Theoretical predictions of the effective thermodiffusion coefficients in porous media

This study presents the determination of the effective Darcy-scale coefficients for heat and mass transfer in porous media including the thermodiffusion effect using a volume averaging technique. The closure problems related to the pore-scale physics and providing effective coefficients are solved over periodic unit cells representative of the porous structure. The results show that, for low Péclet numbers, the effective Soret number in porous media is the same as the one in the free fluid and that it does not depend on the solid to fluid conductivity ratio. On the opposite, in convective regimes, the effective Soret number decreases. In this case, a change of conductivity ratio will change the effective thermodiffusion coefficient as well as the effective thermal conductivity coefficient. The macroscopic model obtained by this method is validated by comparison with direct numerical simulations at the pore-scale. Then, coupling between forced convection and Soret effect for different cases is investigated.