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Stability of a condensing liquid film in a binary vapor mixture system

机译：二元蒸气混合系统中冷凝液膜的稳定性

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摘要

We study stability of a condensing liquid film of a binary vapor mixture. When a binary vapor mixture of some kind is cooled on a substrate, a condensing liquid film emerges to take an inhomogeneous form such as a droplet one due to the solutal Marangoni effect. In order to analyze this phenomenon, we apply the long-wave approximation to the condensing liquid film and derive a nonlinear partial differential equation describing the spatio-temporal evolution of the film thickness. An interfacial boundary condition taking account of an effect of mass gain of the liquid film is adopted. Based on this model, we perform a linear stability analysis around a flat-film solution. We obtain an evolution equation of the amplitude of a disturbance, from which the cutoff and fastest growth wavenumbers are deduced. The maximum value of the cutoff wavenumber relative to the film thickness and its film thickness are estimated for water-ethanol mixture at atmospheric pressure. We numerically verify the long-wave nature of the instability of the condensate liquid film in this system. A significant difference in their values is found for low-ethanol fractions of the ambient vapor whether or not the temperature dependence of the mass transfer coefficient is considered. The wavenumber of a pattern of the liquid film observed in the experiment has the same parameter dependence as that of the fastest growth wavenumber.
机译：我们研究了二元蒸气混合物的冷凝液膜的稳定性。当某种二元蒸气混合物在基板上冷却时，由于溶质的马兰戈尼效应，冷凝液膜出现为不均匀的形式，例如液滴之一。为了分析这种现象，我们将长波近似应用于凝结的液膜，并推导了描述膜厚度时空演化的非线性偏微分方程。采用考虑了液膜的质量增加的影响的界面边界条件。基于此模型，我们围绕平膜解决方案执行线性稳定性分析。我们得到扰动幅度的演化方程，从中推导出截止和最快的增长波数。对于在大气压下的水-乙醇混合物，估计了相对于膜厚度及其膜厚度的截止波数最大值。我们用数值方法验证了该系统中凝结液膜不稳定性的长波性质。无论是否考虑传质系数的温度依赖性，对于环境蒸气的低乙醇含量，它们的值都存在显着差异。实验中观察到的液膜图案的波数与最快的生长波数具有相同的参数依赖性。

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