Multiple finger propagation modes in Hele-Shaw channels of variable depth
Multiple finger propagation modes in Hele-Shaw channels of variable depth
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DOI：
10.1017/jfm.2014.100
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发表时间：
2014-03
影响因子：
3.7
通讯作者：
A. Thompson;A. Juel;A. Hazel
中科院分区：
文献类型：
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作者：
A. Thompson;A. Juel;A. Hazel
摘要我们考虑空气手指在具有空间变化的深度分布的宽广的充液通道中的传播。我们的目的是要了解之前在轴向均匀通道中观察到的多个共存的稳定和振荡传播手指家族的起源，每个都包含一个中心的阶梯状咬合。我们发现，深度平均模型可以再现实验中观察到的所有手指传播模式。此外，该模型还揭示了对称手指传播的新模式。在深度平均方程中包含空间可变的通道深度导致：(I)由于通道的粘性阻力的变化，流体区域内的可变迁移率系数；以及(Ii)动态边界条件中的可变横曲率项，其修改了气液界面上的压力跳跃。我们用我们的模型研究了这两种不同效应的作用，发现这两种效应都对稳态分叉结构有贡献，而横曲率项则是产生不同的振荡传播模式的原因。
Abstract We consider the propagation of an air finger into a wide fluid-filled channel with a spatially varying depth profile. Our aim is to understand the origin of the multiple coexisting families of both steady and oscillatory propagating fingers previously observed in experiments in axially uniform channels each containing a centred step-like occlusion. We find that a depth-averaged model can reproduce all the finger propagation modes observed experimentally. In addition, the model reveals new modes for symmetric finger propagation. The inclusion of a spatially variable channel depth in the depth-averaged equations leads to: (i) a variable mobility coefficient within the fluid domain due to variations in viscous resistance of the channel; and (ii) a variable transverse curvature term in the dynamic boundary condition that modifies the pressure jump over the air–liquid interface. We use our model to examine the roles of these two distinct effects and find that both contribute to the steady bifurcation structure, while the transverse curvature term is responsible for the distinctive oscillatory propagation modes.