Thermocapillary flow between grooved superhydrophobic surfaces: transverse temperature gradients
Thermocapillary flow between grooved superhydrophobic surfaces: transverse temperature gradients
复制标题
凹槽超疏水表面之间的热毛细管流动：横向温度梯度
DOI：
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发表时间：
2019
影响因子：
3.7
通讯作者：
D. Crowdy
中科院分区：
文献类型：
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作者：
E. Yariv;D. Crowdy
我们考虑了两个超疏水表面之间的液体层的热毛细运动，每个超疏水表面由一个周期性的高导电固体板条阵列组成，其中扁平气泡被困在它们之间的凹槽中。根据最近对纵向问题的分析（Yariv，J. Fluid Mech.，第855卷，2018年，pp. 574-594），我们在此解决横向问题，其中驱动流动的宏观温度梯度垂直于凹槽施加，目的是计算两个表面之间的体积通量。我们专注于的情况下，分离的凹槽的板条是长相对于凹槽阵列周期，在这种情况下，在固体部分的超疏水平面的温度是分段均匀的。Baier等人（Phys. Rev. E，vol.82（3），2010，037301）对这种情况进行了数值研究，在本问题中温度场的调和共轭与互换边界上可比较的纵向压力驱动流问题中的单向速度之间存在令人惊讶的相似性。本文的主体是关于深通道的限制，在那里的问题减少到一个单一的表面的热传输和流动的计算和相关的“滑”的速度在大的距离从该表面。利用洛仑兹的互易性，我们得到了速度作为一个简单的求积，提供了类似的表达式由拜尔等人。（2010）在可比的纵向问题。其余的文件是专门的浅通道，这是使用Hele-Shaw近似分析的直径限制，和奇异的小固体分数的限制，在那里我们找到一个对数标度的通量与固体分数。后两种限制不能互换。
We consider the thermocapillary motion of a liquid layer which is bounded between two superhydrophobic surfaces, each made up of a periodic array of highly conducting solid slats, with flat bubbles trapped in the grooves between them. Following the recent analysis of the longitudinal problem (Yariv, J. Fluid Mech., vol. 855, 2018, pp. 574–594), we address here the transverse problem, where the macroscopic temperature gradient that drives the flow is applied perpendicular to the grooves, with the goal of calculating the volumetric flux between the two surfaces. We focus upon the situation where the slats separating the grooves are long relative to the groove-array period, for which case the temperature in the solid portions of the superhydrophobic plane is piecewise uniform. This scenario, which was investigated numerically by Baier et al. (Phys. Rev. E, vol. 82 (3), 2010, 037301), allows for a surprising analogy between the harmonic conjugate of the temperature field in the present problem and the unidirectional velocity in a comparable longitudinal pressure-driven flow problem over an interchanged boundary. The main body of the paper is concerned with the limit of deep channels, where the problem reduces to the calculation of the heat transport and flow about a single surface and the associated ‘slip’ velocity at large distance from that surface. Making use of Lorentz’s reciprocity, we obtain that velocity as a simple quadrature, providing the analogue to the expression obtained by Baier et al. (2010) in the comparable longitudinal problem. The rest of the paper is devoted to the diametric limit of shallow channels, which is analysed using a Hele-Shaw approximation, and the singular limit of small solid fractions, where we find a logarithmic scaling of the flux with the solid fraction. The latter two limits do not commute.