Abstract
Abstract
Highlights
The displacement of an interface between two Newtonian fluids driven through a narrow gap bounded by elastic walls is a fundamental two-phase fluid–structure interaction that occurs in many industrial, geophysical and biological processes (Juel, Pihler-Puzovic & Heil 2018)
In the absence of fluid inertia, the behaviour of the interface is determined by the interplay between the interfacial surface tension; the viscosities of the fluids; and the elastic properties of the wall
Elastic walls are not required to elicit complex behaviour; the Saffman–Taylor viscous fingering instability in a rigid Hele-Shaw channel, a channel whose width is much greater than its height (Saffman & Taylor 1958), is an exemplar of non-trivial interfacial dynamics
Summary
The displacement of an interface between two Newtonian fluids driven through a narrow gap bounded by elastic walls is a fundamental two-phase fluid–structure interaction that occurs in many industrial, geophysical and biological processes (Juel, Pihler-Puzovic & Heil 2018). If a more viscous fluid (oil) is displaced by a less viscous one (air) injected from one end of a rigid Hele-Shaw channel, an initially flat interface can exhibit multiple tips transiently, but a single symmetric finger emerges and propagates at constant speed (Saffman & Taylor 1958). In this geometry, the height of the channel’s cross-section is much smaller than its width and the flow within the channel can be effectively described using a depth-averaged theory. Further details of the implementation can be found in Pihler-Puzovicet al. (2014), Thompson et al (2014), Pihler-Puzovicet al. (2015) and more verification details are provided in appendix B
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