Nonlinear Dynamic Force Balance Mass-spring-damper Model of Laser Droplet Generation from a Metal Wire

In the laser droplet generation process a metal wire is continuously fed into the focus of a pulsed annular laser beam that melts the wire-end and forms a growing pendant droplet that is then detached from the wire. The process is highly complex due to its non-stationarity, non-linearity, and the interplay of numerous physical phenomena. With the aim of describing the process, a low-dimensional, non-linear, dynamic force balance, mass-spring-damper model of the pendant droplet with time-dependent coefficients was formulated based on experimental observations of the process. A comparison between the modelled and experimental droplet centroid vertical position time series and their time-frequency maps showed that the model captures the essential pendant-droplet dynamics in the selected laser-pulse frequency range between 60 Hz and 190 Hz. It was also found that the modelled time of detachment and the detached-droplet diameter were in good agreement with the experimental results, including the bifurcation at the laser-pulse frequency of 120 Hz and the coexistence of two detached-droplet diameter values below that frequency. In addition, the pendent droplet's lateral oscillation and the Rayleigh-Plateau instability were identified as having a significant influence on the process outcome in certain laser-pulse frequency ranges.