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

Abstract

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 timefrequency 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.

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

“…The most important coefficients of those models are the nonlinear spring stiffness and the damping coefficient, which could be theoretically determined based on the droplet's surface-energy gradient and the viscous damping, respectively. However, the resulting theoretical value of the spring stiffness was found to be too large, which is consistent with the results of the ALDG study [16]. In contrast, the theoretically determined viscous damping coefficient was reported to be much too small to match the experimental droplet dynamics, which could be caused by the rotational fluid flow inside the droplet [18].…”

“…The present study is focused on the laser-pulse frequency f p range between 60 Hz and 190 Hz, where the pendant droplet's detachment is triggered by the resonance of the n = 1 eigenmode [15]. In order to provide the reader with the experimental background that forms the starting point of the present study, the main results of the continuous ALDG experimental study [16] are reproduced and briefly commented on here. In the selected frequency range, the main dynamics of the pendant droplet could be described as that of a forced, time-variable, lightly damped, massspring oscillating system, the mass of which increases with time [16].…”

“…In order to provide the reader with the experimental background that forms the starting point of the present study, the main results of the continuous ALDG experimental study [16] are reproduced and briefly commented on here. In the selected frequency range, the main dynamics of the pendant droplet could be described as that of a forced, time-variable, lightly damped, massspring oscillating system, the mass of which increases with time [16]. The effective spring constant k of the system was found to show a power-law dependence on the volume V of the pendant droplet:…”

“…An experimental study of the continuous ALDG has shown that, depending on the laser-pulse frequency, the detachment of the pendant droplet is stimulated by the resonance of a droplet-oscillation eigenmode with the polar wavenumber n = 1, 2, or 3 [15]. In addition, a recent experimental study, based on time series and focused on the n = 1 droplet-oscillation eigenmode in the laser-pulse frequency range between 60 Hz and 190 Hz [16], showed that the essential dynamics of the pendant droplet are very similar to that of a time-varied, mass-spring-damper system. In the study, the effective spring stiffness was determined as a function of the droplet volume and the resonancecaused droplet detachment was confirmed.…”

“…The aim of this work is to formulate a mathematical model of the continuous ALDG process in the form of a low-dimensional, dynamic force balance, massspring-damper system with time-varied coefficients and to evaluate the formulated model by comparing the resulting time series and their time-frequency maps with the experimental ones. To achieve this, the first section briefly describes the continuous ALDG experimental system and process, as well as the relevant results of the previous experimental analysis [16]. Based on these results, in the second section the time-varied coefficients are determined and the dynamic force balance, mass-spring-damper model of droplet growth and detachment is formulated.…”