Droplet breakup and size distribution in an airstream -- effect of inertia

We experimentally investigate the morphology and breakup of a droplet as it descends freely from a height and encounters an airstream. The size distributions of the child droplets are analysed using high-speed shadowgraphy and in-line holography techniques. We found that a droplet falling from various heights exhibits shape oscillations due to the intricate interplay between inertia and surface tension forces, leading to significant variations in the radial deformation of the droplet, influencing the breakup dynamics under an identical airstream condition. Specifically, the droplet undergoes vibrational breakup when introduced at a location slightly above the air nozzle. In contrast, as the release height of the droplet increases, keeping the Weber number defined based on the velocity of the airstream fixed, a dynamic interplay between the inertia of the droplet and the aerodynamic flow field comes into play, resulting in a sequence of breakup modes transitioning from vibrational breakup to retracting bag breakup, bag breakup, bag-stamen, retracting bag-stamen breakup, and eventually returning to vibrational breakup. Our experiments also reveal that the size distribution resulting from retracting bag breakup primarily arises from rim and node fragmentation, leading to a bimodal distribution. In contrast, bag and bag-stamen breakups yield a tri-modal size distribution due to the combined contributions of bag, rim, and node breakup mechanisms. Furthermore, we utilize a theoretical model that incorporates the effective Weber number, considering different release heights. This model accurately predicts the size distribution of the child droplets resulting from the various breakup modes observed in our experiments.