Pattern formation of the three-layer Saffman-Taylor problem in a radial Hele-Shaw cell
Pattern formation of the three-layer Saffman-Taylor problem in a radial Hele-Shaw cell
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DOI：
10.1103/physrevfluids.5.124005
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发表时间：
2020-06
影响因子：
2.7
通讯作者：
Meng Zhao;Pedro H. A. Anjos;J. Lowengrub;Shuwang Li
中科院分区：
文献类型：
--
作者：
Meng Zhao;Pedro H. A. Anjos;J. Lowengrub;Shuwang Li
三层Saffman-Taylor问题引入了两个耦合的运动界面来分离三种流体。最近在径向Hele-Shaw电池装置中对该问题进行的弱非线性分析表明，新出现的指法模式的形态强烈依赖于连接两个界面的中间层的初始厚度。在这里，我们超越了弱非线性状态，并利用光谱精确的边界积分方法探索了完全非线性界面动力学。随着相关物理参数（如粘度和表面张力）的变化，我们量化了两个界面的非线性不稳定性，并表明我们的非线性计算与实验观察和弱非线性分析很好地吻合。非线性模拟表明，由于第二界面的存在，传统的高支化结构被不稳定的结构所取代，在这种结构中，随着初始环隙厚度的减小，指尖劈裂和手指竞争现象明显受到抑制。此外，随着界面耦合强度的增加，高频模式的生长增强，这些新颖的模式在其尖端形成了一系列低幅度的凸起。
The three-layer Saffman-Taylor problem introduces two coupled moving interfaces separating the three fluids. A very recent weakly nonlinear analysis of this problem in a radial Hele-Shaw cell setup has shown that the morphologies of the emerging fingering patterns strongly depend on the initial thickness of the intermediate layer connecting the two interfaces. Here we go beyond the weakly nonlinear regime and explore full nonlinear interfacial dynamics using a spectrally accurate boundary integral method. We quantify the nonlinear instability of both interfaces as the relevant physical parameters (e.g., viscosities and surface tensions) are varied and show that our nonlinear computations are in good agreement with the experimental observations and the weakly nonlinear analysis. Nonlinear simulations reveal that due to the existence of a second interface, the classical highly branched morphologies are replaced by less unstable structures in which finger tip-splitting and finger competition phenomena are evidently restrained as the initial annulus' thickness is reduced. In addition, these novels patterns develop fingers with a series of low-amplitude bumps at their tips, associated with the enhanced growth of high-frequency modes promoted by the increasing coupling strength of interfaces.