Gaussian wave packets in a semi-infinite capillary jet for droplet isolation: Spatial linear analysis and nonlinear simulations.

Abstract

A single droplet can be effectively isolated from a capillary liquid jet by applying a short-duration velocity oscillatory pulse at its exit from the nozzle outlet. The previous temporal analysis of F. J. García et al. [Phys. Rev. E 100, 053111 (2019)2470-004510.1103/PhysRevE.100.053111], which modeled the jet as an infinite liquid column subjected to a local axisymmetric spatial perturbation, revealed that Gaussian wave packets are the optimal choice for this purpose. Here, a more realistic semi-infinite jet model was selected to confirm the validity of the simpler infinite-jet model and identify new phenomena. To this end, a semi-infinite jet subjected to a symmetrical Gaussian oscillatory pulse of velocity at the outlet was investigated through both a linear spatial analysis and nonlinear numerical simulations. The spatiotemporal evolution of the Gaussian wave packets thus generated was described by fitting their relevant parameters and compared with the prediction of the temporal analysis of an infinite jet. Nonlinear simulations confirmed the results of the linear spatial analysis whenever the amplitude remained sufficiently small. A Gaussian wave packet forms during the stimulation stage, which then moves advectively and disperses as if it were on a perturbed infinite jet, even for small velocities. This explains the parametric agreement between the spatial and temporal analyses, especially for brief stimulation pulses. The most relevant discrepancy was a phase shift in the carrier wave, whose magnitude can be explained in terms of the stimulation and initial-transient characteristic times. It could be reverted through an appropriate initial phase of the stimulation pulse. An example with symmetrical breakup pattern was achieved in this way, which could be useful for further isolation of single droplets.