Droplet Dynamics on a Vibrating Vertical Wire

Droplet dynamics along a wire is of great fundamental importance in fluid mechanics. From the practical standpoint, using wire mesh to collect droplets or dust particles is a common method in air filtration systems. In this study, we investigate dynamics of a droplet under the effect of vibrations on a vertical wire both experimentally and theoretically. We observe three different behaviors of the drops in experiments: static, sliding, or shedding. We characterize the phase diagram of these distinct behaviors for varying droplet sizes and vibration accelerations. In general, by increasing the vibration acceleration or the drop volume, the drop transitions from static to sliding to shedding. Notably, the sliding velocity in the sliding regime shows a non-monotonic trend as a function of the vibration amplitude under certain frequencies. Finally, we develop a reduced model to rationalize the drop dynamics in the sliding regime. We also develop simple scaling laws to characterize the threshold of shedding behavior.