近似中受重力和热毛细力影响的自由液膜的问题。使用匹配渐近展开方法和数值使用正交化方法对各种重力加速度值进行稳定性分析，其中薄膜厚度恒定且温度是纵坐标的线性函数的解。从分析和数值上获得的结果非常一致。结果表明，该解是不稳定的，但即使在地球重力下，扰动的增量也很小。