Drops levitated by an air cushion: asymptotic analysis and stability

Liquid drops can be kept from touching a plane solid surface by a gas stream entering from underneath, as observed for example for Leidenfrost drops. We discuss the limit of small flow rates, for which the gap between the drop and the substrate becomes very small, to obtain a full analytical description of the drop shapes and their stability. It is found that above a critical drop radius no stationary drops can exist and that unstable drops develop a gas ``chimney'' that breaks the drop in its middle. We point out similarities with the breakup of drops in a microfluidic T- junctions.