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Stratification effects in fluids near their liquid-vapor critical point

Michael Bestehorn*

Sakir Amiroudine

  • *Contact author: bestehorn@b-tu.de
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Phys. Rev. Fluids 11, 064004 – Published 18 June, 2026

DOI: https://doi.org/10.1103/1s5s-bxxb

Abstract

Near-critical fluids are known to exhibit anomalous behavior in their thermophysical properties, such as diverging compressibility and vanishing surface tension on approaching the critical point. These fluids undergo high-density stratification very close to the critical point. The Navier-Stokes equations coupled to a phase field model are solved with a van der Waals equation of state. The pressure is expanded around the critical point and shows a cubic variation with the reduced density. Density-stratified base states are computed numerically. The supercritical case is treated through the linear stability analysis. The spectrum, the eigenmodes/eigenfunctions, and sound waves are then computed and plotted for temperatures close to the critical point (CP). Very close to CP, the speed of sound significantly changes as a function of the vertical direction, and the frequency bands strongly differ from the situation of an ideal gas. The same process of linearization has been performed for the subcritical state. Here, the Rayleigh-Taylor instability (RTI) is considered. Finally, numerical simulations confirm the propagation of acoustic waves in the supercritical case. In the subcritical case, spinodal decomposition is found for a randomly distributed initial density close to the critical one. Time series in the Rayleigh-Taylor unstable domain show interesting features. The time evolution of the total kinetic energy exhibits three distinct phases: high-frequency sound waves appear at early times, then RTI manifests, and finally, at longer times, surface waves appear with a much smaller frequency.

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Phys. Rev. Fluids 11, 064004– Published 18 June, 2026
  • Received 20 January 2026
  • Accepted 1 June 2026
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