Using experiments and a depth-averaged numerical model, we study
instabilities of two-phase flows in a Hele-Shaw channel with an elastic upper
boundary and a non-uniform cross-section prescribed by initial collapse.
Experimentally, we find increasingly complex and unsteady modes of air-finger
propagation as the dimensionless bubble speed, Ca, and level of collapse are
increased, including pointed fingers, indented fingers and the feathered modes
first identified by Cuttle et al.(J. Fluid Mech., vol. 886, 2020, A20).
By introducing a measure of the viscous contribution to finger propagation,
we identify a Ca threshold beyond which viscous forces are superseded by
elastic effects. Quantitative prediction of this transition between 'viscous'
and 'elastic' reopening regimes across levels of collapse establishes the
fidelity of the numerical model. In the viscous regime, we recover the
non-monotonic dependence on Ca of the finger pressure, which is characteristic
of benchtop models of airway reopening. To explore the elastic regime
numerically, we extend the depth-averaged model introduced by Fontana et al.
(J. Fluid Mech., vol. 916, 2021, A27) to include an artificial disjoining
pressure which prevents the unphysical self-intersection of the interface.
Using time simulations, we capture for the first time the majority of
experimental finger dynamics, including feathered modes. We show that these
disordered states continually evolve, with no evidence of convergence to steady
or periodic states. We find that the steady bifurcation structure
satisfactorily predicts the bubble pressure as a function of Ca, but that it
does not provide sufficient information to predict the transition to unsteady
dynamics which appears strongly nonlinear.Comment: 28 pages, 15 figure