Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, USA.
Phys Rev Lett. 2013 Jul 19;111(3):034502. doi: 10.1103/PhysRevLett.111.034502. Epub 2013 Jul 16.
We study the elastic version of the Saffman-Taylor problem: the Hele-Shaw displacement of a viscous liquid by a gas underneath an elastic membrane. We derive the dynamics of the propagating gas-liquid interface and of the deforming membrane. Even though the displacement of a viscous liquid by a gas is susceptible to viscous fingering, the presence of the elastic boundary can lead to the suppression of the instability. We demonstrate how the mechanism of suppression is provided by surface tension at the gas-liquid interface owing to the tapered flow geometry underneath the deflected membrane. We also determine the critical conditions for the onset of the fingering instability in the presence of the elastic boundary.
我们研究了 Saffman-Taylor 问题的弹性版本：弹性膜下气体对粘性液体的 Hele-Shaw 置换。我们推导出了传播的气液界面和变形膜的动力学。尽管气体对粘性液体的置换容易发生粘性指进，但弹性边界的存在可以抑制不稳定性。我们展示了由于偏转膜下方的锥形流动几何形状，如何通过气液界面处的表面张力来提供抑制机制。我们还确定了存在弹性边界时，指进不稳定性开始的临界条件。
