Ligament pinch-off mechanism of stable satellite droplets stream generation in continuous jet breakup

Regarding satellite droplets as utilizable droplets can address the engineering challenges resulting from the growing need for small droplets in industrial manufacturing. In this paper, we investigate the generation process from ligament to stable satellite droplet, as a prerequisite for utilizing satellite droplets. Following our previous experimental work, we found that stable satellite droplets are generated from downstream pinch-off instead of being conventionally recognized as symmetric pinch-off. A two-dimensional axisymmetric model with periodic flow is applied to describe the liquid dynamics, and the changes in volume and momentum throughout the process are considered. The entire jet breakup process can be divided into three stages: growing, flattening, and necking/pinch-off. Perturbation parameters significantly affect the ligament pinch-off modes. The analysis of field variables at the ligament pinch-off instants for various perturbation amplitudes reveals that the jet velocity decays as the perturbation grows. Based on ligament flattening and necking, we show that perturbation amplitude governs necking-point positions and thus controls the volume evolution from ligament to satellite droplet, providing the basis for analyzing satellite merging modes. A deviation in the downstream necking dynamics of the entire flattening and necking process relative to the self-similar theory alters the conventional correspondence between satellite merging and ligament pinch-off modes. The momentum per volume for the ligament evolution process should be analyzed using the specific capillary impulses in the upstream and downstream necking regions during the flattening stage. This work provides guidance for understanding and modulating ligament pinch-off modes to achieve stable satellite droplet generation.