In the framework of the lubrication approximation, we derive a set of equations describing the steady bottom profile of Leidenfrost drops coupled with the vapor pressure. This allows us to derive scaling laws for the geometry of the concave bubble encapsulated between the drop and the hot plate under it. The results agree with experimental observations in the case of droplets with radii smaller than the capillary length Rcas well as in the case of puddles with radii larger than Rc. © 2012 Académie des sciences.
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