[en] It is shown that extended irreversible thermodynamics (EIT) provides a Unified description of a great variety of processes, including matter diffusion, thermo-diffusion, suspensions, and fluid flows in porous media. This is achieved by enlarging the set of classical variables, as mass, momentum and temperature by the corresponding fluxes of mass, momentum and heat. For simplicity, we consider only Newtonian fluids and restrict ourselves to a linear analysis: quadratic and higher order terms in the fluxes are neglected. In the case of diffusion in a binary mixture, the extra flux variable is the diffusion flux of one the constituents, say the solute. In thermo-diffusion, one adds the heat flux to the set of variables. The main result of the present approach is that the traditional equations of Fick, Fourier Soret, and Dufour are replaced by time-evolution equations for the matter and heat fluxes, such generalizations are useful in high-frequency processes. It is also shown that the analysis can be easily extended to the study of particle suspensions in fluids and to flows in porous media, when such systems can be viewed as binary mixtures with a solid and a fluid component.
Disciplines :
Mechanical engineering Physics
Author, co-author :
Lebon, Georgy ; Université de Liège - ULiège > Services généraux (Faculté des sciences) > Relations académiques et scientifiques (Sciences)
Desaive, Thomas ; Université de Liège - ULiège > Département d'astrophys., géophysique et océanographie (AGO) > Thermodynamique des phénomènes irréversibles
Dauby, Pierre ; Université de Liège - ULiège > Département d'astrophys., géophysique et océanographie (AGO) > Thermodynamique des phénomènes irréversibles
Language :
English
Title :
A unified extended thermodynamic description of diffusion, thermo-diffusion, suspensions, and porous media
Publication date :
January 2006
Journal title :
Journal of Applied Mechanics
ISSN :
0021-8936
eISSN :
1528-9036
Publisher :
Asme-Amer Soc Mechanical Eng, New York, United States - New York
Onsager, L., Reciprocal relations in irreversible thermodynamics (1931) Phys. Rev., 37, pp. 405-426
Prigogine, I., (1961) Introduction to Thermodynamics of Irreversible Processes, , Interscience, New York
Meixner, J., Zur thermodynamik der irreversiblen prozessen in gases mit chemisch reagierenden, dissozierenden und anregbaren komponenten (1943) Ann. Phys., 43, p. 244
Jou, D., Casas-Vazquez, J., Lebon, G., (2001) Extended Irreversible Thermodynamics, 3rd Ed., , Springer, Berlin
Muller, I., Ruggeri, T., (1998) Rational Extended Thermodynamics, , Springer, New York
Cattaneo, C., Sur une forme de l'équation de la chaleur éliminant le paradoxe d'une propagation instantanée (1948) Acad. Sci., Paris, C. R., 247, pp. 431-433
Lebon, G., Depireux, N., Lhuillier, D., A non-equilibrium thermodynamic formulation of suspensions of rigid particles in moving fluids (2002) Progress in Transport Phenomena, pp. 423-428. , S. Dost, H. Struchtrup, and I. Dincer, eds., Elsevier, Paris
Lhuillier, D., Internal variables and the non-equilibrium thermodynamics of colloidal suspensions (2001) J. Non-newtonian Fluid Mech., 96, pp. 19-30
Desaive, T., (2002) Thermo-convection dans les Milieux Poreux: Stabilité et Dynamique Non-linéaire, , PhD thesis, Liège University