Vortex Dynamics During Pinch-off of Micro-Droplets

Microdroplets are extensively used in chemical, biological, and medical research, primarily for conducting various tests on samples, including living organisms, using the microfluidic framework. Recent works have shown that the physiology of bacteria can be significantly altered when subjected to shear stresses. With this motivation, along with the ever-important problem of mixing at small scales, we perform experiments to understand the vortex dynamics involved during the pinch off process till the droplet reaches a steady phase in a crossflow droplet generator. We use the PIV technique to elucidate the vortical structures and the subsequent stresses developed inside droplets. The process of pinching off inherently leads to the acceleration of fluid in the rapidly thinning capillary bridge resulting in a vortex in the separated droplet. This vortex then propels in the forward direction during the unsteady phase, resulting in its decay. The unsteady droplet formation phase involves interplay of capillary forces due to deforming interface and shear forces from continuous phase. We propose scaling laws associated to the vortical flow and a model to predict the maximum circulation production during the pinch-off inside the droplet. Further, the stresses involved during different phases of pinch-off are discussed.