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# Water Droplets Superpropulsion

Fluid dynamic is one of the most complex and interesting things in physics. Slow motion pictures of drops landing on water can give us an insight of what is happening. And the basic physics of fluid flow is expressed by old equations written down in the 19th century. However, those non-linear equations are very difficult to crack and still need to be uncovered today. Many surprising aspects of fluid dynamics are waiting to be fully explored, and droplets are one of those.

Waves follow our boat as we meander across the lake, and turbulent air currents follow our flight in a modern jet. Mathematicians and physicists believe that an explanation […] can be found through an understanding of solutions to the Navier-Stokes equations. Although these equations were written down in the 19th Century, our understanding of them remains minimal. The challenge is to make substantial progress toward a mathematical theory which will unlock the secrets hidden in the Navier-Stokes equations.

Millennium Prizes, http://www.claymath.org/millennium-problems/navier-stokes-equation

Recently, a team of researchers led by Christophe Raufaste has found that droplets ejected by an oscillating surface can at times travel faster than the surface that ejected them. In their paper published in the journal Physical Review Letters, the team describes experiments they conducted by flinging water from a superhydrophobic surface. More precisely, they investigate the behavior of droplets and soft elastic objects propelled with a catapult.

(a) Image sequences of a typical droplet propulsion. In the initial stage of the droplet propulsion, the droplet deformation is not homogeneous but concentrated in its lower part. In an intermediate stage the deformation reaches the top of the droplet. Later on the droplet leaves the catapult with a complex and deformed shape. During its flight, we clearly see the oscillation modes of frequency f0. (b) A space-time diagram is built along the dashed line drawn in image t=0. It illustrates the oscillatory motion of the catapult plate and the difference between the maximum plate velocity and the ejection velocity of the droplet.

In their experiments, they showed that the ejection velocity depends on both the projectile deformation and the catapult acceleration dynamics. In fact, they demonstrated that water droplets will be ejected from a water surface on a bendable piece of vibrating plastic. And in some specific cases, some of those water droplets can actually travel faster into the air than the plastic base that pushed them!

Like a tennis ball, the droplet rebounded as it was being pushed off the surface.

This superpropulsion effect has strong potentialities: actuation of droplets, sorting of objects according to their elastic properties, and energy saving for propulsion engines.