Viscous fingering and dendritic growth under an elastic membrane

TL;DR

This paper studies how viscous fingering patterns form and evolve in an elastic membrane system, revealing how wall inclination influences pattern amplitude and providing insights into nonlinear saturation mechanisms.

Contribution

It introduces a novel experimental setup to analyze viscous fingering in compliant channels and uncovers the relationship between membrane inclination and pattern amplitude.

Findings

Wavelength is determined by viscous fingering mechanism.

Pattern amplitude inversely related to wall inclination angle.

Axial and transverse depth gradients lead to new pattern formations.

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.