Abstract
Boundary conditions are derived to represent the continuity requirements at the boundaries of a porous solid saturated with viscous fluid. They are derived from the physically grounded principles with a mathematical check on the conservation of energy. The poroelastic solid is a dissipative one for the presence of viscosity in the interstitial fluid. The dissipative stresses due to the viscosity of pore-fluid are well represented in the boundary conditions. The unequal particle motions of two constituents of porous aggregate at a boundary between two solids are explained in terms of the drainage of pore-fluid leading to imperfect bonding. A mathematical model is derived for the partial connection of surface pores at the porous-porous interface. At this interface, the loose-contact slipping and partial pore opening/connection may dissipate a part of strain energy. A numerical example shows that, at the interface between water and oil-saturated sandstone, the modified boundary conditions do affect the energies of the waves refracting into the isotropic porous medium.
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Communicated by Zhe-wei ZHOU
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Sharma, M.D. Boundary conditions for porous solids saturated with viscous fluid. Appl. Math. Mech.-Engl. Ed. 30, 821–832 (2009). https://doi.org/10.1007/s10483-009-0702-6
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DOI: https://doi.org/10.1007/s10483-009-0702-6