Dynamics of droplet coalescence on a vibrating vertical surface

Abstract

A mass-spring-damper theoretical model with a phenomenological equation is established to clarify the underlying physics of the dynamics of droplets on a vertical surface driven by vibration. It is found experimentally and theoretically that the phase shift between droplet and plate appears and peaks at a lower frequency for a larger droplet. At a certain frequency, two droplets could move in the opposite direction. Based on the phase shift mechanism, we propose a strategy aimed at promoting droplet coalescence. Compared to the necessity of precise control of frequency for resonance-induced events, the strategy accepts a higher tolerance for frequency, at which opposite-motion-induced droplet coalescence could occur. The optimal frequency where there is a maximum phase shift between two droplets is derived, and a large-bandwidth frequency range, which allows at least 90% maximum phase shift, is defined. The good agreement between the experimental and theoretical results collectively shows that the motion of the larger droplet is in the opposite direction to that of the smaller one only at large-bandwidth frequency range and the two droplets coalesce with high enough amplitude. Our findings are helpful for the utilization of vibrating surfaces for droplet removal.