This article investigated the effects of driving and jet parameters on the deformation characteristics of the droplet generated by a Rayleigh jet breakup for the first time. The deformation characteristics of the droplet include its oscillation amplitude and oscillation period. The driving parameters are the dimensionless wavenumber and the initial amplitude of the perturbation. The jet parameters are non-dimensionalized as the Ohnesorge number. The non-dimensional Navier–Stokes equations were numerically solved to simulate the spatial instability of the jet breakup and obtain the complete oscillation process of the droplet. An equivalent oscillation amplitude was formulated based on the hydrodynamic similarity principle and energy method to explain the source of the oscillation of the droplet. The dependence of the oscillation amplitude was explained for the first time by analyzing the growth of the various harmonics of the perturbation derived from the Fourier expansion of axial velocity distribution. The results show that the higher harmonics caused by the non-linearity of the jet breakup have a certain influence on the dependence of the oscillation amplitude. The dependence of the oscillation period was formulated according to the linear solution of the problem of oscillating droplets.

Uniform droplets generated by Rayleigh breakup of liquid jet are widely applied in science and engineering. The droplets are produced by imposing a periodic velocity perturbation on a micro-sized liquid jet. In practical situations, the frequency of droplet generation is not perfectly steady like the preset perturbation frequency. This unwanted timing jitter poses kinds of problems. We studied the fluid mechanism of the jitter at short working distance and its dependence on various parameters. We found that at short distance, the jitter is mainly affected by the reduction rather than the dispersion in the droplet velocity. The magnitude of the jitter is related to the velocity reduction and the unsteadiness of the perturbation. The velocity difference between the droplet and the jet is analytically obtained based on one-dimensional linear analysis of drop formation in liquid jet, and numerical simulations validate the results. The influence of the unsteady perturbation is explained by the evolution of control volumes with different initial amplitudes. The degree of jitter is finally deduced, and its relationships with each variable are compared with experiments. Optimization methods are given to mitigate jitter by adjusting the perturbation parameters and jet properties.

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Monodisperse droplets induced by Plateau-Rayleigh instability of liquid jet are widely applied. Due to spatial jitter, the spacing between droplets becomes uneven as the working distance increases. We found that the jitter can be ameliorated by uniformly charging the droplets. Under the electrostatic forces, the droplets align at uniform spacing over a long distance. Nevertheless, radial jitter emerges when the charging voltage is too high. The effect of charging on the jitter was modeled and validated by experiments. A recommended charging parameters configuration is given considering a trade-off between axial and radial jitter to obtain evenly distributed droplets.

There have been a number of studies on the Plateau–Rayleigh instability and the influence of the initial jet perturbation on the jet breakup. Our study observed that the threshold lengths of jet breakup varied with the voltage applied to the piezoelectric sheets during the droplet generation for extreme-ultraviolet (EUV) source and wafer cleaning. Combining acoustics and fluid mechanics, we investigated the process and mechanism to interpret the impact of the horn vibration on the jet breakup. The whole process of the vibration delivery from the horn to the jet was summarized: generated by the horn, the vibration transmits into the water, spreads in the chamber, stimulates the jet through the orifice, and grows continuously, causing the jet breakup. In order to validate the analysis, a series of experiments were carried out and compared with the theoretical predictions. The vibration mode and amplitude of the horn were determined by the scanning laser vibrometer. With the hydrophone detection, the distribution of the vibration in the axial direction at the nozzle outlet was studied, and the delivery of the vibration in the chamber was discussed. To verify the influence of the vibration in the chamber on the jet breakup, we compared the results of jet breakup under different sound pressures. Besides, a theoretical model of the jet breakup length versus the piezoelectric sheet voltage was proposed. The study of the whole process provides guidance for changing the jet breakup length by adjusting the voltage and helps to investigate other parameters of the jet breakup process.