We consider the motion of shallow two-dimensional gravity currents of a purely viscous and relatively heavy power-law fluid of flow behavior index n in a uniform saturated porous layer above a horizontal impermeable boundary, driven by the release from a point source of a volume of fluid increasing with time like t^alpha. The equation of motion for power-law fluids in porous media is a modified Darcy’s law taking into account the nonlinearity of the rheological equation. Coupling the flow law with the mass balance equation yields a nonlinear differential problem which admits a self-similar solution describing the shape of the current, which spreads like t^((alpha+n )/(2+n)), generalizing earlier results for Newtonian fluids. For the particular values alpha = 0 and 2, closed-form solutions are derived; else, a numerical integration is required; the numerical scheme is tested against the analytical solutions. Two additional analytical approximations, valid for any alpha, are presented. The space-time development of the gravity current is discussed for different flow behavior indexes.

Similarity solutions for spreading of a two-dimensional non-Newtonian gravity current in a porous layer

DI FEDERICO, VITTORIO;ARCHETTI, RENATA;
2012

Abstract

We consider the motion of shallow two-dimensional gravity currents of a purely viscous and relatively heavy power-law fluid of flow behavior index n in a uniform saturated porous layer above a horizontal impermeable boundary, driven by the release from a point source of a volume of fluid increasing with time like t^alpha. The equation of motion for power-law fluids in porous media is a modified Darcy’s law taking into account the nonlinearity of the rheological equation. Coupling the flow law with the mass balance equation yields a nonlinear differential problem which admits a self-similar solution describing the shape of the current, which spreads like t^((alpha+n )/(2+n)), generalizing earlier results for Newtonian fluids. For the particular values alpha = 0 and 2, closed-form solutions are derived; else, a numerical integration is required; the numerical scheme is tested against the analytical solutions. Two additional analytical approximations, valid for any alpha, are presented. The space-time development of the gravity current is discussed for different flow behavior indexes.
2012
V. Di Federico; R. Archetti; S. Longo
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/116319
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