Thin-film Rayleigh–Taylor instability in the presence of a deep periodic corrugated wall
Thin-film Rayleigh–Taylor instability in the presence of a deep periodic corrugated wall
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DOI：
10.1017/jfm.2021.960
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发表时间：
2021-11
影响因子：
3.7
通讯作者：
B. Dinesh;T. Corbin;R. Narayanan
中科院分区：
文献类型：
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作者：
B. Dinesh;T. Corbin;R. Narayanan
摘要研究了被动型流体上覆薄液膜附着于周期波状深波纹壁上时的瑞利-泰勒不稳定性。降阶长波模型表明，当界面模式与壁模式为次谐波时，波状壁增强了破裂的不稳定性。对于壁面由两个满波组成，界面由一个满波组成的特殊情况，得到了壁面振幅任意值的近似不稳定增长常数表达式。界面演化的非线性计算表明，当考虑单液膜覆盖在被动流体上时，波壁会阻止滑动，而当考虑由顶部波壁和底部平壁夹成的双层液膜时，则不一定。在后一种情况下，界面跟踪表明，由于对称破坏，主槽和次槽将演变并随后沿着平壁滑动。进一步表明，根据流体的持率，这种界面滑动运动最终可以被顶部波浪壁阻止。换句话说，存在一个界面位置的临界值，超过这个临界值，可以观察到滑动运动的开始，低于这个临界值，滑动总是被阻止。
Abstract Rayleigh–Taylor instability of a thin liquid film overlying a passive fluid is examined when the film is attached to a periodic wavy deep corrugated wall. A reduced-order long-wave model shows that the wavy wall enhances the instability toward rupture when the interface pattern is sub-harmonic to the wall pattern. An expression that approximates the growth constant of instability is obtained for any value of wall amplitude for the special case when the wall consists of two full waves and the interface consists of a full wave. Nonlinear computations of the interface evolution show that sliding is arrested by the wavy wall if a single liquid film residing over a passive fluid is considered but not necessarily when a bilayer sandwiched by a top wavy wall and bottom flat wall is considered. In the latter case interface tracking shows that primary and secondary troughs will evolve and subsequently slide along the flat wall due to symmetry-breaking. It is further shown that this sliding motion of the interface can ultimately be arrested by the top wavy wall, depending on the holdup of the fluids. In other words, there exists a critical value of the interface position beyond which the onset of the sliding motion is observed and below which the sliding is always arrested.