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.
Highlights
Morphological growth ranging from tumour angiogenesis (Giverso & Ciarletta 2016) and growth (Brú et al 2003), to bacterial colonies (Golding et al 1998) and electrodeposition (Schneider et al 2017) is susceptible to interfacial instabilities which can lead to pattern formation and the emergence of disordered dynamics (Couder 2000)
The experiments revealed a wide variety of finger morphologies, depending on the value of the flow rate, which either persisted or evolved over the region of interest (ROI)
We plot with cyan triangles the bubble pressure pB of all the persistent fingers as a function of the non-dimensional bubble speed Ca
Summary
Morphological growth ranging from tumour angiogenesis (Giverso & Ciarletta 2016) and growth (Brú et al 2003), to bacterial colonies (Golding et al 1998) and electrodeposition (Schneider et al 2017) is susceptible to interfacial instabilities which can lead to pattern formation and the emergence of disordered dynamics (Couder 2000). When the flow is confined to a rectangular channel, a single steady mode of propagation is observed: a finger of air, symmetric about the centreline of the channel, which evolves from initially planar fronts (Saffman & Taylor 1958). Beyond a threshold value of the driving parameter that depends on the roughness of the channel, this finger becomes unstable to tip splitting and side branching, leading to the emergence of complex patterns (Tabeling, Zocchi & Libchaber 1987; Moore et al 2002). As the steady solution is found to be linearly stable at all computed flow rates (Bensimon 1986), any further instabilities observed must arise subcritically; that is, they result from finite-amplitude perturbations which drive the system away from equilibrium
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