A novel formulation for the boundary conditions to be applied at a porous surface is proposed. Interfaces between porous and clear media and porous and solid media are considered. The well known Beavers & Joseph boundary condition is applicable for interfaces betweeen porous and clear media. An equivalent boundary condition is obtained for interfaces between porous and impermeable media, namely v_n = sqrt(k) nabla_t v_t, where v is the velocity field inside the porous medium, the subscripts n and t refer to components normal and tangential to the interface, respectively, while k stands for the permeability. A sample problem is solved for the flow fields exterior to a porous spherical particle and interior to it, assuming that the particle has a rigid concentric core and that the submerging flow field is Newtonian, Stokesian and uniform at infinity. Both Brinkman's equation and Darcy's law are utilized to obtain general forms of the velocity and pressure fiels. Comparison of the two solutions yields the desired boundary conditions applicable to the Darcy problem.

Boundary Conditions for Darcy's Flow through Porous Media

MAURI, ROBERTO
1983

Abstract

A novel formulation for the boundary conditions to be applied at a porous surface is proposed. Interfaces between porous and clear media and porous and solid media are considered. The well known Beavers & Joseph boundary condition is applicable for interfaces betweeen porous and clear media. An equivalent boundary condition is obtained for interfaces between porous and impermeable media, namely v_n = sqrt(k) nabla_t v_t, where v is the velocity field inside the porous medium, the subscripts n and t refer to components normal and tangential to the interface, respectively, while k stands for the permeability. A sample problem is solved for the flow fields exterior to a porous spherical particle and interior to it, assuming that the particle has a rigid concentric core and that the submerging flow field is Newtonian, Stokesian and uniform at infinity. Both Brinkman's equation and Darcy's law are utilized to obtain general forms of the velocity and pressure fiels. Comparison of the two solutions yields the desired boundary conditions applicable to the Darcy problem.
Haber, S; Mauri, Roberto
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/7558
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