Critical slowing down and fading away of the piston effect in porous media

Bernard Zappoli (1) , Raphaël Cherrier (2) , Didier Lasseux (2) , Jalil Ouazzani (3, 4) , Yves Garrabos (3, 4)

1 PMMH - Physique et mécanique des milieux hétérogenes (UMR 7636)
2 TREFLE - Transferts, écoulements, fluides, énergétique
3 ICMCB - Institut de Chimie de la Matière Condensée de Bordeaux
4 ESEME : Équipe du Supercritique pour l'Environnement, les Matériaux et l'Espace : Équipe commune CEA-CNRS (2000-2014)

We investigate the critical speeding up of heat equilibration by the piston effect (PE) in a nearly supercritical van der Waals (vdW) fluid confined in a homogeneous porous medium. We perform an asymptotic analysis of the averaged linearized mass, momentum and energy equations to describe the response of the medium to a boundary heat flux. While nearing the critical point (CP), we find two universal crossovers depending on porosity, intrinsic permeability and viscosity. Closer to the CP than the first crossover, a pressure gradient appears in the bulk due to viscous effects, the PE characteristic time scale stops decreasing and tends to a constant. In infinitly long samples the temperature penetration depth is larger than the diffusion one indicating that the PE in porous media is not a finite size effect as it is in pure fluids. Closer to the CP, a second cross over appears which is characterized by a pressure gradient in the thermal boundary layer (BL). Beyond this second crossover, the PE time remains constant, the expansion of the fluid in the BL drops down and the PE ultimately fades away.

Mots clés: Critical point; Piston effect; Porous media

Domaines: Matériaux; Mécanique statistique [cond-mat.stat-mech]

Bernard Zappoli, Raphaël Cherrier, Didier Lasseux, Jalil Ouazzani, Yves Garrabos. Critical slowing down and fading away of the piston effect in porous media. 2006. ⟨hal-00016710⟩