Abstract
The propagation of small perturbation in a gas filled porous matrix is investigated. The skeleton is supposed rigid and governed by the energy balance equation, where the heat exchanged between the two phases is taken into account. The Boltzmann equation is written for the gas where the integrals of the collisions between gas and solid particles are evaluated as those for the particles of a mixture. Different choices of the time and space scales lead to models equations which hold for different rarefaction regimes. The wave propagation characteristics are then dealt with in various situations.
Similar content being viewed by others
References
Bear, J.: 1972, Dynamics of Fluids in Porous Media, par. 1.3 and 5.3, Elsevier, New York.
Biot, M. A.: 1956a, Theory of propagation of elastic waves in fluid-saturated porous solid. I. Lowfrequency range, J. Acoust. Soc. Am. 28, 168–178.
Biot, M. A.: 1956b, Theory of propagation of elastic waves in fluid-saturated porous solid. II. Higher frequency range, J. Acoust. Soc. Am. 28, 179–191.
Bowen, R. M.: 1976, Theory of mixtures, In: A. C. Eringen (ed.), Continuum Physics. III. Mixtures and Elastic Medium Field Theories, Academic Press, New York.
Bowen, R. M.: 1982, Compressible porous media models by use of the theory of mixtures, Int. J. Eng. Sci. 6, 697–735.
Cercignani, C.: 2000, Rarefied Gas Dynamics, Cambridge Texts in Applied Mathematics, Cambridge University Press, London, p. 129ff.
Cercignani, C., Illner, R. and Pulvirenti, M.: 1994, The mathematical theory of dilute gases, In: Applied Mathematical Sciences, Vol. 106, Springer, New York, p. 312ff.
De Boer, R.: 1998, Theory of porous media – past and present, ZAMM 78, 441–466.
de Socio, L. M. and Ianiro, N.: 1995, Hydrodynamics of a model gas in a slab, Math. Mod. Meth. Appl. Sci. 5, 335–349.
de Socio, L. M., Ianiro, N. and Marino, L.: 2001, A model for the compressible flow through a porous medium, Math. Mod. Meth. Appl. Sci. 11, 1273–1283.
Degond, P. and Lucquin-Desreux, B.: 1996, Transport coefficients of plasmas and disparate mass binary gases, Trans. Theory Stat. Phys. 25, 595–633.
Esposito, R., Lebowitz, J. L. and Marra, R.: 1999, On the derivation of hydrodynamics from the Boltzmann equation, Phys. Fluids 11, 2354–2366.
Foch, J. and Ford, G. W.: 1970, The dispersion of sound in monoatomic gases, In: J. De Boer and G. E. Uhlenbeck (eds), Studies in Statistical Mechanics, Vol. 5, North-Holland, Amsterdam.
Ianiro, N. and Triolo, L.: 1988, Stationary Boltzmann equation for a degenerate gas in a slab: boundary value problem and hydrodynamics, J. Stat. Phys. 51, 677–690.
Lachowicz, M.: 1995, Asymptotic analysis of nonlinear kinetic equation: the hydrodynamical limit, in: N. Bellomo (ed.), Lecture Notes on Mathematical Theory of the Boltzmann Equation, World Scientific, Singapore.
Mason, E. A. and Malinauskas, A. P.: 1983, Gas Transport in Porous Media: The Dusty Gas Approach, Elsevier, New York.
Wilmanski, K.: 2000, Mathematical theory of porous media, In: Lecture Notes, XXV Summer School on Mathematical Physics, Ravello.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
De Socio, L.M., Ianiro, N. & Ponziani, D. Kinetic Models for a Gas Filled Porous Matrix. WAVE PROPAGATION. Transport in Porous Media 52, 95–109 (2003). https://doi.org/10.1023/A:1022356610023
Issue Date:
DOI: https://doi.org/10.1023/A:1022356610023