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

## TL;DR

This paper develops a thermocapillary fluid model incorporating density gradients to better describe inhomogeneous fluids near the critical point, showing that liquid-vapor interfaces behave similarly to classical models.

## Contribution

It introduces a modified non-convex state law including entropy and temperature gradients, providing a more realistic description of inhomogeneous fluids near criticality.

## Key findings

- Liquid-vapor interfaces behave similarly to classical models near the critical point.
- Entropy density and temperature do not vary with mass density in interfaces.
- The model aligns with molecular theories of realistic potentials.

## Abstract

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.