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Fingering instability in buoyancy-driven fluid-filled cracks

  • T. TOUVET (a1), N. J. BALMFORTH (a2) (a3), R. V. CRASTER (a4) (a5) and B. R. SUTHERLAND (a6)

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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Corresponding author

Email address for correspondence: r.craster@imperial.ac.uk or theo.touvet@ens-lyon.org

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Present address: Département de Mécanique, École Polytechnique, 91128 Palaiseau CEDEX, France.

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References

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