Transport in Porous Media

, Volume 32, Issue 1, pp 21–47 | Cite as

A Thermodynamic Model of Compressible Porous Materials with the Balance Equation of Porosity

  • Krzysztof Wilmanski


The paper is devoted to the construction of a thermodynamic continuous model of porous media with changing porosity. It is shown that these changes are described by a balance equation. The flux in this equation is connected with a relative motion of components and the source describes a spontaneous relaxation of microstructure. Deformations of the skeleton can be arbitrary and a consistent Lagrangian description of motion of all components is applied.

continua with microstructure changing porosity hyperbolic field equations 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Biot, M. A.: General theory of three-dimensional consolidation, J. Appl. Phys. 12(2) (1941), 155–164.Google Scholar
  2. 2.
    Bowen, R. M.: Compressible porous media models by use of the theory of mixtures, Int. J. Engg. Sci. 20(6) (1982), 697–735.Google Scholar
  3. 3.
    Goodman, M. A. and Gowin, S. C.: A continuum theory for granular materials, Arch. Rat. Mech. Anal. 48 (1972), 249–266.Google Scholar
  4. 4.
    Wilmanski, K.: Lagrangean model of two-phase porous material, J. Non-equilib. Thermodyn. 20 (1995), 50–77.Google Scholar
  5. 5.
    Bear, J.: Dynamics of Fluids in Porous Media, Dover Publ. New York, 1988.Google Scholar
  6. 6.
    Truesdell, C.: Sulle basi della termomeccanica, Acad. Naz. dei Lincei, Rend. della Classe di Scienze Fisiche, Matematiche e Naturali, 22(8) (1957), 33–38, 158–166.Google Scholar
  7. 7.
    Wilmanski, K.: On weak discontinuity waves in porous materials, In: J. Rodrigues (ed.), Trends in Applications of Mathematics to Mechanics, Longman, Harlow, 1995.Google Scholar
  8. 8.
    Wilmanski, K.: Dynamics of porous materials under large deformations and changing porosity, In: R. Batra and M. Beatty (eds), Contemporary Research in the Mechanics and Mathematics of Materials, CIMNE, Barcelona, 1996, pp. 343–356.Google Scholar
  9. 9.
    Wilmanski, K.: Porous media at finite strains — the new model with the balance equation of porosity, Arch. Mech. 48(4) (1996), 591–628.Google Scholar
  10. 10.
    Wilmanski, K.: Porous media at finite strains, In: K. Markov (ed.), Continuum Models of Discrete Systems 8, World Publishing, 1996, pp. 317–324.Google Scholar
  11. 11.
    Truesdell, C.: Rational Thermodynamics, 2nd edn, Springer, New York, 1984.Google Scholar
  12. 12.
    Sandri, G.: A new method of expansion in mathematical physics, I, Nuovo Cimento 36(1) (1965), 67–93.Google Scholar
  13. 13.
    Chen, Zhangxin: Large-scale averaging analysis of multiphase flow in fractured reservoirs, Transport in Porous Media 21 (1995), 269–295.Google Scholar
  14. 14.
    Maugin, G. and Muschik, W.: Thermodynamics with internal variables, Part I. General Concepts, J. Non-equilibr. Thermodyn. 19 (1994), 217–249.Google Scholar
  15. 15.
    Albers, B. and Wilmanski, K.: An axisymmetric steady-state flow through a poroelastic medium under large deformations, Arch. Appl. Mech. (in print), also: Preprint #406, WIAS Berlin (1998).Google Scholar
  16. 16.
    Kempa, W.: On the description of the consolidation phenomenon by means of a two-component continuum, Arch. Mech. 49(5) (1997), 893–917.Google Scholar
  17. 17.
    Müller, I.: Thermodynamics, Pitman, Boston, 1985.Google Scholar
  18. 18.
    Wilmanski, K.: Thermomechanics of Continua, Springer-Verlag, Berlin, Heidelberg, 1998.Google Scholar

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Krzysztof Wilmanski
    • 1
  1. 1.Weierstrass institute for Applied Analysis and StochasticsBerlinGermany

Personalised recommendations