Low amplitude, high frequency vibrations can induce in fluids under weightlessness behaviors that resemble those induced by gravity. Supercritical fluids (above their gas-liquid critical point) are used in the space industry and also display universal behavior. They are particularly sensitive to gravity effects. When submitted to vibration (typically $0.1\text{to}0.5\mathrm{mm}$ amplitude, $10\text{to}50\mathrm{Hz}$ frequency), a Rayleigh-Bénard-like instability is observed in experiments with ${\mathrm{H}}_2$ and $\mathrm{C}{\mathrm{O}}_2$ under weightlessness. The thermal boundary layer created during a temperature change displays periodic fingering perpendicular to the vibration direction. A systematic two-dimensional numerical study by the finite volume method is performed in $\mathrm{C}{\mathrm{O}}_2$ that shows that the fingering pattern is due to a thermovibrational instability, characterized by a vibrational Rayleigh number. The simulation and a simplified dimensional analysis show that the fingering wavelength and the vibrational Rayleigh number decrease as a power law with the distance in temperature to the critical point. However, due to the oversimplification of the analysis, the exponent in the simulation is found to be somewhat different than in the theoretical approach, calling for a more complete investigation of the problem.

• Received 10 February 2008

DOI:https://doi.org/10.1103/PhysRevE.78.036325