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Fingering instability in buoyancy-driven fluid-filled cracks

Published online by Cambridge University Press:  24 February 2011

T. TOUVET ,
N. J. BALMFORTH ,
R. V. CRASTER  and
B. R. SUTHERLAND
T. TOUVET
Affiliation:
Département de Physique, École Normale Supérieure de Lyon, Université de Lyon, 46 allée d'Italie, 69364 Lyon CEDEX 07, France
N. J. BALMFORTH
Affiliation:
Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC V6T 1Z2, Canada Department of Earth and Ocean Science, University of British Columbia, 6339 Stores Road, Vancouver, BC V6T 1Z4, Canada
R. V. CRASTER*
Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, T6G 2G1, Canada Department of Mathematics, Imperial College London, South Kensington, London SW7 2AZ, UK
B. R. SUTHERLAND
Affiliation:
Department of Physics, University of Alberta, Edmonton, T6G 2G1, Canada
*
‡Email address for correspondence: r.craster@imperial.ac.uk or theo.touvet@ens-lyon.org
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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.

JFM classification

Interfacial Flows (free surface): Fingering instability Geophysical and Geological Flows: Magma and lava flow Interfacial Flows (free surface): Thin films

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 672 , 10 April 2011 , pp. 60 - 77
Copyright
Copyright © Cambridge University Press 2011

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Footnotes

†

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

References

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