On dispersion relation for Faraday waves in a near-critical fluid under weightlessness

One reports experiments and numerical simulations of Faraday waves at the liquid - vapor interface of fluids (typically CO₂ and H₂) near its critical point when submitted to vibration in a weightlessness environment. It is known that in such a system striation is formed under the action of vibrations. The boundary between the liquid and gas phases is located perpendicular to the direction of vibrations, and a streaky structure in the form of periodic stripes (striations) is formed in the cavity. It is shown that under vibrations of sufficient intensity an instability develops on the striation interface perpendicular to the direction of vibrations, leading to Faraday waves. A theoretical and numerical study of this instability is carried out, the critical parameters of the appearance of Faraday waves are determined taking into account the interaction of waves on adjacent striations. Dispersion relations for Faraday waves are obtained numerically. It is shown that in the vicinity of the critical point there is a significant deviation of the dispersion relation from the classical theoretical dependence.