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 is rarely addressed. Here, we present an experimental study of air displacing a viscous fluid within a collapsed, compliant channel-a model for pulmonary airway reopening. Air injected at a constant flow rate from one end of the liquid-filled, collapsed channel results in the propagation of a reopening finger. Depending on the imposed flow rate, we observe a wide variety of finger-tip morphologies, which occur persistently or evolve transiently as the finger propagates. Persistent fingers are stable in the sense that they propagate with approximately constant bubble pressure. We find that their pressure increases monotonically as a function of bubble speed along two disconnected lines. Although the line associated with higher bubble speed exhibits a minimum pressure value, the low-speed line supports finger propagation down to the smallest flow rates investigated. We present evidence that the lower and higher-speed fingers are dominated by viscous and elastic forces, respectively. We also find a range of bubble speeds separating the two pressure lines where no stable finger propagation is observed. Instead, complex transient dynamics leads to the long-term selection of stable fingers depending on initial conditions. The early transient evolution of these fingers is characterised by an increase in bubble pressure alongside a reduction in bubble speed. We hypothesise the existence of a weakly unstable, steady mode, which orchestrates the transient evolution of the finger towards either low-or high-speed modes of propagation.