Abstract
The compatibility conditions matching macroscopic mechanical fields at the contact surface between fluid-saturated porous solid and adjacent bulk fluid are considered. Special attention is paid to the derivation of conditions for tangential components of the fluid flow velocities and to the verification of validity of the condition postulated by Beavers and Joseph. It has been shown that at the contact surface between two media, a dissipation of mechanical energy due to the fluid viscosity does exist and thus the form of a dissipation function has been proposed. It has been proven that this relation determines the form of two linear compatibility conditions derived for the tangential components of the relative fluid velocities and that these conditions describe the experimental results more precisely than the condition postulated by Beavers and Joseph.
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Ateshian, G. A.: 1997, A theoretical formulation for boundary friction in articular cartilage, J. Biomech. Engng. 119, 81-86.
Bear, J. and Bahmat, Y.: 1984, Transport phenomena in porous media basic equation, In: J. Bear and M. Y. Corapcioglu (eds), Fundamentals of Transport Phenomena in Porous Media, Martinus Nijhoff, Dordrecht, pp. 5-61.
Biot, M. A.: 1956, Theory of propagation of elastic waves in a fluid saturated porous solid, J. Acoust. Soc. Am. 28(2), 168-191.
Beavers, G. S. and Joseph, D. D.: 1967, Boundary conditions at a naturally permeable wall, J. Fluid. Mech. 30, 197-207.
Brinkman, H. C.: 1947, A calculation of the viscous force exerted by a flowing fluid on a dense swarm of Particles, Appl. Sci. Res. A 1, 27-34.
Cieszko, M. and Kubik, J.: 1993, On the compatibility conditions in the fluid-fluid saturated porous solid contact problems, Arch. Mech. 45(1), 77-91.
Cieszko, M. and Kubik, J.: 1996a, Constitutive relations and internal equilibrium condition for fluid-saturated porous solid. Nonlinear theory, Arch. Mech. 48(5), 893-910.
Cieszko, M. and Kubik, J.: 1996b, Constitutive relations and internal equilibrium condition for fluid-saturated porous solid. Linear description, Arch. Mech. 48(5), 911-923.
Gogete, G. R. and Munjal, M. L.: 1996, Sound propagation in ducts with bulk reacting lining in the presence of laminar mean flow, J. Acoust. Soc. Am. 99(3), 1779-1782.
Hou, J. S., Holmes, M. H., Lai, W. H. and Mow, V. C.: 1989, Boundary conditions at the cartilage-synovial fluid interface for joint lubrication and theoretical verifications, J. Biomech. Engng. 111, 78-87.
Hutter, K., Johnk, K. and Svendsen, B.: 1994, On interfacial transition conditions in two phase gravity flow, ZAMP 45, 746-762.
Johnson, D. L.: 1986, Recent developments in the acoustic properties of porous media, In: Frontiers in Physical Acoustics, XCIII Corso, Soc. Italiana di Fisica Bologna.
Joseph, D. D. and Tao, L. N.: 1966, Lubrication of a porous bearing Stockes' solution, J. Appl. Mech. 33, 753-760.
Koplik, J., Levine, H. and See, A.: 1983, Viscosity renormalization in the Brinkman equation, Phys. Fluids 26, 10.
Kubik, J.: 1986a, On the internal coupling in dynamic equations of fluid-saturated porous solid, Int. J. Engng. Sci. 24(6), 981-989.
Kubik, J.: 1986b, A macroscopic description of geometrical pore structure of porous solid, Int. J. Engng. Sci. 24(6) 971-980.
Kubik, J.: 1992, Pore structure in dynamic behaviour of saturated materials, Transport in Porous Media 9, 15-24
Landau, D. D. and Lifshitz E. M.: 1986, Hydromechanics (in Russian), Nauka, Moskva.
Leigh, D. C.: 1968, Nonlinear Continuum Mechanics, McGraw-Hill, New York.
Levy, T. and Sanchez-Palencia, E.: 1975, On the boundary conditions for fluid flowin porous media, Int. J. Engng. Sci. 13, 923-940.
Raats, R. A. C.: 1972, The role of inertia in the hydrodynamics of porous media, J. Rational Mech. Anal. 44, 267-280.
Rhodes, C. A. and Rouleau, W. T.: 1966, Hydrodynamic lubrication of partial porous metal bearings, J. Basic Engng. Trans. ASME D 88(1), 53-60.
Richardson, S.: 1971, A model for the boundary condition of porous material, Part II, J. Fluid Mech. 49, 327-336.
Saffman, P. G.: 1971, On the boundary condition at the surface of a porous medium, Studies in Appl. Mech. L 2, 93-101.
Shir, C. C. and Joseph, D. D.: 1966, Lubrication of a porous bearing Reynolds' solution, J. Appl. Mech. 33, 761-767.
Taylor, G. I.: 1971, A model for the boundary condition of a porous material, Part I, J. Fluid Mech. 49, 319-326.
Wilmanski, K.: 1985, Phenomenological thermodynamics, In: Engineering Mechanics, Vol. 1, Foundations of Mechanics (in Polish), PWN, Warsaw.
Wilmanski, K.: 1995, Lagrangian model of two-phase porous material, J. Non-Equil. Thermodyn. 20, 50-77.
Wu, T., Johnk, K., Svendsen, B. and Hutter, K.: 1996, On the gravity-driven shear flow of an ice-till mixture, Ann. of Glaciol. 23, 124-128.
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Cieszko, M., Kubik, J. Derivation of Matching Conditions at the Contact Surface Between Fluid-Saturated Porous Solid and Bulk Fluid. Transport in Porous Media 34, 319–336 (1999). https://doi.org/10.1023/A:1006590215455
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DOI: https://doi.org/10.1023/A:1006590215455