Self-propelled Leidenfrost drops on a thermal gradient: A theoretical study

We theoretically investigate the behavior of Leidenfrost drops on a flat substrate submitted to a horizontal thermal gradient and highlight that they are able to self-propel in a preferential direction. Namely, they are found to travel towards the colder parts of the substrate, as if they were trying to maximize their lifetime. In particular, a centimetric water drop can reach velocities of the order of cm/s for thermal gradients of the order of a few K/mm. In general, the presented model, based upon the lubrication approximation in the vapor cushion as in the work of Sobac et al. [“Leidenfrost effect: Accurate drop shape modeling and new scaling laws,” Phys. Rev. E 90, 053011 (2014)] and here formulated for simplicity for a 2D drop, enables predicting the values of these velocities as a function of the thermal gradient, drop size, superheat, and fluid properties. Surprisingly, the variability of vapor properties with temperature turns out to be instrumental for the drop to move, even if the vapor film profile is always asymmetric anyway. Finally, this asymmetry being typically weak, its effect also proved to be well captured by linearization around the corresponding symmetric Leidenfrost state.