Feb 26 2019
Liquid droplets take up complicated shapes and behave differently, each with a unique resonance—similar to a violin string or a drum head—based on the complex interrelationship of the liquid, the gas surrounding it, and the solid it lands on.
The movements of droplets find applications for everything from manufacturing silicon chips to measuring bodily fluids; however, to date, there was no method for categorizing their motion.
A research team headed by Paul Steen, the Maxwell M. Upson Professor in Engineering, has developed a periodic table of droplet motions, partly motivated by parallels between the symmetries of atomic orbitals, which determine positions of elements 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?
Paul Steen, Maxwell M. Upson Professor in Engineering, Cornell University
Steen is also the lead author of “Droplet Motions Fill a Periodic Table,” published in the Proceedings of the National Academy of Sciences on February 21st, 2019. The co-authors were his former students, Chun-Ti Chang, PhD ’14, now at National Taiwan University, and Joshua Bostwick, PhD ’11, now at Clemson University.
Additionally, Steen’s group created a “wettability spectrometer” to measure the ease with which droplets move forward or backward over a surface. In December 2019, astronauts on the International Space Station intend to test Steen’s discoveries on wettability to measure how droplets interact and behave 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.”
As part of a previous study, Bostwick deciphered an equation to calculate the frequencies of motion of the droplets; Chang employed those theoretical solutions in the lab to show where to seek the frequencies at which the droplets resonate. The shapes of droplets correspond to particular frequencies similar to how a violin string waveform does.
The scientists observed the similarity of droplet equation with the Schrödinger equation, which is also a partial differential equation that explains wave motions. That offered them the concept of using the classic periodic table to classify “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.”
Furthermore, they observed that the droplet motions could be categorized by their unique shape symmetries. For instance, droplets that take the shape of a star with five points would all be placed in one group.
“We call them motion-elements,” stated Steen, in a nod to the classic periodic table. Each motion element in the new table—which could possibly have a countless number of entries, depending on numerous variables—categorizes a single mode of a droplet’s motion. “You can use combinations of these to understand motion-molecules.”
In the research, the team led by Steen identified the first 35 predicted motion elements for water droplets that resonate on a surface with an angle of contact of around 60°.
According to Steen, potential applications for this periodic table—which could help scientists to understand where a droplet originates from—could include crime-scene forensics. Analysts could make use of the table’s classifications to blood and the applicable surface to find out the energies involved, and then better conclude what might have caused particular spatter patterns.
Once you recognize what a particular motion can be decomposed into, it tells you more about where it originated.
Paul Steen, Maxwell M. Upson Professor in Engineering, Cornell University
Similar to the classic periodic table, the droplet table includes irregularities in its ordering, which begin to explain how droplets might behave in a different universe with different chemical properties. “That’s the most speculative side of this,” stated Steen.
The work was supported in part by the National Science Foundation.