Eur. Phys. J. Special Topics 146, 3-12 (2007)
https://doi.org/10.1140/epjst/e2007-00164-1

A thermodynamic description of thermo-diffusion in suspensions of rigid particles^*

¹ Département d'Astrophysique, Géophysique et Océanographie, Université de Liège, 17 allée du 6 Août, 4000 Liège, Belgique
² Modélisation en Mécanique, Université Paris 6, 4 place Jussieu, Tour 66, 75252 Paris, France
³ Dipartimento di Matematica, Università di Messina, Contrada Papardo, Salita Sperone 31, 98166 Messina, Italia

Corresponding author: G.Lebon@ulg.ac.be

Abstract

The relative motion between solute molecules and a solvent in presence of a thermal gradient is usually described by Soret and Dufour's laws. When considering a suspension of supra-particles in a solvent, the relative motion requires a more complex description. This problem of thermo-diffusion is here considered in the framework of Extended Irreversible Thermodynamics whose main characteristic is to raise the fluxes of matter and heat to the status of independent variables. The description is rather complex but it appears to receive a rather simple interpretation by comparing with other approaches like the internal variable theory, classical irreversible thermodynamics and the two-fluid model of suspensions. We obtain new and interesting generalizations of Soret and Dufour's laws and in particular, a novel expression for the non-dissipative part of the force exerted by the fluid on the particles.