Self-propulsion of Leidenfrost drops
Lay-language version of "Leidenfrost Drop on a Step"Authors:
Guillaume Lagubeau (PMMH-ESPCI), Elise Lorenceau (PMMH-ESPCI), Marie Le Merrer (PMMH-ESPCI), Christophe Clanet (Ladhyx-Ecole Polytechnique), and
David Quéré (PMMH-ESPCI)
A Leidenfrost drop forms when a liquid is deposited on a surface the temperature of which is large enough to create a film of vapour between the drop and the surface. In the case of water, this happens for temperatures larger than 180°C. An example of such levitating drop is presented in figure 1.
Fig.1 Millimetric water droplet in Leidenfost state, on a silicon plate at T=400°C (image from A.L Biance )
Linke et al  have reported in 2006 that such Leidenfrost drops can spontaneously move when deposited on a sawtooth-shaped surfaces. The sequence from Linke is reproduced in figure 2, where the drop is observed to move in the direction were it climbs the steps at a velocity of the order of 5 cm.s-1
Fig.2 Nitrogen drop in leidenfrost state moving at 5cm.s-1 on a sawtooth-shaped surface (image from Linke )
Here we try to investigate the mechanism that leads to this self propulsion. Using an tilted surface (Fig.3), we have first determined the maximal slope that the drop can climb: 0°30’! and deduce the magnitude of the driving force: 10-6N.
Fig.3 Leidenfrost drops climbing a slightly inclined plane.
In a second step, we have changed the volume of the drop (fig.4 left) and imposed a lateral confinement (fig.4 right). We find that the driving force is proportional to the surface of the drop facing the surface, and is independent of the aspect ratio. Surprisingly, the terminal velocity as not the same behaviour: it is independent of the surface in the unconfined state but does increase with the surface in the confined limit: the longer the drop the higher the velocity.
Fig.4 Droplet moving on a ratcheted surface left: unconfined, right confined between two rails.
Then, we reduced the surface to a single step and tried to answer the question: what happen when a Leidenfrost drop moves towards a facing (or back facing) step?
The answer is: all depend on the temperature and vapour film thickness.
Let us be more precise: In most of the cases, a drop moving towards a facing step at small velocity will not climb it if its kinetic energy is not sufficient to win against the gravity. But, under certain conditions (detailed below), it will.
In the same way, most of the drops moving towards a back facing step will go down the step. However, figure 5 shows that a small velocity drop moving towards a back facing step “bounces” on the step and goes back.
One deduces from these observations that there is a force created by the step directed towards the upper level.
Fig.5 leidenfrost drop climbing back a 50µm step (video)
The conditions for a drop to climb spontaneously a facing step are: the step thickness has to be of the order of the vapour film thickness (50µm) and the temperature of the plate should not be too high (typically less than 250°C for water droplet). The temperature dependency suggests a mechanism involving the local boiling of the drop.
Even if this must be further confirmed, our present understanding of the self-propulsion of Leidenfrost drops is that it is similar to a rocket effect: due to the dissymmetry of the substrate geometry the vapour is mainly ejected towards the less resisting side and propels the drop towards the opposite side through action/reaction principle. This mechanism is enhanced when boiling occurs.
 A-L. Biance and al, Leidenfrost drops, Physics of Fluids 15, n°6 1632-1637 (2003)
 H.Linke and al., Self-Proppelled Leidenfrost Droplets, Physical Review Letters 96, 154502 (2006)