Perturbation spectrum of a plane liquid-liquid interface in the presence of high-frequency tangential vibrations in weightlessness

Abstract

We study the spectra of time-dependent equilibrium perturbations and stability of a plane interface between two layers of liquids with different but commensurable densities under high-frequency tangential vibrations in weightlessness. Plane, spiral and spatial perturbations are considered. The layers of equal and different (one of the layers is ten times thicker than the other) thickness are analyzed. The monotonous plane perturbations are found to be most dangerous. At sufficiently large values of the vibration parameter, the growing spiral oscillatory perturbations (traveling waves) appear. With increasing vibrations, these oscillatory perturbations disappear. For the layers of unequal thickness, the wavelength of most dangerous perturbations is of order of the layer that is thinner. We attribute the appearance of alternating strata experimentally observed in the two-layer system under high-frequency vibrations in weightlessness to the growth of perturbations with maximum increment. Quantitative comparison between theoretical predictions and experimental results is made.