Linear instability of a liquid sheet in a transverse standing acoustic field

Abstract

This work examines the instability of a plane liquid sheet under the action of a transverse acoustic field. The mechanical definition of the acoustic field is introduced first, and the Floquet theory is applied to derive the dispersion equation and dispersion curve. The dominant instability mechanism of each unstable region on the dispersion curve is distinguished by calculating the oscillation frequencies of the disturbance waves. Next, the parameters within the dispersion equation are set as variables to analyze the development of the instability mechanisms of the unstable regions on the dispersion curve and the oscillation modes on the two surfaces of the liquid sheet. The results prove that the distribution of unstable regions can be affected by the amplitude and frequency of the acoustic field, the viscosity and surface tension of the liquid sheet, and the density ratio of the two gas–liquid phases. Variation in the thickness of the liquid sheet causes development and competition within the oscillation modes, which were found to be related to the development of the instability mechanism. Such evolutionary competition between the sinuous and the varicose oscillation modes was also reflected in the experimental study, where it was observed that the disturbance wave has the characteristics of Faraday waves.