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

We consider a spherical particle levitating above a liquid bath owing to the Leidenfrost effect, where the vapour of either the bath or sphere forms an insulating film whose pressure supports the sphere's weight. Starting from a reduced formulation based on a lubrication-type approximation, we use matched asymptotics to describe the morphology of the vapour film assuming that the sphere is small relative to the capillary length (small Bond number) and that the densities of the bath and sphere are comparable. We find that this regime is comprised of two formally infinite sequences of distinguished limits which meet at an accumulation point, the limits being defined by the smallness of an intrinsic evaporation number relative to the Bond number. These sequences of limits reveal a surprisingly intricate evolution of the film morphology with increasing sphere size, starting from the formation of a neck-bubble morphology typical of a Leidenfrost drop levitating above a flat solid substrate and ultimately reaching a uniform-film morphology similar to that in the case of a large liquid drop levitating above a liquid bath.