Displacement flows under elastic membranes. Part 2. Analysis of interfacial effects
Displacement flows under elastic membranes. Part 2. Analysis of interfacial effects
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DOI：
10.1017/jfm.2015.589
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发表时间：
2015-12-01
影响因子：
3.7
通讯作者：
Lister, John R.
中科院分区：
文献类型：
--
作者：
Peng, Gunnar G.;Pihler-Puzovic, Draga;Lister, John R.
本文研究了无粘性气体注入到刚性基板和弹性薄板之间的狭窄充液间隙中的问题。在早期瞬态之后，其中气体使片材偏转成大的气泡，被膨胀气泡移位的粘性液体开始积聚在楔形物中，该楔形物随着弹性片材从基部剥离而前进。我们从理论上分析了粘性力、弹性（弯曲或拉伸）力和毛细力之间的相互作用。渐近表达式推导出的气泡的传播速度，这表明，在气泡尖端的毛细压降的效果是吸下来的液体楔片，从而降低速度。我们表明，系统通过三个不同的渐近制度的顺序。在早期，毛细作用很弱，因此气泡的扩展主要由楔形尖端的粘性剥离过程控制。毛细管力的重要性随着时间的推移而增加，并且在后期它们支配粘性效应并与弹性力平衡，从而导致准静态铺展。最后，在很晚的时候，毛细吸力在楔形尖端产生一个狭窄的瓶颈，这推动了一个大的脊液体ahead it. These结果持有的标准润滑理论的框架，以及与改进的润滑模型，它考虑到膜的润湿液体沉积在前进的气泡尖端后面。该模型的预测被证明是在很好的协议与Navier-Stokes模拟和实验结果从第1部分的这项工作。
We investigate the injection of inviscid gas into the narrow liquid-filled gap between a rigid base plate and an overlying elastic sheet. After an early-time transient in which the gas deflects the sheet into a large blister, the viscous liquid displaced by the expanding bubble starts to accumulate in a wedge which advances as the elastic sheet peels away from the base. We analyse theoretically the subsequent interaction between viscous forces, elastic (bending or tension) forces and capillary forces. Asymptotic expressions are derived for the speed of spreading of the bubble, which reveal that the effect of the capillary pressure drop at the bubble tip is to suck down the sheet over the liquid wedge and thereby reduce the speed. We show that the system passes through three different asymptotic regimes in sequence. At early times, capillary effects are weak and hence the spreading of the bubble is controlled dominantly by the viscous-peeling process at the wedge tip. The capillary forces grow in importance with time, and at late times they dominate viscous effects and balance with elastic forces, leading to quasi-static spreading. Finally, at very late times, the capillary suction generates a narrow bottleneck at the wedge tip, which pushes a large ridge of liquid ahead of it. These results hold in the framework of standard lubrication theory as well as with an improved lubrication model, which takes into account films of wetting liquid deposited behind the advancing bubble tip. The predictions of the model are shown to be in excellent agreement with the Navier-Stokes simulations and experimental results from Part 1 of this work.