Controlling fingering instabilities in Hele-Shaw flows in the presence of wetting film effects
Controlling fingering instabilities in Hele-Shaw flows in the presence of wetting film effects
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DOI：
10.1103/physreve.103.063105
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发表时间：
2021-06-11
影响因子：
2.4
通讯作者：
Li, Shuwang
中科院分区：
文献类型：
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作者：
Anjos, Pedro H. A.;Zhao, Meng;Li, Shuwang
本文研究了Hele-Shaw腔体受限几何中两种不相容粘性流体之间的界面运动。通过引入对界面速度的非线性依赖关系，我们考虑了驱替流体后面的薄润湿膜对流体-流体界面压降的动态影响。在这个框架中，分析了两种有趣的情况：注入驱动流动(膨胀演化)和升力板流(收缩演化)。特别是，我们研究了当考虑润湿效应时，控制这两种不同的Hele-Shaw装置中指法不稳定性发展的可能性。利用线性稳定性理论，求出了合适的随时间变化的注入速率Q(T)和随时间变化的举升速度。B(T)分别控制扩张进化和收缩进化过程中出现的指数。我们的结果表明，与非润湿策略相比，考虑润湿会导致q(T)[和b(T)]的大小增加。此外，利用频谱精确的边界积分方法在动力学的完全非线性区域检验了控制协议的有效性和有效性，并证实了所提出的注入和提升格式是在有润膜存在的情况下描述所产生图案的形态的可行策略。
In this paper, the interfacial motion between two immiscible viscous fluids in the confined geometry of a Hele-Shaw cell is studied. We consider the influence of a thin wetting film trailing behind the displaced fluid, which dynamically affects the pressure drop at the fluid-fluid interface by introducing a nonlinear dependence on the interfacial velocity. In this framework, two cases of interest are analyzed: The injection-driven flow (expanding evolution), and the lifting plate flow (shrinking evolution). In particular, we investigate the possibility of controlling the development of fingering instabilities in these two different Hele-Shaw setups when wetting effects are taken into account. By employing linear stability theory, we find the proper time-dependent injection rate Q(t) and the time-dependent lifting speed. b (t) required to control the number of emerging fingers during the expanding and shrinking evolution, respectively. Our results indicate that the consideration of wetting leads to an increase in the magnitude of Q(t) [and b(t)] in comparison to the nonwetting strategy. Moreover, a spectrally accurate boundary integral approach is utilized to examine the validity and effectiveness of the controlling protocols at the fully nonlinear regime of the dynamics and confirms that the proposed injection and lifting schemes are feasible strategies to prescribe the morphologies of the resulting patterns in the presence of the wetting film.