Spontaneous dynamics of Leidenfrost drops

Leidenfrost drops are liquid drops levitated by their vapor above a superheated substrate. They are famous for their spectacular mobility, which has traditionally been attributed to the lack of direct contact between the drop and the substrate. Recent experiments, however, have revealed that Leidenfrost drops may also undergo “symmetry breaking” leading to a spontaneous “rolling” motion in the absence of external gradients [A. Bouillant et al., Nat. Phys. 14, 1188 (2018)]. 

Motivated by these experiments, we theoretically investigate the translational and rotational dynamics of Leidenfrost drops on the basis of a two-dimensional model, focusing on drops small relative to the capillary length. The model couples the equations of motion of the drop, which flows as a rigid wheel, and instantaneous thin-film equations governing the vapor film.

Our model predicts an instability of the symmetric Leidenfrost drop, which leads to spontaneous motion.  It is shown that the key instability mechanism is the nonlinear coupling between the internal flow within the droplet and the external lubrication flow in the vapor film.  Our results serve to illuminate several key aspects of the experiments, including the origins of the experimentally measured propulsion force.