Bubbles in a Hele–Shaw cell: Numerical simulation of three‐dimensional effects
Bubbles in a Hele–Shaw cell: Numerical simulation of three‐dimensional effects
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DOI：
10.1063/1.857404
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发表时间：
1989-06
影响因子：
4.6
通讯作者：
E. Meiburg
中科院分区：
文献类型：
--
作者：
E. Meiburg
对Hele-Shaw池中不混溶气泡的传播过程进行了时间相关的数值模拟。Pennsylvania二维计算仅显示细长气泡的传播速度比粘性流体快，与Tanveer的结果一致。对于小的毛细管数，这些气泡呈现圆形，而它们的速度接近一个平台。通过包括对跨界面的压力跃变的首阶三维效应，可以观察到以较小速度迁移的较宽和较短的气泡。特别是，扁平的气泡和气泡比粘性相慢被发现。即使这些气泡也接近高表面张力值的圆形形状，没有观察到的速度平台。虽然注意到三维效应促进了尖端不稳定性，但实验观察到的多种形状和过渡只能部分解释。
Time‐dependent numerical simulations of immiscible bubbles propagating in a Hele–Shaw cell are presented. Purely two‐dimensional calculations only show elongated bubbles propagating faster than the viscous fluid, in agreement with Tanveer’s results. For small capillary numbers, these bubbles assume circular shapes while their velocity approaches a plateau. By including the leading‐order three‐dimensional effects on the pressure jump across the interface, wider and shorter bubbles migrating at smaller velocities can be observed. In particular, flattened bubbles and bubbles slower than the viscous phase are found. Even though these bubbles also approach circular shapes for high surface tension values, a velocity plateau is not observed. While noticing that the three‐dimensional effects promote a tip instability, the multiple shapes and transitioins observed experimentally can only be partially explained.