Abstract In this work, we study unidirectional, fully developed, layered two-phase flows in microchannels, where the interface meets the wall at an arbitrary contact angle. Interfacial tension causes the interface to take the form of a circular arc, with a radius that depends on the contact angle. The momentum equations must therefore be solved on a domain with boundaries that are, in general, not iso-coordinate surfaces. We adopt the technique developed by Shankar (2005a), which extends the use of eigenfunctions to arbitrary shaped domains, and apply it to layered flows for rectangular and circular cross-sections of the channel. This method is computationally efficient and allows us to analyze in detail the effect of the contact angle on flow properties. We focus on the case of a rectangular channel, which is commonly encountered in microfluidic applications, and consider two distinct cases: (a) free interface whose equilibrium contact angle is a function of fluid wetting properties, and (b) pinned interface whose apparent contact angle is determined by fluid flow rates. We calculate the relationship between the volume fractions (holdups) and flow rate fractions of the fluids and show that a non-zero contact angle can significantly restrict the range of permissible flow rates. This range is greater when the less viscous fluid has a greater affinity for the wall. For fixed flow rates, the residence time of a fluid is found to increase as its affinity for the wall increases. The pressure drop, which directly impacts operational costs, is found to be lower when the more viscous fluid is more wetting. This non-intuitive result is explained in terms of the corresponding variation in fluid volume fractions.

中文翻译：

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具有任意界面-壁接触角的微通道中的分层两相流

摘要 在这项工作中，我们研究了微通道中单向、完全发展、分层的两相流，其中界面以任意接触角与壁相接。界面张力导致界面呈圆弧形，其半径取决于接触角。因此，动量方程必须在具有边界的域上求解，这些域通常不是等坐标表面。我们采用 Shankar (2005a) 开发的技术，该技术将特征函数的使用扩展到任意形状的域，并将其应用于矩形和圆形通道横截面的分层流。这种方法计算效率高，使我们能够详细分析接触角对流动特性的影响。我们专注于矩形通道的情况，这在微流体应用中经常遇到，并考虑两种不同的情况：(a) 自由界面，其平衡接触角是流体润湿特性的函数，以及 (b) 固定界面，其表观接触角由流体流速决定。我们计算了流体的体积分数（滞留率）和流速分数之间的关系，并表明非零接触角可以显着限制允许流速的范围。当粘性较小的流体对壁具有较大的亲和力时，该范围更大。对于固定流速，发现流体的停留时间随着其对壁的亲和力增加而增加。发现直接影响运营成本的压降在粘度越大的流体越润湿时越低。