  The elastic Leidenfrost effect occurs when a vaporizable soft solid is
lowered onto a hot surface. Evaporative flow couples to elastic deformation,
giving spontaneous bouncing or steady-state floating. The effect embodies an
unexplored interplay between thermodynamics, elasticity, and lubrication:
despite being observed, its basic theoretical description remains a challenge.
Here, we provide a theory of elastic Leidenfrost floating. As weight increases,
a rigid solid sits closer to the hot surface. By contrast, we discover an
elasticity-dominated regime where the heavier the solid, the higher it floats.
This geometry-governed behavior is reminiscent of the dynamics of large liquid
Leidenfrost drops. We show that this elastic regime is characterized by
Hertzian behavior of the solid's underbelly and derive how the float height
scales with materials parameters. Introducing a dimensionless elastic
Leidenfrost number, we capture the crossover between rigid and Hertzian
behavior. Our results provide theoretical underpinning for recent experiments,
and point to the design of novel soft machines.
