Mathematicians Demonstrate a Gravity-Defying Result

It's close to magic. Mathematicians from the University of Bristol have demonstrated that droplets can move uphill — if the plate on which the droplets lie is vigorously shaken up and down. The droplets can defy gravity even on a vibrating incline as steep as 85 degrees.

Applied mathematicians Philippe Brunet, Jens Eggers, and R.D. Deegan, who specialize in fluids, conducted experiments to obtain this result. It applies to a variety of liquids but not to water.

"As the shaking plate rises the drop is compressed, while it bulges upward as the plate falls," Eggers said. "If the shaking is vigorous enough to overcome the surface tension experienced as the drop is compressed, the drop will tend to lean forward, producing a net force which drives the drop uphill."

This method for moving droplets may prove helpful in understanding small-scale manipulation of fluids. But there's a caveat. Because the droplets must withstand a fair amount of force that is pushing and pulling them, they are in danger of breaking apart. Therefore, the droplets cannot be too large and the fluid has to be a bit thicker than water. Pure water droplets break apart before the forces are strong enough to cause them to climb. On the other hand, if the fluid is too thick, the droplets move very slowly.

"Moving small droplets — such as thousands of spots of DNA arranged on a solid surface (a DNA microarray) — is very difficult as their small size causes them to stick to the surface," Brunet said. "So improving our understanding of what causes droplets to move on surfaces will help with this and similar problems."

The results are in the paper "Vibration-Induced Climbing of Drops," published in Physical Review Letters.

Source: University of Bristol, Oct. 3, 2007