Thermocapillary fluid and adiabatic waves near the critical point

TL;DR

This paper develops a theoretical framework for analyzing thermocapillary and adiabatic waves near the critical point of fluids, incorporating gradient effects of density and entropy, and finds that shock waves cannot form in such media.

Contribution

It introduces an extended van der Waals model with gradient-dependent internal energy to describe interfacial waves near the critical point.

Findings

Wave celerity depends on thermodynamic conditions at the critical point.

Shock waves are not possible in the studied non-homogeneous fluids.

Waves are tangential to the interface near the critical point.

Abstract

Isothermal interfacial zones are investigated starting from a local energy which can be considered as the sum of two terms: one corresponding to a medium with a uniform composition equal to the local one and a second one associated with the non-uniformity of the fluid. In an extended van der Waals theory, the volume internal energy is proposed with a gradient expansion depending not only on the gradient of density but also on the gradient of entropy. We obtain the equation of conservative motions for non-homogeneous fluids near its critical point. For such a medium, it is not possible to obtain shock waves. The waves are tangential to the interface and the wave celerity is expressed depending on thermodynamic conditions at the critical point.