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.
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
Origin : Publisher files allowed on an open archive
Loading...