Leidenfrost levitation of a spherical particle above a liquid bath: evolution of the vapor-film morphology with particle size

We consider a spherical particle levitating above a liquid bath owing to the Leidenfrost effect, where the vapor of either the bath or sphere forms a thin insulating film whose pressure supports the sphere's weight. Starting from a reduced formulation based on a lubrication-type approximation, we use scaling arguments and matched asymptotics to describe the morphology of the vapor film assuming that the sphere is small relative to the capillary length (small Bond number). We find that this regime is comprised of two formally infinite sequences of distinguished limits, the limits being defined by the smallness of an intrinsic evaporation number relative to the Bond number. As the drop size increases, the vapor-film morphology initially forms a neck-bubble structure, similar to that in the classical Leidenfrost scenario of a liquid drop levitating above a flat substrate; in contrast to the classical scenario, however, the morphology then continues to evolve and ultimately consists of a nearly uniform film bounded by localised capillary waves.