In this paper, a stress boundary condition at the interface between a porous medium saturated by a viscoelastic fluid and the free viscoelastic fluid is derived. The volume averages are used to upscale the problem. The boundary condition is obtained on the assumption that the free fluid stress is transferred partially to the fluid within the porous medium and partially to the solid skeleton. To this end the momentum balance on the solid skeleton saturated by the viscoelastic fluid is derived and a generalised Biot's equation is obtained, which is coupled with the generalised Brinkman's equation derived in Part I of the paper. They together state that the whole stress carried by the porous medium, sum of that of the fluid and that of the solid skeleton, is not dissipated. The boundary condition here derived does not show any stress jump and as in Part I, to emphasize the effect of elasticity, a second order fluid of Coleman and Noll is considered as viscoelastic fluid. Also the stress boundary condition at the interface between a homogeneous solid and the porous medium saturated by the viscoelastic fluid is obtained.

Modelling the flow of a second order fluid through and over a porous medium using the volume averages. II. The stress boundary condition

MINALE, Mario
2016

Abstract

In this paper, a stress boundary condition at the interface between a porous medium saturated by a viscoelastic fluid and the free viscoelastic fluid is derived. The volume averages are used to upscale the problem. The boundary condition is obtained on the assumption that the free fluid stress is transferred partially to the fluid within the porous medium and partially to the solid skeleton. To this end the momentum balance on the solid skeleton saturated by the viscoelastic fluid is derived and a generalised Biot's equation is obtained, which is coupled with the generalised Brinkman's equation derived in Part I of the paper. They together state that the whole stress carried by the porous medium, sum of that of the fluid and that of the solid skeleton, is not dissipated. The boundary condition here derived does not show any stress jump and as in Part I, to emphasize the effect of elasticity, a second order fluid of Coleman and Noll is considered as viscoelastic fluid. Also the stress boundary condition at the interface between a homogeneous solid and the porous medium saturated by the viscoelastic fluid is obtained.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11591/362446
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