Travelling waves near a critical point of a binary fluid mixture

TL;DR

This paper investigates traveling wave solutions in binary fluid mixtures near a critical point, using a non-local free energy model, revealing non-monotonic density profiles and potential extensions to other fields.

Contribution

It introduces a universal approach to analyze traveling waves near critical points in binary mixtures, accounting for density gradients and non-local free energy effects.

Findings

Traveling wave solutions exhibit non-monotonic density profiles.

The model can be rescaled to resemble a single fluid system.

Results may extend to finance and biology contexts.

Abstract

Travelling waves of densities of binary fluid mixtures are investigated near a critical point. The free energy is considered in a non-local form taking account of the density gradients. The equations of motions are applied to a universal form of the free energy near critical conditions and can be integrated by a rescaling process where the binary mixture is similar to a single fluid. Nevertheless, density solution profiles obtained are not necessarily monotonic. As indicated in Appendix, the results might be extended to other topics like finance or biology.