弹性-刚性通道中手指传播的模拟
Modelling finger propagation in elasto-rigid channels
摘要：
我们进行了理论研究的两相流结构的相互作用问题中，空气被驱动在恒定的体积流量到一个充满液体的Hele-Shaw通道，其上边界是一个弹性片。采用一个以气液界面为参考系的深度平均模型，通过数值模拟研究了定常和非定常的界面传播模式。在轻微塌陷的渠道，courly-propagating接口采用的形状是类似于经典的Saffman-Taylor指刚性Hele-Shaw细胞。由于初始崩溃的水平增加的诱导梯度在通道深度改变传播手指的形态，并促进各种不稳定性，从尖端分裂到小规模的指状弯曲的界面上，定性与实验一致。该模型有一个复杂的解决方案的结构，具有广泛的稳定和不稳定，稳定和时间周期模式，其中许多具有相似的驱动压力。我们发现我们的模型与Ducloué等人（J. Fluid Mech. vol. 819，2017，p 121）的指宽，片材轮廓和指压的实验数据之间具有良好的定量一致性，前提是模型中包含了用于解释通道上下壁上存在液膜的校正。
英文摘要：
We conduct a theoretical study of a two-phase-fluid-structure interaction problem in which air is driven at constant volume flux into a liquid-filled Hele-Shaw channel whose upper boundary is an elastic sheet. A depth-averaged model in the frame of reference of the advancing air-liquid interface is used to investigate the steady and unsteady interface propagation modes via numerical simulation. In slightly collapsed channels, the steadily-propagating interface adopts a shape that is similar to the classic Saffman--Taylor finger in rigid Hele-Shaw cells. As the level of initial collapse increases the induced gradients in channel depth alter the morphology of the propagating finger and promote a variety of instabilities from tip-splitting to small-scale fingering on the curved interface, in qualitative agreement with experiments. The model has a complex solution structure with a wide range of stable and unstable, steady and time-periodic modes, many of which have similar driving pressures. We find good quantitative agreement between our model and the experimental data of Ducloué et al. (J. Fluid Mech. vol. 819, 2017, p 121) for the finger width, sheet profile and finger pressure, provided that corrections to account for the presence of liquid films on the upper and lower walls of the channel are included in the model.
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