Time series analysis based study of a mass-spring-like oscillation and detachment of a metal pendant droplet

• Oscillating metal pendant droplet detachment was studied using time series analysis.
• A t–f map of the pendant droplet vertical displacement time series was calculated.
• Based on the t–f map, the pendant droplet was described as a mass-spring system.
• The t–f map showed the resonant nature of the pendant droplet detachment.
• The detached droplet diameter was predicted by an algebraic formula.

The subject of this study is the vertical mass-spring-like oscillation of a pendant droplet and its resonant detachment, which was experimentally observed in the process of laser droplet generation from a metal wire. The process was characterized by various time series, which were generated from a sequence of infrared intensity images of the process. Following a visual inspection of pendant droplet images and an analysis of a wavelet based time-frequency map of the droplet’s vertical displacement time series, the pendant droplet’s oscillation is described by a time-variable mass-spring system. Based on the characteristics of the time-frequency map, the resonant nature of the pendant droplet detachment was demonstrated. Additionally, an algebraic expression was formulated, which can be used to predict the detached droplet’s diameter as a function of the laser pulse frequency.