论文标题
在低雷诺数下，可混杂的滴升升高或掉落在另一个液体中
The dissolution of a miscible drop rising or falling in another liquid at low Reynolds number
论文作者
论文摘要
“流体动力学中的一个基本且基本上无法解决的问题是确定一种升高的气泡的演变和另一个有可能的液体下降的演变” [1]。在这里，我们解决了这一重要文献差距，并提出了第一个预测雷诺数低的速度，体积和组成的速度，体积和组成的理论。对于从下降的扩散可以忽略不计的情况，我们获得了普遍的缩放定律。对于更一般的情况，扩散进入和从滴水中出现，整个动力学受到无参数的一阶普通微分方程的控制，其封闭形式解决方案存在，仅取决于初始条件。我们的分析主要取决于通过界面边界层扩散率的“滴度尺度”有效参数。我们根据糖浆中悬浮在糖浆中的水滴的实验数据来验证我们的结果，这对应于水与糖浆之间的某些质量交换比率，并通过这种明确识别该理论的滴度尺度参数。 [1]约瑟夫，D.D。和Renardy，Y.Y.，2013年。两流体动力学的基本原理：第二部分：润滑运输，滴落和有性液体（第4卷）。 Springer科学与商业媒体。
'A basic and basically unsolved problem in fluid dynamics is to determine the evolution of rising bubbles and falling drops of one miscible liquid in another' [1]. Here, we address this important literature gap and present the first theory predicting the velocity, volume and composition of such drops at low Reynolds numbers. For the case where the diffusion out of the drop is negligible, we obtain a universal scaling law. For the more general case where diffusion occurs into and out of the drop, the full dynamics is governed by a parameter-free first-order ordinary differential equation, whose closed form solution exists, and only depends on the initial condition. Our analysis depends primarily on 'drop-scale' effective parameters for the diffusivity through the interfacial boundary layer. We validate our results against experimental data for water drops suspended in syrup, corresponding to certain regimes of the mass exchange ratio between water and syrup, and by this explicitly identify the drop-scale parameters of the theory. [1] Joseph, D.D. and Renardy, Y.Y., 2013. Fundamentals of two-fluid dynamics: part II: lubricated transport, drops and miscible liquids (Vol. 4). Springer Science & Business Media.
