  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.
