Vortex-ring-induced internal mixing upon the coalescence of initially stationary droplets

This study numerically investigates the internal jetlike mixing upon the coalescence of two initially stationary droplets of unequal sizes by employing the volume of fluid method with an adaptive mesh refinement algorithm. The emergence of the internal jet is attributed to the formation of a main vortex ring, as the jetlike structure shows a strong correlation with the main vortex ring inside the merged droplet. By tracking the evolution of the main vortex ring together with its circulation, we identified two mechanisms that are essential to the internal-jet formation: the vortex-ring growth and the vortex-ring detachment. Recognizing that the initiation of the vortex-ring-induced jet energetically relies on the merged interface but the manifestation of the jet physically relies on the competition between the convection and viscous dissipation of the vortex ring, we further developed and substantiated a vortex-ring-based Reynolds number (ReJ=ΓVD/4πν) criterion, where ΓVD is the circulation of the detached main vortex ring and ν is the liquid kinematic viscosity, to interpret the occurrence of the internal jet at various Ohnesorge numbers and size ratios. For the merged droplet with apparent jet formation, the average mixing rate after jet formation increases monotonically with ReJ, which therefore serves as an approximate measure of the jet strength. In this respect, stronger internal jet is responsible for enhanced mixing of the merged droplet.