Non-keplerian orbits of drops levitating on a cryogenic bath

An “inverse Leidenfrost” state is observed when ambient temperature drops are deposited on a liquid nitrogen bath: fast evaporation of the pool is sufficient to generate and sustain a vapor film that keeps the drops in levitation. Isolated suspended drops then move in straight lines with near-zero friction. Here, we discuss the case of two gliding drops approaching each other. Each drop locally deforms the surface of the bath to balance its weight, and interaction between the two menisci generates mutual attraction. This is a frictionless version of the so-called “Cheerios effect”. In first approach, such a two-body system shares similarities with gravitational attraction between planets. However, the fundamental difference in the nature of the attractive potential gives rise to a set of trajectories quite distinct from the classical Keplerian orbits (ellipse, parabola or hyperbola). We first reconstruct the Cheerios attractive potential from experimental measurement of the drops motion, and then, by pushing the comparison further, we use the reconstructed potential to predict the most unusual trajectories that were experimentally observed . Finally, this approach enables us to determine the necessary conditions to obtain closed orbits.