The life and fate of a bubble in a geometrically perturbed Hele-Shaw channel
The life and fate of a bubble in a geometrically perturbed Hele-Shaw channel
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DOI：
10.1017/jfm.2020.844
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发表时间：
2021-03-05
影响因子：
3.7
通讯作者：
Juel, Anne
中科院分区：
文献类型：
--
作者：
Gaillard, Antoine;Keeler, Jack S.;Juel, Anne
出于了解流体流动中复杂瞬态行为的愿望，我们研究了由具有中心深度扰动的 Hele-Shaw 通道内悬浮粘性流体的稳态运动驱动的气泡动力学。通过实验和深度平均模型的数值模拟，我们研究了规定体积的初始居中气泡随流速和初始形状的变化。这些实验展示了丰富多样的有组织的瞬态动力学，包括气泡破裂以及相互作用的相邻气泡的聚集和合并。长期结果是单个气泡或多个分离的气泡，按照速度递增的顺序沿着通道定位。在中等流速下，气泡的寿命和命运是可再现的，并且可以通过参数平面的简单连接区域中发生的少量特征行为进行分类。增加流速会导致时间演变的可重复性降低，同时对通道中的初始条件和扰动的敏感性增加。人们发现，允许分解和聚结的时间相关数值模拟可以重现实验观察到的大部分动力学行为，包括在高流速下增强的灵敏度。该系统的一个不寻常的特征是，稳定和周期性解集可以在时间演化过程中发生变化，因为气泡的数量及其尺寸分布都会因破裂和合并事件而演化。对单气泡和双气泡情况下的稳定和不稳定解的计算表明，瞬态动力学是由系统的弱不稳定解精心策划的，这些解会随着气泡数量的变化而出现和消失。
Motivated by the desire to understand complex transient behaviour in fluid flows, we study the dynamics of an air bubble driven by the steady motion of a suspending viscous fluid within a Hele-Shaw channel with a centred depth perturbation. Using both experiments and numerical simulations of a depth-averaged model, we investigate the evolution of an initially centred bubble of prescribed volume as a function of flow rate and initial shape. The experiments exhibit a rich variety of organised transient dynamics, involving bubble breakup as well as aggregation and coalescence of interacting neighbouring bubbles. The long-term outcome is either a single bubble or multiple separating bubbles, positioned along the channel in order of increasing velocity. Up to moderate flow rates, the life and fate of the bubble are reproducible and can be categorised by a small number of characteristic behaviours that occur in simply connected regions of the parameter plane. Increasing the flow rate leads to less reproducible time evolutions with increasing sensitivity to initial conditions and perturbations in the channel. Time-dependent numerical simulations that allow for breakup and coalescence are found to reproduce most of the dynamical behaviour observed experimentally, including enhanced sensitivity at high flow rate. An unusual feature of this system is that the set of steady and periodic solutions can change during temporal evolution because both the number of bubbles and their size distribution evolve due to breakup and coalescence events. Calculation of stable and unstable solutions in the single- and two-bubble cases reveals that the transient dynamics is orchestrated by weakly unstable solutions of the system that can appear and disappear as the number of bubbles changes.