Elimination of satellite droplets in droplet streams by superposing harmonic perturbations

In tin-droplet laser-produced plasma sources, uniform droplet streams with large droplet spacing are desired to minimize the interference of explosion on neighboring droplets. Such droplet streams can be generated in low wavenumber regimes. However, satellite droplets easily appear among main droplets in those regimes, resulting in plenty of undesirable debris. Herein, a novel odd harmonic superposition perturbation method is proposed to eliminate satellite droplets and enhance droplet spacing of uniform droplet streams. The superposition number (N) and the phase difference (θ) of odd harmonic perturbations are adjusted to facilitate the coalescence of satellite droplets with main droplets. First, the superposed odd-order harmonic components could induce additional disturbance growth in jet surfaces, and finally lead to the asymmetric necking on filaments formed between two adjacent main droplets, featured as various carrot-shaped configurations. This asymmetric necking will cause unbalanced surface tension forces at the two sides of filaments, resulting in a velocity difference between satellite and main droplets. Based on this principle, by setting N and k to 3 and 0.2, respectively, satellite droplets positioned above main droplets accelerate, while those below decelerate, achieving complete coalescence between main and satellite droplets. Furthermore, the phase difference is found to determine the jet breakup location and satellite droplet merging characteristics. As θ varies from 0° to 90°, the droplet size significantly decreases while the droplet spacing remains constant since the perturbation energy increases. The merge direction of satellite droplets reverses from upward to downward due to enhanced unbalanced surface tension forces and velocity differences. As θ continuously increases to 270°, the droplet size further decreases along with a slight decrease in droplet spacing. Finally, by setting N = 3 and θ = 0°, mono-disperse tin droplet streams with a mean diameter of 31.5 μm and a maximum droplet spacing-to-diameter ratio of 17.7 are successfully formed. This work presents a novel approach for eliminating satellite droplets to achieve uniform tin droplet streams with large droplet spacing without increasing the droplet diameter.