Coutinho Írio M, Miranda José A
Departamento de Física, Universidade Federal de Pernambuco, CCEN, Recife, Pernambuco 50670-901, Brazil.
Phys Rev E. 2023 Aug;108(2-2):025104. doi: 10.1103/PhysRevE.108.025104.
The lifting Hele-Shaw cell setup is a popular modification of the classic, fixed-gap, radial viscous fingering problem. In the lifting cell configuration, the upper cell plate is lifted such that a more viscous inner fluid is invaded by an inward-moving outer fluid. As the fluid-fluid interface contracts, one observes the rising of distinctive patterns in which penetrating fingers having rounded tips compete among themselves, reaching different lengths. Despite the scholarly and practical relevance of this confined lifting flow problem, the impact of interfacial rheology effects on its pattern-forming dynamics has been overlooked. Authors of recent studies on the traditional injection-induced radial Hele-Shaw flow and its centrifugally driven variant have shown that, if the fluid-fluid interface is structured (i.e., laden with surfactants, particles, proteins, or other surface-active entities), surface rheological stresses start to act, influencing the development of the viscous fingering patterns. In this paper, we investigate how interfacial rheology affects the stability as well as the shape of the emerging fingered structures in lifting Hele-Shaw flows, at linear and early nonlinear dynamic stages. We tackle the problem by utilizing the Boussinesq-Scriven model to describe the interface and by employing a perturbative mode-coupling scheme. Our linear stability results show that interfacial rheology effects destabilize the interface. Furthermore, our second-order findings indicate that interfacial rheology significantly alters intrinsically nonlinear morphological features of the shrinking interface, inducing the formation of narrow sharp-tip penetrating fingers and favoring enhanced competition among them.
提升式Hele-Shaw细胞装置是经典的固定间隙径向粘性指进问题的一种流行变体。在提升式细胞配置中，上细胞板被提升，使得更粘稠的内部流体被向内流动的外部流体侵入。随着流体-流体界面收缩，人们观察到独特图案的上升，其中具有圆形尖端的穿透指状物相互竞争，达到不同的长度。尽管这个受限提升流问题在学术和实际应用中都具有相关性，但界面流变学效应对其图案形成动力学的影响却被忽视了。最近关于传统注射诱导的径向Hele-Shaw流及其离心驱动变体的研究作者表明，如果流体-流体界面是结构化的（即负载有表面活性剂、颗粒、蛋白质或其他表面活性物质），表面流变应力就会开始起作用，影响粘性指进图案的发展。在本文中，我们研究了在线性和早期非线性动态阶段，界面流变学如何影响提升式Hele-Shaw流中出现的指状结构的稳定性和形状。我们通过利用Boussinesq-Scriven模型来描述界面，并采用微扰模式耦合方案来解决这个问题。我们的线性稳定性结果表明，界面流变学效应使界面失稳。此外，我们的二阶结果表明，界面流变学显著改变了收缩界面固有的非线性形态特征，诱导形成狭窄的尖顶穿透指状物，并促进它们之间增强的竞争。
