Collision-induced jet-like mixing for droplets of unequal-sizes

The internal mixing of droplets upon coalescence is of fundamental importance to a number of applications in microfluidics, micro-scale heat and mass transfer, and rocket engine propulsion. Compared to the well-known surface-tension-induced jet-like mixing in the coalescence of inertialess droplets, collision-induced jet-like mixing was observed recently and remains inadequately understood. In the present study, the collision dynamics and internal mixing of droplets of unequal sizes was numerical simulated by using the lattice Boltzmann phase-field method, with emphasis on unraveling the mechanism of the internal jet formation and therefore on exploring strategies to facilitate such a mixing pattern. The results show that the formation of the internal jet requires two synergetic flow motions favoring low Oh number and high We number: the capillary-pressure-driven radial converging flow induced by the crater restoration to detach the spreading smaller droplet from the surface, and the impact-inertia-driven axial motion along the crater surface to drive the penetration of the detached fluid. The jet-like structure was found to correlate with the evolution of a main vortex ring, which is formed by the vorticity generation on the interface during initial impact, and transported into the droplet during subsequent oscillations. However, due to the absence of the bulge retraction that generates a significant amount of vorticity and to the extended duration for the jet formation, the main vortex is much less intensive compared to that formed by the inertialess droplet coalescence and is therefore less capable of inducing obvious vortex-ring structure in the mixing pattern. Further simulations by manipulating the disparity of the droplet sizes and the disparity of the liquid viscosities show that, the collision of a larger droplet with lower viscosity with a smaller droplet with higher viscosity is effective in facilitating jet-like mixing.