BOUNDARY-ELEMENT ANALYSIS OF THE TIME-DEPENDENT MOTION OF A SEMIINFINITE BUBBLE IN A CHANNEL
BOUNDARY-ELEMENT ANALYSIS OF THE TIME-DEPENDENT MOTION OF A SEMIINFINITE BUBBLE IN A CHANNEL
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DOI：
10.1006/jcph.1994.1202
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发表时间：
1994-12-01
影响因子：
4.1
通讯作者：
GAVER, DP
中科院分区：
文献类型：
--
作者：
HALPERN, D;GAVER, DP
我们提出了一种边界元方法来研究二维气泡在宽度为2a的通道中随时间的平移，通道中含有粘度为μ和表面张力为γ的流体。在我们的分析中，流速Q（*）被指定，并且手指以非恒定速度向前前进，直到它达到稳态速度U-*。非定常公式中的主要无量纲参数为Ca-Q = μ Q（*）/2a γ，表示粘性力与表面张力的比值。稳态结果以毛细管数的常规形式给出，Ca-U = μ U-*/γ。给出了在比先前公布的大得多的Ca-U范围内（0.05小于或等于Ca-U小于或等于10（4））的手指的稳态形状、手指尖端的压降及其曲率半径。在Reinelt和Saffman的研究范围内（0.05小于或等于Ca-U小于或等于3），以及Tabeling等人的实验数据（其研究范围扩展到Ca-U = 0.2），与有限差分结果有很好的一致性。超过Ca-U = 20，我们预测稳态弯月面界面形状对Ca不敏感，并且压降与粘性压力标度成正比。指宽（β）与Ca-U的回归分析得出β近似为1 - 0.417（1 - Exp（-1.69 Ca-U（0.5025），这给出了小Ca-U和大Ca-U的正确行为。这个回归结果可以被认为是Bretherton的低毛细血管渐近预测的延伸，Bretherton发现Ca的Ca-U（2/3）依赖性非常小（Ca-U < 0.02）。该回归分析的结果与Taylor对圆管中的残余膜厚度的测量一致，其显示Ca-U < 0.09的值的Ca-U（1/2）依赖性。(C)1994年出版社出版。
We present a boundary element method to investigate the time-dependent translation of a two-dimensional bubble in a channel of width 2a containing a fluid of viscosity mu and surface tension gamma. In our analysis, the flow rate, Q(*), is specified, and the finger progresses forward at a nonconstant velocity until it reaches a steady-state velocity U-*. The primary dimensionless parameter in the unsteady formulation is Ca-Q = mu Q(*)/2a gamma, representing the ratio of viscous forces to surface-tension forces. Steady-state results are given in terms of the conventional form of the capillary number, Ca-U = mu U-*/gamma. The steady-state shape of the finger, the pressure drop across the tip of the finger, and its radius of curvature are presented for a range of Ca-U much larger than has previously been published (0.05 less than or equal to Ca-U less than or equal to 10(4)). Good agreement is shown to exist with the finited-difference results of Reinelt and Saffman in the range of their studies (0.05 less than or equal to Ca-U less than or equal to 3), and with the experimental data of Tabeling et al. whose studies extend to Ca-U = 0.2. Beyond Ca-U = 20, we predict that the steady-state meniscus interface shape is insensitive to Ca, and that the pressure drop is directly proportional to a viscous pressure scale. A regression analysis of the finger width (beta) versus Ca-U yields beta approximate to 1 - 0.417(1 - Exp(- 1.69 Ca-U(0.5025))), which gives the correct behavior for both small and large Ca-U. This regression result may be considered an extension of the low-capillary asymptotic predictions of Bretherton, who found a Ca-U(2/3) dependence for Ca very small (Ca-U < 0.02). The result of this regression analysis is consistent with Taylor's measurements of residual film thickness in circular tubes, which shows a Ca-U(1/2) dependence for values of Ca-U < 0.09. (C) 1994 Academic Press, Inc.