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Fingering instability in buoyancy-driven fluid-filled cracks

Abstract : The stability of buoyancy-driven propagation of a fluid-filled crack through an elastic solid is studied using a combination of theory and experiments. For the theory, the lubrication approximation is introduced for fluid flow, and the surrounding solid is described by linear elasticity. Solutions are then constructed for a planar fluid front driven by either constant flux or constant volume propagating down a pre-cut conduit. As the thickness of the pre-cut conduit approaches zero, it is shown how these fronts converge to zero-toughness fracture solutions with a genuine crack tip. The linear stability of the planar solutions towards transverse, finger-like perturbations is then examined. Instabilities are detected that are analogous to those operating in the surface-tension-driven fingering of advancing fluid contact lines. Experiments are conducted using a block of gelatin for the solid and golden syrup for the fluid. Again, planar cracks initiated by emplacing the syrup above a shallow cut on the surface of the gelatin develop transverse, finger-like structures as they descend. Potential geological applications are discussed.
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Submitted on : Wednesday, May 15, 2013 - 1:06:54 AM
Last modification on : Tuesday, January 18, 2022 - 2:26:04 PM
Long-term archiving on: : Monday, August 19, 2013 - 4:06:00 PM

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Théo Touvet, Neil Balmforth, Richard Craster, Bruce Sutherland. Fingering instability in buoyancy-driven fluid-filled cracks. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2011, 672, pp 60-77. ⟨10.1017/S0022112010005860⟩. ⟨ensl-00822596⟩

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