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An Extended Thermodynamic Approach to Transport Phenomena in Porous Media*

Published online by Cambridge University Press:  28 February 2011

J. A. del Rio  and
M. López de Haro
J. A. del Rio
Affiliation:
Laboratorio de Energia Solar. IIM-UNAM. Zona Cultural Xochicalco, A.P. 34. 62580, Temixco, Mor. Mexico
M. López de Haro
Affiliation:
Laboratorio de Energia Solar. IIM-UNAM. Zona Cultural Xochicalco, A.P. 34. 62580, Temixco, Mor. Mexico
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Abstract

A formalism of extended irreversible thermodynamics (EIT) is used to study the physical aspects of heat, momentum and mass transport through porous media.

The thermodynamic space is enlarged with respect to that of classical linear irreversible thermodynamics (LIT) to include the mass, heat and momentum fluxes as independent variables. The time evolution equations for such variables are derived self-consistently and reduce to the usual constitutive equations of LIT when the appropriate limits are taken. Equations that involve effects characterized by terms of second order in the gradients of conserved variables (such as the Darcy-Brinkman law) may also be derived within the same formalism. Finally, EIT provides the natural framework beyond LIT to introduce non-isothermal effects in the study of transport phenomena in porous media.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 195: Symposium S – Physical Phenomena in Granular Materials , 1990 , 283
Copyright
Copyright © Materials Research Society 1990

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Footnotes

**

On sabbatical leave from Area de Fisica, Universidad Autonoma Chapingo. 56230, Texcoco, Edo. de Mdxico, Mexico

*

Work supported by PAPIID of DGAPA-UNAM under project IN-01-02-89

References

REFERENCES

1. Onsager, L., Phys. Rev. 37 405. (1931).Google Scholar
2. Groot, S.R. de, and Mazur, P.., “NON-EQUILIBRIUM THERMODYNAMICS” (Dover, Pub. N.Y. 1984).84).Google Scholar
3. Jou, D., Casas-Vdzquez, J. and Lebon, G., Rep. Prog. Phys. 51, 1105 (1988).Google Scholar
4. Garcia-Colin, L., Haro, M. Lopez de, Rodriguez, R.F., Jou, D., and Casas-Vazquez, J., J. Stat. Phys. 37, 465 (1984).Google Scholar
5. Scheidegger, A.E., J. Appl. Phys. 25, 994. (1954).Google Scholar
6. Sposito, G., Water Resour. Res. 14, 474 (1978); 14, 479 (1978).Google Scholar
7. Mokadam, R.G., Transactions of ASME J. Appl. Mech. 1961, 208.Google Scholar
8. Taylor, S.A., and Cary, J.W.. Soil Sci. Soc. Proc. 1964, 167.Google Scholar
9. Groenevelt, P.H., and Bolt, G.H., J. of Hydrology. 7, 358 (1969); C.L. Carnahan, J. of Hydrology 31, 125 (1976) ; G. Sposito, V.K. Gupta, and R.N. Bhattacharya, Adv. Water Res. 2, 59 (1979); H.F.M. ten Berge, and G.H. Bolt Transport in Porous Media 3, 35 (1988).Google Scholar
10. Cary, J.W., Soil Sci. 100, 168 (1965); J. Letey, and D. Kemper, Soil Sci. Soc. Amer. Proc. 33, 25 (1969); H.W. Olsen, Soil Sci. Soc. Amer. Proc. 33, 338 (1969); P.H. Groenevelt, D.E. Elrick, and K.B. Laryea, Soil Sci. Soc. Am. J. 44, 1168 (1980); S.K.J. Kung, and T.S. Steenhuis, Soil Sci. Soc. Amer. J. 50, 1114 (1986).Google Scholar
11. Garcia-Colin, L., Rev. Mex. Fis. 34, 334 (1988).Google Scholar
12. Rodriguez, R.F., and Haro, M. López de, J.Non-equilib. Thermodyn. 14, 37 (1989).Google Scholar
13. Rio, J.A. del and Haro, M. López de to be published in J. Non-equilib. Thermodyn (1990).Google Scholar
14. Vázquez, F., and Rio, J.A. del, Rev. Mex. Fis. 36, 1, (1990).Google Scholar
15. Rio, J.A. del, M. Sc. Thesis. UNAM, Mexico, 1987.Google Scholar
16. Sen, A.K., Int. J. Heat Mass Transfer. 30, 855 (1989)Google Scholar
17. Whitaker, S., Transport in Porous Media 1, 3 (1986).Google Scholar
18. Durlofsky, L. and Brady, J.F., Phys. Fluids 30, 3329 (1987).Google Scholar
19. Lebon, G. and Cloot, A., Int. J. Heat Mass Transfer. 29, 381 (1986).Google Scholar