TY - JOUR
T1 - Peeling fingers in an elastic Hele-Shaw channel
AU - Fontana, J. V.
AU - Cuttle, C.
AU - Pihler-Puzovic, D.
AU - Hazel, A. L.
AU - Juel, A.
N1 - Publisher Copyright:
© The Author(s), 2024. Published by Cambridge University Press.
PY - 2024/4/16
Y1 - 2024/4/16
N2 - 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 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a measure of the viscous contribution to finger propagation, we identify a threshold beyond which viscous forces are superseded by elastic effects.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 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 that 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 evolve continually, 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, but that it does not provide sufficient information to predict the transition to unsteady dynamics that appears strongly nonlinear.
AB - 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 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 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 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 that 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 evolve continually, 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, but that it does not provide sufficient information to predict the transition to unsteady dynamics that appears strongly nonlinear.
KW - Fingering instability
KW - Hele-Shaw flows
KW - flow–vessel interactions
U2 - 10.1017/jfm.2024.210
DO - 10.1017/jfm.2024.210
M3 - Article
SN - 0022-1120
VL - 985
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
ER -