The European Physical Journal E ( IF 1.8 ) Pub Date : 2021-06-19 , DOI: 10.1140/epje/s10189-021-00082-1 Elena S Pikina 1, 2, 3 , Boris I Ostrovskii 2, 4 , Sergey A Pikin 4
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Abstract
We study theoretically internal flows in isotropic droplets formed in horizontal free-standing smectic films (FSSF) overheated above the bulk smectic-isotropic transition. The convection is due to vertical temperature gradient in the film and is driven by the surface tension variations at the drop interfaces. Using a conventional linear instability theory, we have found analytically the conditions under which the mechanical equilibrium within isotropic droplets in FSSFs becomes unstable relative to the thermocapillary convection. An explicit expression for the Marangoni number characterizing the onset of the convection as a function of the wave vector of in-plane instability and parameters of heat transfer is obtained. The cellular instability in FSSF with isotropic droplets behaving as a normal fluid (surface tension is a decreasing function of temperature) is possible for both directions of thermal gradient across the film: from bottom to top and conversely. We propose possible experimental observations enabling to check our predictions.
Graphicabstract
中文翻译：
过热独立式近晶薄膜中各向同性液滴内的贝纳德-马兰戈尼对流
抽象的
我们从理论上研究了在整体近晶-各向同性转变之上过热的水平独立近晶薄膜（FSSF）中形成的各向同性液滴的内部流动。对流是由于薄膜中的垂直温度梯度造成的，并且是由液滴界面处的表面张力变化驱动的。使用传统的线性不稳定性理论，我们通过分析发现了 FSSF 中各向同性液滴内的机械平衡相对于热毛细管对流变得不稳定的条件。获得了马兰戈尼数的显式表达式，该马兰戈尼数将对流的开始表征为面内不稳定性波矢和传热参数的函数。 FSSF 中的细胞不稳定性与各向同性液滴表现得像正常流体一样（表面张力是温度的递减函数），这对于整个薄膜的两个热梯度方向都是可能的：从下到上，反之亦然。我们提出了可能的实验观察，以验证我们的预测。
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