Fluid driven fingering instability of a confined elastic meniscus

TL;DR

This paper develops an asymptotic theory to explain fluid-driven fingering instability in confined elastic layers, predicting critical pressure and finger wavelength, and links it to elastic stretching transitions, validated by finite-element simulations.

Contribution

The paper introduces a theoretical framework for elastic fingering instability, connecting fluid pressure and elastic stretching, supported by simulations and experimental observations.

Findings

Fingering transition is first-order and bistable.

Predicted critical pressure matches experimental data.

Theory links fluid-driven and stretch-driven fingering mechanisms.

Abstract

When a fluid is pumped into a cavity in a confined elastic layer, at a critical pressure, destabilizing fingers of fluid invade the elastic solid along its meniscus (Saintyves, Dauchot, and Bouchaud, 2013). These fingers occur without fracture or loss of adhesion and are reversible, disappearing when the pressure is decreased. We develop an asymptotic theory of pressurized highly elastic layers trapped between rigid bodies to explain these observations, with predictions for the critical fluid pressure for fingering, and the finger wavelength. We also show that the theory links this fluid-driven fingering with a similar transition driven instead by transverse stretching of the elastic layer. We further verify these predictions by using finite-element simulations on the two systems which show that, in both cases, the fingering transition is first-order (sudden) and hence has a region of bistability. Our predictions are in good agreement with recent observations of this elastic analog of the classical Saffman-Taylor interfacial instability in hydrodynamics.