  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 into account 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.
