Fluid-driven fingering instability of a confined elastic meniscus

¹ Cavendish Laboratory, University of Cambridge - JJ Thomson Ave, Cambridge, CB3 0HE, UK
² School of Engineering and Applied Sciences, Harvard University - Cambridge, MA 02138, USA
³ Department of Physics, Harvard University - Cambridge, MA 02138, USA

^(a) lm@seas.harvard.edu

Received: 3 December 2014
Accepted: 15 April 2015

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 B. et al., Phys. Rev. Lett., 111 (2013) 047801). 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 in both rectilinear and circular geometries, with predictions for the critical fluid pressure for fingering, and the finger wavelength. Our results are in good agreement with recent experimental observations of this elastic interfacial instability in a radial geometry. Our theory also shows that, perhaps surprisingly, this lateral-pressure–driven instability is analogous to a transverse-displacement–driven instability of the elastic layer. We verify these predictions by using non-linear 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.