The evaporating meniscus in a channel
The evaporating meniscus in a channel
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DOI：
10.1017/s0022112003006153
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发表时间：
2003-11-10
影响因子：
3.7
通讯作者：
Morris, SJS
中科院分区：
文献类型：
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作者：
Morris, SJS
我们考虑过热壁处于常温的通道中完全润湿液体的蒸发弯液面。热通过纯传导从壁流到相界面；在那里，蒸发引起小规模液体流集中在接触线附近。液体不断地流入通道，因此界面是静止的，但由于小规模流动引起的压力差而扭曲。为了确定热流，我们根据诱导流的速度在消失毛细管数的极限下对这个自由边界问题进行了系统分析。由于表面张力很大，诱导流只能在接触线附近的一小部分内部区域使相界面变形；其效果是根据毛细管数创建表观接触角 Theta。虽然一般来说，在这个小的内部区域内可能存在显着的热流，但问题中存在额外的小参数意味着，实际上，热流仅在较大的外部区域内才显着，其中界面形状由流体静力学和 Theta 确定。我们推导了热流公式，并表明通道几何形状仅通过接触线处的界面曲率值影响热流。因此，通道的热流关系可以应用于其他几何形状。
We consider the evaporating meniscus of a perfectly wetting liquid in a channel whose superheated walls are at common temperature. Heat flows by pure conduction from the walls to the phase interface; there, evaporation induces a small-scale liquid flow concentrated near the contact lines. Liquid is continually fed to the channel, so that the interface is stationary, but distorted by the pressure differences caused by the small-scale flow. To determine the heat flow, we make a systematic analysis of this free-boundary problem in the limit of vanishing capillary number based on the velocity of the induced flow. Because surface tension is then large, the induced flow can distort the phase interface only in a small inner region near the contact lines; the effect is to create an apparent contact angle Theta depending on capillary number. Though, in general, there can be significant heat flow within that small inner region, the presence of an additional small parameter in the problem implies that, in practice, heat flow is significant only within the large outer region where the interface shape is determined by hydrostatics and Theta. We derive a formula for the heat flow, and show that the channel geometry affects the heat flow only through the value of the interface curvature at the contact line. Consequently, the heat flow relation for a channel can be applied to other geometries.