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Bouncing Droplets

December 3, 2015

An occasional theme in early cinema was dripping water keeping someone awake. In the cartoon world, a hibernating bear was the most likely victim. Dripping water would keep me awake some nights, not because I could hear it in the bedroom, but because I knew I would need to fix a leaky water faucet. I do most of my own plumbing; and, as a rule, I find that all plumbing jobs escalate to a much larger task than expected, just like software development.

The United States has benefited from abundant water for agriculture and personal use, but times have changed. For the past four years there's been a severe drought in the Colorado River basin, and California, which uses a third of that river's flow, has been greatly affected.[1] This exceptional drought affects not just some western states, but all states that receive agricultural goods from these areas. California has been exporting "virtual water" out of the state at an unsustainable rate.

Virtual water is water used in the growth, harvesting and packaging of food, or the manufacture of commodities. I wrote about the concept of virtual water in two previous articles, Virtual Water, March 4, 2013 and Virtual Water in the Roman Empire, January 22, 2015. California exports large quantities of virtual water not just through agriculture, but in electronics. It takes gallons of water to produce a single integrated circuit.

According to Mother Jones, it might be better from a conservation of virtual water standpoint to have wine rather than walnut muesli for breakfast. The following table shows how many gallons of virtual water are contained in the following produce items.[2]

 ItemGallons of Water
 One Walnut4.9
 One Head of Lettuce3.5
 One Tomato3.3
 One Almond1.1
 One Pistachio0.75
 One Strawberry0.4
 One Grape0.3

I mentioned fixing leaky faucets in my house. While water drops don't seem to amount to much, the U.S. Environmental Protection Agency estimates that water leaks in a typical household waste more than 10,000 gallons of water annually.[3] This amounts to more than a trillion (million-million) gallons wasted annually nationwide. One out of every ten homes have leaks wasting 90 gallons or more per day.[3] The following map shows current water usage across the United States.[4]

US water use by state

US water use by state, gallons per day per person. (Modified EPA image.)[4)]


While drips and drops seem quite ordinary, there's a lot of physics behind the formation, movement, and impact of droplets. I've written several articles about droplets, including the technologically important processes of hydrophilicity and hydrophobicity (Evaporation, August 7, 2013, Icing-Resistant Surfaces, August 8, 2012, Superhydrophobic Anti-Glare Glass, May 2, 2012, and Tiny Droplets, March 6, 2012). Mechanical engineers from the Swiss Federal Institute of Technology (ETH, Zurich, Switzerland) have just discovered an unusual phenomenon associated with water droplets on superhydrophobic textured surfaces in low-pressure environments.[5-6]

Hydrophobicity, in which a surface resists wetting, is technologically important. Hydrophobic surfaces that resists icing are important for aviation, and for power transmission lines. The ETH research team discovered that a particular microstructuring creates a superhydrophobic surface that will self remove water droplets in a low-pressure environment. The droplets suddenly levitate and bounce off the surface in a trampoline-like bouncing behavior. Sequential collisions with the surface accelerate the droplets until they bounce away.[5-6]

In the ETH experiments, one millimeter-sized water droplets were placed on a rigid, microstructured, silicon surface and the air pressure was reduced. Using a high speed camera to monitor these droplets, it was found that they first remain motionless on the surface; then, at about a twentieth of atmospheric pressure, they suddenly jump up. When they land again on the surface, they jump again, only to a higher height.[6]

Artist's impression of a droplet bouncing from a microstructured silicon surface (ETH-Zurich).

Artist's impression of a droplet bouncing from a microstructured silicon surface.

The microstructured silicon surface repels water droplets so strongly that they catapult upwards.

(Digit Works/ETH Zurich image.)


Such behavior is confusing. While the rigid silicon surface can't provide any additional energy to the droplets, the restitution coefficient, the ratio of speed after the collision of before the collision is greater than one, an apparent violation of the second law of thermodynamics.[5-6] Of course, experiment showed that no perpetual motion is involved. Vapor pressure from evaporation of the droplet, contained by voids in the surface texture and the initial adhesion of the droplet, launches the droplet upwards at each impact.[5-6]

If the evaporating water supercools below its freezing point and ice crystals form, the latent heat of fusion will heat the droplet to the freezing point in a few milliseconds, leading to explosive evaporation, and the droplet shoots up like a rocket.[6] This effect lifts icy drops the moment that they freeze.[5]

The process was optimized by arranging the microstructure to have columns a few micrometers wide spaced about five micrometers apart. The surface needs to be rough enough to be superhydrophobic, but not so rough as to let the water vapor escape too quickly through the surface channels.[6] Says ETH professor, Dimos Poulikakos,
"From the results of our research we can deduce what qualities surfaces need to have in general in order for them to violently repel water and ice, and then design them accordingly."[6]
These observations are for droplets in a low-pressure environment, so it remains to be seen how this could be useful in real-world applications.[5-6]

High speed imaging of a droplet bouncing from a microstructured silicon surface.

High speed imaging of a droplet bouncing from a microstructured silicon surface. The droplet bounces higher on each successive bounce. (ETH Zurich image by Tom Schutzius.)


References:

  1. Abrahm Lustgarten, Lauren Kirchner, Amanda Zamora and ProPublica, Scientific American, "America's water crisis is so much bigger than California," Salon, June 27, 2015.
  2. Alex Park and Julia Lurie, "It Takes How Much Water to Grow an Almond?!" Mother Jones, February 24, 2014.
  3. WaterSense - Fix a Leak Week, US Environmental Protection Agency, October 16, 2016.
  4. WaterSense - Our Water - Tomorrow & Beyond, US Environmental Protection Agency, October 16, 2016.
  5. Thomas M. Schutzius, Stefan Jung, Tanmoy Maitra, Gustav Graeber, Moritz Köhme, and Dimos Poulikakos, "Spontaneous droplet trampolining on rigid superhydrophobic surfaces," Nature, vol. 527, no. 7576 (November 5, 2015), pp. 82-85, doi:10.1038/nature15738.
  6. Trampolining water droplets, Eidgenössische Technische Hochschule Zürich Press release, November 4, 2015.

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