  The levitating Leidenfrost (LF) state of a droplet on a heated substrate is
often accompanied by fascinating behaviors such as star-shaped deformations,
self-propulsion, bouncing, and trampolining. These behaviors arise due to the
vapor flow instabilities at the liquid-vapor interface beneath the droplet at
sizes typically comparable to the capillary length scale of the liquid. Here,
we report on the spontaneous bouncing, trampolining, and hovering behavior of
an unconstrained LF water droplet. We observe that the water droplet exhibits
an increase in bouncing height at specific radii with intermittent reduction in
the height of bounce leading to a quiescent LF state. The reemergence of the
trampolining behavior from the quiescent hovering state without any external
forcing is observed at sizes as low as 0.1 times the capillary length. We
attribute the droplet bouncing behavior to the dynamics of vapor flow beneath
the LF droplet. We propose that the trampolining behavior of the droplet at
specific radii is triggered by harmonic and subharmonic resonance between the
natural frequency of the vapor layer and Rayleigh frequency of the droplet.
This proposed mechanism of resonance-driven trampolining of LF droplets is
observed to be applicable for different liquids irrespective of the initial
volume and substrate temperatures, thus indicating a universality of the
behavior. We attribute the intermittent trampolining events to the change in
the natural frequency of the droplet and the vapor layer due to evaporative
mass loss.
