Temperature profile in a liquid-vapor interface near the critical point

Henri Gouin (1) , Pierre Seppecher (2, 3)

1 M2P2 - Laboratoire de Mécanique, Modélisation et Procédés Propres
2 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]
3 IMATH - Institut de Mathématiques de Toulon - EA 2134

Thanks to an expansion with respect to densities of energy, mass and entropy, we discuss the concept of thermocapillary fluid for inhomogeneous fluids. The non-convex state law valid for homogeneous fluids is modified by adding terms taking account of the gradients of these densities. This seems more realistic than Cahn and Hilliard's model which uses a density expansion in mass-density gradient only. Indeed, through liquid-vapor interfaces, realistic potentials in molecular theories show that entropy density and temperature do not vary with the mass density as it would do in bulk phases. In this paper, we prove using a rescaling process near the critical point that liquid-vapor interfaces behave essentially in the same way as in Cahn and Hilliard's model.

Mots clés: phase transition; temperature profile; rescaling process; Fluid critical-point

Domaines: Matière Molle [cond-mat.soft]; Mécanique des fluides [physics.class-ph]; Physique mathématique [math-ph]

Henri Gouin, Pierre Seppecher. Temperature profile in a liquid-vapor interface near the critical point. Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences, 2017, 473 (20170229), pp.1-13. ⟨10.1098/rspa.2017.0229⟩. ⟨hal-01492802v2⟩