ANALYSIS OF THE SURFACE WAVE INSTABILITY OF A SEMI-SPHERICAL DROPLET UNDER VERTICAL EXCITATION

Surface destabilization of droplets under external excitation has always been a matter of interest in the field of fluid dynamics. Waveforms with different morphologies or secondary droplets would appear in the surface under different excitation conditions. In this paper, the analysis of the dynamic characteristics and generation mechanism of latitudinal and longitudinal waves was conducted. Firstly, an experimental system of droplet oscillation with controllable excitation amplitude and frequency was established. The experimental results show that different forcing amplitudes lead to different droplet interface instability modes. The longitudinal waves are generated only when the amplitude is large enough, and its evolution frequency is half of the driving frequency, while the latitudinal waves are always present whose frequency equals to the driving frequency. A change in driving frequency causes a shift in destabilization modes, and an increase in driving frequency increases the number of surface wave modes and decreases the wavelength of the surface waves. When the driving frequency exceeds a certain threshold, the waveform will shift from a latitudinal wave mode only to a latitudinal wave superimposed on a longitudinal wave mode. Meanwhile, three-dimensional numerical simulations were conducted. By studying the velocity and pressure fields of droplets, combined with the phase relationship between droplet vertex displacement and inertial force, the mechanism of droplet formation of latitudinal waves is elucidated: under the combined action of inertial force and surface tension, the droplet surface wave completes periodic energy conversion and transition. The surface wave characteristics dominated by the Faraday instability are analyzed comparatively for vertical versus radial acceleration direction. It is found that the geometrical characteristics of the droplet generate radial forces normal to the contact line, and when the vertical inertial force increases so that the radial force reaches a certain threshold, the droplet undergoes longitudinal instability, and the corresponding longitudinal wave frequency is half of the driving frequency.