Dynamics of front propagation in a compliant channel

Abstract

Front-propagating systems provide some of the most fundamental physical examples of interfacial instability and pattern formation. However, their nonlinear dynamics are rarely addressed. Here, we present an experimental study of air displacing a viscous fluid within a collapsed, compliant channel -a model system for pulmonary airway reopening. We show that compliance induces fingering instabilities absent in the rigid channel and we present the first experimental observations of the counter-intuitive 'pushing' behaviour previously predicted numerically, for which a reduction in air pressure results in faster flow. We find that pushing modes are unstable and moreover, that the dynamics of the air-fluid front involves a host of transient finger shapes over a significant range of experimental parameters.

Modelling finger propagation in elasto-rigid channels

“…the initial level of collapse increases), the profile steepens in the reopening region and the finger tip (x 1 = 0) is displaced towards the most collapsed region so that the volume of fluid ahead of the interface is reduced to a small wedge. These changes in the channel geometry near the finger tip are associated with a gradual reduction of the importance of viscous stresses relative to elastic stresses resulting in the development of an elastic peeling mode (Gaver, Samsel & Solway 1990;Gaver et al 1996) as A ∞ decreases, see also Peng et al (2015), Peng & Lister (2019) and Cuttle et al (2020).…”

“…Cuttle et al. (2020) also identified regions of non-trivial transient dynamics that suggested the existence of unstable states mediating the transition between different steadily propagating states.…”

“…Ducloué et al (2017a) conjectured that the small-scale fingers are analogous to those that develop during peeling of an adhesive strip (McEwan & Taylor 1966) and those seen in the printer's instability on an interface between two rotating rigid cylinders (Couder 2000). Cuttle, Pihler-Puzović & Juel (2020) investigated the behaviour of a strongly collapsed elasto-rigid channel experimentally and found a number of different finger morphologies whose geometric complexity increased with increasing propagation speed from simple Saffman-Taylor-like fingers to highly disordered interfaces with multiple tips that evolve continually in time. Cuttle et al (2020) also identified regions of non-trivial transient dynamics that suggested the existence of unstable states mediating the transition between different steadily propagating states.…”

A Review of One-Phase Hele-Shaw Flows and a Level-Set Method for Nonstandard Configurations

“…Since this experiment, numerous studies have been performed to generate further insight into how the taper angle influences viscous fingering [2,3,14,73,86,99]. Other popular physical alterations to the Hele-Shaw cell include uniformly separating the plates in time [43,44,83,100,122,133,143], rotating the entire Hele-Shaw cell at a given angular velocity [5,17,43,119], or replacing one of the plates with an elastic membrane [1,32,48,85,89,[108][109][110][111]. All of these configurations have been shown to produce patterns distinct from traditional Saffman-Taylor fingering.…”

A review of one-phase Hele-Shaw flows and a level-set method for non-standard configurations

“…Since this experiment, numerous studies have been performed to give further insight into how the taper angle influences viscous fingering [1,2,13,69,93]. Other popular physical alterations to the Hele-Shaw cell include uniformly separating the plates in time [42,78,94,116,127,135], rotating the entire Hele-Shaw cell at a given angular velocity [7,16,113], or replacing one of the plates with an elastic membrane [3,31,80,83,[102][103][104][105]. All of these configurations have been shown to produce patterns distinct from traditional Saffman-Taylor fingering.…”