  Droplets can self-propel when immersed in another liquid in which a
concentration gradient is present. Here we report the experimental and
numerical study of a self-propelling oil droplet in a vertically stratified
ethanol/water mixture: At first, the droplet sinks slowly due to gravity, but
then, before having reached its density matched position, jumps up suddenly.
More remarkably, the droplet bounces repeatedly with an ever increasing jumping
distance, until all of a sudden it stops after about 30 min. We identify the
Marangoni stress at the droplet/liquid interface as responsible for the
jumping: its strength grows exponentially because it pulls down ethanol-rich
liquid, which in turn increases its strength even more. The jumping process can
repeat because gravity restores the system. Finally, the sudden death of the
jumping droplet is also explained. Our findings have demonstrated a type of
prominent droplet bouncing inside a continuous medium with no wall or sharp
interface.
