Bubble formation, motion and interaction in a Hele-Shaw cell
Bubble formation, motion and interaction in a Hele-Shaw cell
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DOI：
10.1017/s002211208600109x
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发表时间：
1986-12
影响因子：
3.7
通讯作者：
T. Maxworthy
中科院分区：
文献类型：
--
作者：
T. Maxworthy
我们考虑了当空气被注入粘性流体中时形成的扁平气泡的运动，粘性流体包含在两个平行板之间的狭窄缝隙中，这两个平行板构成了传统的Hele-Shaw单元，与水平方向成x角倾斜。当空气连续注入细胞时，我们提供了一些关于气泡流的形成和相互作用的定性观察。这篇论文的主要内容是关于单个孤立气泡在大范围的气泡尺寸和细胞倾斜度范围内的形状和上升速度。我们将这些结果与Taylor&Saffman(1959)和Tanveer(1986)的理论进行了比较。由Taylor&Saffman(1959)和Tanveer(1986)的一个特别推测所发现的气泡特征似乎只在极限α→0时和大气泡宽度(D)下与实验结果一致。对于有限的α值，为了使用更一般的泰勒和萨夫曼公式来计算上升速度，必须使用测量的气泡形状。对于小D，偏离这些理论可以通过考虑靠近气泡表面的细微流动的影响来解释。
We consider the motion of the flattened bubbles which form when air is injected into a viscous fluid contained in the narrow gap between two flat, parallel plates which make up a conventional Hele-Shaw cell, inclined at an angle x to the horizontal. We present a number of qualitative observations on the formation and interaction of the streams of bubbles that appear when air is injected continuously into the cell. The majority of this paper is then concerned with the shape and velocity of rise of single, isolated bubbles over a wide range of bubble size and cell inclination. We compare these results to theories by Taylor & Saffman (1959), and Tanveer (1986). It appears that the bubble characteristics found by an ad hoc speculation in Taylor & Saffman (1959) and by Tanveer (1986) only agree with the experimental results in the limit α → 0, and for large bubble widths (D). For finite values of α, it is necessary to use the measured bubble shape in order to calculate the rise velocity using the more general Taylor & Saffman (1959) formulation. Deviations from these theories for small D can be explained by considering the effects of the detailed flow close to the bubble surface.