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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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Théo Touvet, Neil J. Balmforth, Richard V. Craster, Bruce R. 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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