# Travelling waves of density for a fourth-gradient model of fluids

## TL;DR

This paper develops a fourth-gradient fluid model derived from mean-field theory, capturing complex wave phenomena and interface profiles with higher precision than classical models, especially near critical points.

## Contribution

It introduces a fourth-gradient model based on molecular mean-field theory, providing more accurate density profiles and wave behaviors than traditional models like Cahn-Hilliard.

## Key findings

- More precise interface density profiles than Cahn-Hilliard
- Density profiles follow an Extended Fisher-Kolmogorov equation near critical points
- Observation of oscillating pulse waves and critical opalescence phenomena

## Abstract

In mean-field theory, the non-local state of fluid molecules can be taken into account using a statistical method. The molecular model combined with a density expansion in Taylor series of the fourth order yields an internal energy value relevant to the fourth-gradient model, and the equation of isother-mal motions takes then density's spatial derivatives into account for waves travelling in both liquid and vapour phases. At equilibrium, the equation of the density profile across interfaces is more precise than the Cahn and Hilliard equation, and near the fluid's critical-point, the density profile verifies an Extended Fisher-Kolmogorov equation, allowing kinks, which converges towards the Cahn-Hillard equation when approaching the critical point. Nonetheless, we also get pulse waves oscillating and generating critical opalescence.