Bubble propagation in Hele-Shaw channels with centred constrictions
Bubble propagation in Hele-Shaw channels with centred constrictions
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DOI：
10.1088/1873-7005/aaa5cf
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发表时间：
2018-04-01
影响因子：
1.5
通讯作者：
Juel, Anne
中科院分区：
文献类型：
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作者：
Franco-Gomez, Andres;Thompson, Alice B.;Juel, Anne
我们研究了Hele-Shaw通道中有限气泡的传播，其中引入了中心闭塞（称为铁路）以提供小的轴向均匀深度收缩。对于宽到足以跨越通道的气泡，系统的行为类似于半无限指状物的行为，并且对称静态解是稳定的。在这里，我们专注于更小的气泡，在这种情况下，对称静态解决方案是不稳定的，静态气泡被转移到轨道两侧的通道的更深的区域之一。使用深度平均模型的实验和数值模拟相结合，我们表明，气泡轴向传播，由于一个小的施加流速可以稳定在一个稳定的对称模式中心的铁路通过稳定的粘性力和不稳定的表面张力之间的微妙的相互作用。然而，对于足够大的毛细管数Ca，粘性力与表面张力的比率，粘性力又变得不稳定，从而使气泡返回到偏心传播状态。随着气泡尺寸的减小，稳定的中心传播是稳定的Ca的范围减小，并最终消失，通过两个超临界干草叉分叉的合并。深度平均模型被发现准确地预测实验观察到的所有稳定的传播模式，并提供了一个全面的图片的基本稳定的分叉结构。然而，对于足够大的施加流速，我们发现，最初集中的气泡不收敛到一个稳定的传播模式。相反，它们会短暂地探索弱不稳定的稳定模式，这种演变导致它们分裂并最终进入拓扑结构变化的稳定传播状态。
We study the propagation of finite bubbles in a Hele-Shaw channel, where a centred occlusion (termed a rail) is introduced to provide a small axially uniform depth constriction. For bubbles wide enough to span the channel, the system's behaviour is similar to that of semi-infinite fingers and a symmetric static solution is stable. Here, we focus on smaller bubbles, in which case the symmetric static solution is unstable and the static bubble is displaced towards one of the deeper regions of the channel on either side of the rail. Using a combination of experiments and numerical simulations of a depth-averaged model, we show that a bubble propagating axially due to a small imposed flow rate can be stabilised in a steady symmetric mode centred on the rail through a subtle interaction between stabilising viscous forces and destabilising surface tension forces. However, for sufficiently large capillary numbers Ca, the ratio of viscous to surface tension forces, viscous forces in turn become destabilising thus returning the bubble to an off-centred propagation regime. With decreasing bubble size, the range of Ca for which steady centred propagation is stable decreases, and eventually vanishes through the coalescence of two supercritical pitchfork bifurcations. The depth-averaged model is found to accurately predict all the steady modes of propagation observed experimentally, and provides a comprehensive picture of the underlying steady bifurcation structure. However, for sufficiently large imposed flow rates, we find that initially centred bubbles do not converge onto a steady mode of propagation. Instead they transiently explore weakly unstable steady modes, an evolution which results in their break-up and eventual settling into a steady propagating state of changed topology.