Abstract
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.
Highlights
High-frequency droplet generation with uniform size and velocity has numerous applications in science and technology, such as in dynamic surface tension measurement,1,2 printing technology,3,4 liquid metal droplet generators for extreme ultraviolet (EUV) sources,5–7 and damage-free single wafer cleaning.8 Uniform droplets can be generated by two regimes, namely, dripping and Rayleigh jet breakup.9–11 The corresponding droplet generators are the drop-on-demand (DOD) droplet generator and the droplet stream generator.12 A typical piezoelectric DOD droplet generator uses a piezoelectric material in a liquid-filled chamber behind the nozzle, which forces the droplet to form from the nozzle by changing the volume of the cavity under an electric pulse signal
We focused on the deformation characteristics of the main droplets generated by a Rayleigh jet breakup and revealed their dependence on the driving and jet parameters
The influence of the initial perturbation on the growth of various harmonics can be divided into two parts according to the wavenumbers: (1) When k′ is small (k′ < 0.6), as shown in Fig. 14(a), as the initial perturbation increases, the contributions of the higher harmonics decrease since the amplitude caused by the fundamental harmonic enlarges while the amplitude caused by the higher ones changes little, resulting in the enhancement of the mass and oscillation amplitude of the main droplet
Summary
High-frequency droplet generation with uniform size and velocity has numerous applications in science and technology, such as in dynamic surface tension measurement, printing technology, liquid metal droplet generators for extreme ultraviolet (EUV) sources, and damage-free single wafer cleaning. Uniform droplets can be generated by two regimes, namely, dripping and Rayleigh jet breakup. The corresponding droplet generators are the drop-on-demand (DOD) droplet generator and the droplet stream generator. A typical piezoelectric DOD droplet generator uses a piezoelectric material in a liquid-filled chamber behind the nozzle, which forces the droplet to form from the nozzle by changing the volume of the cavity under an electric pulse signal. There has been little research on the effect of the jet and driving parameters on the shape characteristics of droplets generated by a Rayleigh jet breakup. We focused on the deformation characteristics of the main droplets generated by a Rayleigh jet breakup and revealed their dependence on the driving and jet parameters. To simplify the analysis of these dependences, the analysis was partially based on the results of the breakup of a liquid bridge since the temporal instability of a capillary liquid bridge is equivalent to the spatial instability of a semi-infinite liquid jet when the average stream speed is much higher than the capillary wave speed.
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