  Recent experimental results have shown that vibro-fluidized, binary granular
materials exhibit Rayleigh-Taylor-like instabilities that manifest themselves
in rising plumes, rising bubbles and the sinking and splitting of granular
droplets. This work explores the physics behind the splitting of a granular
droplet that is composed of smaller and denser particles in a bed of larger and
lighter particles. During its sinking motion, a granular droplet undergoes a
series of binary splits resembling the fragmentation of a liquid droplet
falling in a miscible fluid. However, different physical mechanisms cause a
granular droplet to split. By applying particle-image-velocimetry and numerical
simulations, we demonstrate that the droplet of high-density particles causes
the formation of an immobilized zone underneath the droplet. This zone
obstructs the downwards motion of the droplet and causes the droplet to spread
and ultimately to split. The resulting fragments sink at inclined trajectories
around the immobilized zone until another splitting event is initiated. The
occurrence of consecutive splitting events is explained by the re-formation of
an immobilized zone underneath the droplet fragments. Our investigations
identified three requirements for a granular droplet to split: 1) frictional
inter-particle contacts, 2) a higher density of the particles composing the
granular droplet compared to the bulk particles and 3) and a minimal granular
droplet diameter.
