On the vortex ring formation and mixing in thin films upon droplet impact

Abstract

When a droplet impacts a liquid film, a vortex ring form and govern momentum and species transport. We experimentally investigate vortex ring formation, propagation and instability during droplet impact onto liquid films, with particular emphasis on vortex ring-wall interactions. Particle image velocimetry and laser-induced fluorescence are used to study the effects of Reynolds number Re, Weber number We and dimensionless film thickness \delta over ranges Re \leq 3900, We \leq 61 and 0.09 \leq \delta \leq 1.35. As film thickness decreases, a transition from a single axisymmetric vortex ring to azimuthally unstable, multi-vortex structures is observed. A regime map in Re-\delta space is constructed, showing that vortex ring instabilities occur at lower Re for thinner films, while no instabilities are detected for thick films up to the highest Re studied. The azimuthal wave number increases with Re and decreases with \delta. Thinner films exhibit faster decay of primary vortex ring circulation due to wall interactions, accompanied by the formation of secondary vortex ring at lower Re. An empirical model is proposed to predict the temporal evolution of total vortex ring circulation, accounting for both generation and decay.