Spontaneous Formation Mechanisms of Droplets in Step Emulsification

Droplet step emulsification has been proven to possess the unique advantage of decoupling the flow parameters, which obviously contributes to the realization of the mass production of monodisperse droplets. However, a complete understanding of the dynamic characteristics underlying droplet spontaneous formation in step emulsification has not been fully revealed and remains a challenge because the channel confinement effect always results in the complexity in interface spatiotemporal evolution under various conditions. In this work, the spontaneous formation mechanisms of droplets in step emulsification are numerically investigated via a VOF-CSF model. The physics behind the two distinct flow patterns regarding dripping and jetting are deeply revealed based on the local flow field structures and pressure distribution, and it was found that in dripping, before final pinch-off of the neck, a finite time singularity usually exists, thus leading to infinite velocity and pressure inside the neck. However, in jetting, as the droplet steadily expands, the velocity and pressure inside the neck finally reach an equilibrium state. Besides, by taking multiple variables with a wide range into account, the flow pattern diagram and the prediction correlation of droplet size are established with several dimensionless numbers, exhibiting excellent universality. In particular, the force field characteristics previously undocumented for droplet step emulsification are also quantitatively clarified from a new perspective of momentum conservation. The results obtained in this study reveal the spontaneous formation mechanisms of droplets in step emulsification, thus providing theoretical guidance for precisely regulating the emulsification process.