论文标题
在Elasto-Rigid通道中对手指传播进行建模
Modelling finger propagation in elasto-rigid channels
论文作者
论文摘要
我们对两相融合结构的相互作用问题进行了理论研究，其中空气以恒定体积通量驱动到液体填充的Hele-Shaw通道，其上边界是弹性板。在前进的空气界面的参考框架中，深度平均模型用于通过数值模拟研究稳定且不稳定的界面传播模式。在略微崩溃的通道中，稳定传播的界面采用的形状与经典的Saffman-刚性Hele-Shaw细胞中的泰勒手指相似。随着初始崩溃的水平增加了通道深度的诱导梯度改变了传播手指的形态，并促进了各种不稳定性，从尖端切割到弯曲界面上的小规模指纹，与实验的定性一致。该模型具有复杂的解决方案结构，具有广泛的稳定且不稳定，稳定和时间周期模式，其中许多模式具有相似的驾驶压力。我们发现我们的模型与Ducloué等人的实验数据之间有很好的定量一致性。 （J. Fluid Mech。Vol。819，2017，p 121）对于手指宽度，薄板剖面和手指压力，规定在模型中包括校正以说明通道上壁和下壁上存在液体膜的校正。
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.
