Motived by recent ground-based and microgravity experiments investigating the interfacial dynamics of a volatile liquid (FC-72, $Pr=12.34$) contained in a heated cylindrical cell, we numerically study the thermocapillary-driven flow in such an evaporating liquid layer. Particular attention is given to the prediction of the transition of the axisymmetric flow to fully three-dimensional patterns when the applied temperature increases. The numerical simulations rely on an improved one-sided model of evaporation by including heat and mass transfer through the gas phase via the heat transfer Biot number and the evaporative Biot number. We present the axisymmetric flow characteristics, show the variation of the transition points with these Biot numbers, and more importantly elucidate the twofold role of the latent heat of evaporation in the stability; evaporation not only destabilizes the flow but also stabilizes it, depending upon the place where the evaporation-induced thermal gradients come into play. We also show that buoyancy in the liquid layer has a stabilizing effect, though its effect is insignificant. At high Marangoni numbers, the numerical simulations revealed smaller-scale thermal patterns formed on the surface of a thinner evaporating layer, in qualitative agreement with experimental observations. The present work helps to gain a better understanding of the role of a phase change in the thermocapillary instability of an evaporating liquid layer.

中文翻译：

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加热圆柱池中蒸发液层中的热毛细管流动转变

最近基于地面和微重力实验研究了加热的圆柱形电池中包含的挥发性液体（FC-72，$Pr=12.34$）的界面动力学，我们数值研究了这种蒸发液体层中的热毛细管驱动流动。当施加的温度增加时，特别注意预测轴对称流向完全三维模式的转变。数值模拟依赖于一种改进的单侧蒸发模型，包括通过传热 Biot 数和蒸发 Biot 数通过气相进行的热量和质量传递。我们展示了轴对称流动特性，展示了这些 Biot 数的转变点的变化，更重要的是阐明了蒸发潜热在稳定性中的双重作用；蒸发不仅使流动不稳定，而且使流动稳定，这取决于蒸发引起的热梯度发挥作用的位置。我们还表明，液体层中的浮力具有稳定作用，尽管其影响微不足道。在高 Marangoni 数下，数值模拟揭示了在较薄的蒸发层表面形成的较小尺度的热模式，与实验观察定性一致。目前的工作有助于更好地理解相变在蒸发液体层的热毛细管不稳定性中的作用。虽然它的影响微乎其微。在高 Marangoni 数下，数值模拟揭示了在较薄的蒸发层表面形成的较小尺度的热模式，与实验观察定性一致。目前的工作有助于更好地理解相变在蒸发液体层的热毛细管不稳定性中的作用。虽然它的影响微乎其微。在高 Marangoni 数下，数值模拟揭示了在较薄的蒸发层表面形成的较小尺度的热模式，与实验观察定性一致。目前的工作有助于更好地理解相变在蒸发液体层的热毛细管不稳定性中的作用。