Viscous fingering and dendritic growth under an elastic membrane

Abstract

We investigate the viscous fingering instability that arises when air is injected from the end of an oil-filled, compliant channel. We show that induced axial and transverse depth gradients foster novel pattern formation. Moreover, the steady propagation of the interface allows us to elucidate the nonlinear saturation of a fingering pattern first observed in a time-evolving system (Pihler-Puzovic et al. PRL 108, 074502, 2012): the wavelength is set by the viscous fingering mechanism, but the amplitude is inversely proportional to the tangent of the compliant wall's inclination angle.

References in corpus (3)

• Fingering versus stability in the limit of zero interfacial tension
• Excess wing in glass-forming glycerol and LiCl-glycerol mixtures detected by neutron scattering
• Reopening modes of a collapsed elasto-rigid channel

Cited by in corpus (6)

• Numerical investigation of controlling interfacial instabilities in non-standard Hele-Shaw configurations
• The engulfment of aqueous droplets on perfectly wetting oil layers
• Modelling finger propagation in elasto-rigid channels
• Growth morphology and symmetry selection of interfacial instabilities in anisotropic environments
• Intermittent air invasion in pervaporating compliant microchannels
• Dynamics of front propagation in a compliant channel