epl draft Threshold of Bénard-Marangoni instability in drying liquid films
epl draft Threshold of Bénard-Marangoni instability in drying liquid films
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发表时间：
2012
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通讯作者：
F. Chauvet;S. Dehaeck;P. Colinet
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作者：
F. Chauvet;S. Dehaeck;P. Colinet
我们在这里展示了蒸发/冷凝过程如何导致沿液/气界面的有效热传播，从而抑制热波动并阻碍热毛细流动。这种机制作为气相的有效导热系数，当后者由纯蒸汽制成时，它显示出发散。我们的简单（无拟合参数）理论很好地符合干燥液膜中bsamnard - marangoni不稳定性临界条件的测量结果。在非线性状态下，热扩散对波长选择也有强烈的影响。除了为分析复杂蒸发驱动模式之间的转变提供定量框架外，这也为更好地控制基于干燥的沉积技术开辟了新的视角。蒸发和冷凝是自然界和技术中广泛存在的过程，无论是在大尺度上（如水循环、盐湖干燥等）还是在小尺度上（如热交换器、沉积和涂层技术等）。在后一种情况下，这种相变现象通常伴随着所谓的马兰戈尼流，这是由沿界面的表面张力梯度引起的。对于蒸发到空气中的纯液体，后者是由于潜热消耗所产生的温度梯度，往往导致bsamad型模式[1,2]。相反，当气相只包含蒸汽时（例如在沸腾应用中），这种流动通常不存在，因为界面必须保持接近饱和温度（例如[3]，在这种情况下显示浮力的优势）。然而，尽管有许多应用，这种界面温度均质过程的性质仍然不清楚，并且从未被准确地量化为气相蒸汽含量的函数。直观地说，可以预期温度是通过能量（以潜热的形式）沿表面从热/蒸发区域传输到冷/冷凝区域而均匀化的。因此，我们的目标是评估这种“热传播”机制的效率作为流体性质和环境条件的函数。在描述了在相当一般的条件下这种效应的简单模型之后，我们分析了不同挥发性的液体在干燥到环境空气中的液体膜中对b<s:1>纳德-马兰戈尼（BM）模式的影响（挥发性最大的液体最终接近纯蒸汽的极限情况）。众所周知，在这方面，BM不稳定性的临界条件在某种程度上取决于气相中的热对流过程，通常集中在经验确定的传热系数[4]中。尽管已经提出了各种理论来推广这些片面的方法并计算（有效的）传热系数（参见例[5,6]），但它们都没有通过与精确实验的直接比较得到验证。实际上，在实验中只对非挥发性液体检查了模式开始的临界马兰戈尼数Mac，在这种情况下，该值约为80[4,7]。鉴于上面讨论的热扩散机制，因此人们期望不稳定性有很强的阻尼，因此当波动性增加时，mac值会大得多。在本工作中，通过检测当干燥膜厚度减小到某个阈值以下时从对流状态到导电状态的转变，详细研究了这一点。除了允许对我们的新理论进行准确验证之外，值得注意的是，这封信中提出的结果可以为使用干燥膜（如聚合物涂层[8]或纳米颗粒沉积[9]）的更好控制技术开辟有趣的视角。
We here show how evaporation/condensation processes lead to efficient heat spreading along a liquid/gas interface, thereby damping thermal fluctuations and hindering thermocapillary flows. This mechanism acts as an effective thermal conductivity of the gas phase, which is shown to diverge when the latter is made of pure vapor. Our simple (fitting-parameter-free) theory nicely agrees with measurements of critical conditions for Bénard-Marangoni instability in drying liquid films. Heat spreading is also shown to strongly affect wavelength selection in the nonlinear regime. In addition to providing a quantitative framework for analyzing transitions between complex evaporation-driven patterns, this also opens new perspectives for better controlling deposition techniques based on drying. Evaporation and condensation are widespread processes in nature and technology, both at large scales (e.g. water cycle, salt lake drying, ...) and small scales (e.g. heat exchangers, deposition and coating techniques, ...). In the latter case, such phase change phenomena are generally coupled with so-called Marangoni flows, resulting from surface tension gradients along the interface. For pure liquids evaporating into air, the latter are due to temperature gradients generated by the consumption of latent heat, often resulting in Bénard-type patterns [1, 2]. In contrast, when the gas phase contains only vapor (e.g. in boiling applications), such flows are typically absent since the interface is bound to remain close to the saturation temperature (see e.g. [3], showing the predominance of buoyancy in that case). However, despite the numerous applications, the nature of such interfacial temperature homogenization process remains unclear, and has never been accurately quantified as a function of the vapor content of the gas phase. Intuitively, it can be expected that temperature gets uniformized by transport of energy (in the form of latent heat) from hot/evaporating to cold/condensing regions along the surface. Our goal here is therefore to assess the efficiency of this “heat spreading” mechanism as a function of fluid properties and ambient conditions. After having described a simple modeling of this effect in quite general conditions, we analyze its impact on Bénard-Marangoni (BM) patterns in liquid films drying into ambient air, for liquids of different volatilities (the most volatile ones eventually approaching the limiting case of pure vapor). It is well known in that respect that the critical conditions for BM instability somehow depend on thermo-convective processes in the gas phase, generally lumped into an empirically determined heat transfer coefficient [4]. Even though various theories have been proposed to generalize these one-sided approaches and to calculate the (effective) heat transfer coefficients (see e.g. [5, 6]), none of them was ever validated by direct comparison with accurate experiments. Actually, the critical Marangoni number Mac for the onset of patterns was experimentally checked only for non-volatile liquids, in which case the value is about 80 [4,7]. In view of the heat spreading mechanism discussed above, one therefore expects a strong damping of the instability, hence much larger values ofMac, when volatility increases. In the present work, this is investigated in details by detecting the transition from the convective to the conductive state occurring when the drying film thickness decreases below some threshold value. In addition to allowing an accurate validation of our new theory, it is worth noting that results presented in this Letter could open interesting perspectives to better control techniques using drying films such as polymer coating [8] or nanoparticle deposition [9].