Timing jitter of monodisperse droplets generated by capillary jet breakup

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.