Liquid droplets assume complex shapes and behave in different ways, each with a distinct resonance – like a drum head or a violin string – depending on the intricate interrelationship of the liquid, the solid it lands on and the gas surrounding it.

Droplets’ movements have implications for everything from manufacturing silicon chips to measuring bodily fluids, but until now there was no way of classifying their motion.

A team led by Paul Steen, the Maxwell M. Upson Professor in Engineering, has created a periodic table of droplet motions, inspired in part by parallels between the symmetries of atomic orbitals, which determine elements’ positions on the classic periodic table, and the energies that determine droplet shapes.

“The question was, can we put these in some sort of organization that allows us to make a little more sense out of them?” said Steen, lead author of “Droplet Motions Fill a Periodic Table,” which published in the Proceedings of the National Academy of Sciences Feb. 21. His former students, Chun-Ti Chang, Ph.D. ’14, now at National Taiwan University, and Joshua Bostwick, Ph.D. ’11, now at Clemson University, were co-authors.

Steen’s group also developed a “wettability spectrometer,” to measure the ease with which droplets advance or recede across a surface. In December, astronauts on the International Space Station plan to test Steen’s findings on wettability to gauge how droplets behave and interact on a support.

“When you reduce gravity, as happens at the space station, it makes things look larger … it’s essentially a microscope for being able to view things at a small scale,” he said. “More importantly, it also changes the time scale, slowing time down, so we’ll be able to see these motions with resolutions that would be very challenging to see on Earth. Taken together, small and fast on Earth becomes large and slow in space for these motions.”

In prior research, Bostwick solved an equation to predict the frequencies of the droplets’ motion; Chang used those theoretical solutions in the lab to guide where to look for the frequencies at which the droplets resonate. The droplets’ shapes correspond to certain frequencies the same way a violin string waveform does.

The researchers noticed the droplet equation’s similarity to the Schrödinger equation, also a partial differential equation that describes wave motions. That gave them the idea of using the classic periodic table to organize “this zoo of solution shapes and frequencies,” Steen said.

“The ordering is much like the periodic table of chemical elements,” he said. “We go from higher energy to lower energy, left to right, top to bottom.”

They also saw that the droplet motions could be classified by their distinctive shape symmetries. For example, droplets that form a star-like shape with five points would all be in one group.

“We call them motion-elements,” said Steen, in a nod to the classic periodic table. Each motion element in the new table – which could conceivably have an infinite number of entries, depending on several variables – classifies a single mode of a droplet’s motion. “You can use combinations of these to understand motion-molecules.”

In the study, Steen’s team discovered the first 35 predicted motion elements for water droplets vibrated on a surface with an angle of contact of about 60 degrees.

Potential applications for this periodic table, which could help researchers understand where a droplet comes from, could include crime-scene forensics, Steen said. Analysts could apply the table’s classifications to blood and the applicable surface to identify the energies involved, and then better infer what might have caused certain spatter patterns.

“Once you recognize what a particular motion can be decomposed into, it tells you more about where it originated,” he said.

Just like the classic periodic table, the droplet table has irregularities in its ordering. These irregularities begin to suggest how droplets might behave in a different universe with different chemical properties. “That’s the most speculative side of this,” Steen said.

The research was partly supported by the National Science Foundation.