Fingering instability in buoyancy-driven fluid-filled cracks

Théo Touvet (1) , Neil J. Balmforth (2, 3) , Richard V. Craster (4, 5) , Bruce R. Sutherland (6)

1 Département de Physique [ENS Lyon]
2 UBC Mathematics - Department of Mathematics [Vancouver]
3 EOS - Department of Earth and Ocean Sciences [Vancouver]
4 Department of Mathematics [Imperial College London]
5 Dpt of Mathematical and Statistical Sciences [Alberta]
6 Department of Physics [Edmonton]

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.

Keywords: fingering instability; magma and lava flow; thin films

Domains: Physics [physics]; Mechanics [physics]; Fluid mechanics [physics.class-ph]; Engineering Sciences [physics]; Mechanics [physics.med-ph]; Fluids mechanics [physics.class-ph]; Physics [physics]; Physics [physics]; Fluid Dynamics [physics.flu-dyn]; Physics [physics]; Physics [physics]; Geophysics [physics.geo-ph]; Sciences of the Universe [physics]; Earth Sciences; Geophysics [physics.geo-ph]; Sciences of the Universe [physics]; Earth Sciences; Volcanology; Environmental Sciences; Global Changes; Sciences of the Universe [physics]; Earth Sciences; Geomorphology

Théo Touvet, Neil J. Balmforth, Richard V. Craster, Bruce R. Sutherland. Fingering instability in buoyancy-driven fluid-filled cracks. Journal of Fluid Mechanics, 2011, 672, pp 60-77. ⟨10.1017/S0022112010005860⟩. ⟨ensl-00822596⟩