Universal scaling of droplet retraction dynamics on vibrating surfaces

Abstract

Over the past decade, extensive efforts have been made in the study of droplet impact, especially on stationary surfaces, owing to its direct applications in thermal cooling, self-cleaning, and power generation. However, many practical applications, such as ultrasonic cleaning, aerosolized drug delivery, and vibration-assisted welding, involve the direct interaction of droplets with vibrating surfaces, on which droplets undergo spreading and retraction. Distinct from stationary surfaces where the retraction behaviors, such as the retraction velocity and rate, are mainly governed by the surface wettability and droplet inertia, the retraction behaviors on vibrating surfaces become complicated due to the vibration velocity, which dictates the outcomes of droplet impact, such as the pinning, bouncing, gyrating, and jetting. Here, we revealed the synergistic effect of droplet inertia and vibration velocity on droplet retraction. We found that the droplet retraction behaviors on both stationary and vibrating surfaces could be characterized by a universal scaling law, allowing us to analyze and predict the maximum droplet retraction velocities. Moreover, we found that the maximum retraction rate increased with the maximum spreading radius at low Weber numbers. We demonstrated that the droplet retraction dynamics at both low Weber numbers and high Weber numbers could be unified into one integrated model, which indicates the decisive role of the maximum droplet spreading in droplet retraction dynamics.