论文标题
在径向Hele-Shaw细胞中三层Saffman-Taylor问题的模式形成
Pattern formation of the three-layer Saffman-Taylor problem in a radial Hele-Shaw cell
论文作者
论文摘要
三层Saffman-Taylor问题引入了两个耦合的运动界面，将三个流体分开。在径向Hele-Shaw细胞设置中对该问题的最新弱非线性分析表明，新兴指法模式的形态在很大程度上取决于连接两个接口的中间层的初始厚度。在这里，我们超越了弱的非线性制度，并使用频谱准确的边界积分方法探索完整的非线性界面动力学。我们将两个接口的非线性不稳定性量化为相关的物理参数（例如，粘度和表面张力）的变化，并表明我们的非线性计算与实验观测值和弱非线性分析非常吻合。非线性模拟表明，由于存在第二个界面，经典的高度分支形态被不稳定的结构所取代，在这种结构中，由于最初的环的厚度降低了手指尖端 - 分裂和手指竞争现象显然受到限制。此外，这些小说的模式在其尖端上以一系列低振幅凸起的形式形成了手指，这与界面的耦合强度提高所促进的高频模式的增长有关。
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.
