Leidenfrost Ratchet

July 29, 2011

In a previous article (Solar Ceria, July 7, 2011), I reviewed the second law of thermodynamics and the requirement that a temperature difference is needed to do work. This requirement was questioned in 1900 by Gabriel Lippmann, who subsequently won the 1908 Nobel Prize in Physics for work in color photography. Lippmann's argument was based on the operation of the mechanical ratchet, a device well known to mechanical engineers.

A ratchet (1) and pawl (2). (Image via Wikimedia Commons).

Lippmann's argument was that a ratchet attached axially to a paddle wheel immersed in a gas would preferentially move in one direction only, so work could be done. This was called a Brownian ratchet, named after the Brownian motion of the gas particles that would drive the paddle wheel. Richard Feynman, who worked in so many areas of physics, gave a convincing analysis in 1962 that work could be done only if the temperature of the paddle wheel was greater than the temperature of the ratchet, thereby vindicating the second law.

The Leidenfrost effect is probably known to most school children, although probably not by name. It may, in fact, be a physics effect known more among girls than boys. This effect, first described in detail in 1756 by the German physician, Johann Gottlob Leidenfrost, is responsible for the dancing of liquid droplets (usually water droplets) on a hot pan. The hot pan generally needs to be about 250°C for the best performance for water droplets.

The heat of the pan turns the water to steam in a thin layer at the contact surface. The steam layer levitates the water droplet above the hot surface, thereby insulating it from the heat, so it keeps the water from vaporizing too rapidly, and the waters droplets are free to move around the pan.

In 2006, a multidisciplinary team of scientists from the Materials Science Institute and Physics Department of the University of Oregon (Eugene, Oregon), the School of Physics, University of New South Wales (Sydney, Australia), and the Department of Mechanical Engineering, Oregon State University (Corvallis, Oregon) decided to combine the Leidenfrost effect with a ratchet to demonstrate directed motion of liquid droplets on a hot plate.[1-2] In this case, the ratchet was a sawtooth pattern formed onto the hot plate.

Leidenfrost ratchet. Droplets accelerate to the right on the sawtooth pattern, since vapor flow, as shown by the arrows, pulls them along. Forces cancel when no pattern is present.

The research team found that they could produce directed droplet motion of several centimeters/sec when the droplets were placed on a brass plate with a sawtooth pattern, as shown in the figure, above. Being thorough, as experimentalists usually are, they tried many liquids over a wide range of boiling temperatures. These included nitrogen (-195.79°C), acetone (56.5°C), methanol (65°C), ethanol (78°C), water (100°C) and hexadecane (287°C).

The research team believes that the droplet motion is driven by forces exerted in the asymmetrical vapor flow between the solid and the liquid.[1] The principal investigator, Heiner Linke, told BBC News that "The vapor mostly flows in one direction, and the droplet sits on the flowing vapor, a bit like a boat carried along in a flowing river."[2] The droplets can scale inclines of up to twelve degrees.[2] There are videos of this phenomenon available on the University of Oregon web site.[3] A screen-capture of this effect appears below.

Droplet motion on a sawtooth-patterned hot plate. (Screen-capture from University of Oregon movie).[3]

Another team, composed of French physicists, has extended this work to sublimation of solids and measurement of the propulsion force on the droplets.[4] They used the sublimation of dry ice for their experiments and the bending of glass fibers in the path of the droplets to measure the force. Forces as high as tens of micro-Newtons per droplet were measured, and the droplet velocities were generally about 10 cm/sec.[4]

Is there any utility in all this? One idea that Linke's group posted on its web site is that the effect may be useful for separating particles by size.[5] The effect may be useful also in cooling integrated circuits, since you can have fluid flow without an actual pump; and, since the action happens only when a certain temperature is reached, it could be used as a thermostat.[2]

References:

1. H. Linke, B. J. Alemán, L. D. Melling, M. J. Taormina, M. J. Francis, C. C. Dow-Hygelund, V. Narayanan, R. P. Taylor, and A. Stout, "Self-Propelled Leidenfrost Droplets," Phys. Rev. Lett., vol. 96, no. 15 (April 19, 2006), Document No. 154502 (4 pages).
2. Roland Pease, "Scientists make water run uphill," BBC, April 30, 2006.
3. Droplet movie, University of Oregon; Another droplet movie, University of Oregon.
4. Guillaume Lagubeau, Marie Le Merrer, Christophe Clanet and David Quéré, "Leidenfrost on a ratchet," Nature Physics May 2011, Volume 7 No 5 pp.395-398.
5. Web site of Linke Group at the University of Oregon.
6. Jearl Walker, "Essay On The Leidenfrost Effect," (125 kB PDF file).
7. Leidenfrost Effect page on Wikipedia.