New Patterns for an Old Effect
Researchers have discovered new behavior in a pattern-forming process that has been studied for more than 200 years. When fine grains are scattered on a thin, vibrating, horizontal plate, the grains form patterns that trace out the “nodal” lines where there is no motion. Now a team in Finland has found that if the plate is underwater, the particles instead head for the regions with the greatest vibration amplitude. The researchers also show that a computer algorithm can tune the vibrations to guide particles along prescribed paths, which could be useful for moving small objects such as powder grains or biological cells.
In 1787 the German scientist Ernst Chladni found that sand scattered over a metal plate forms intricate patterns when the plate is vibrated with a violin bow. In the following century, Michael Faraday explained that the particles jump about until coming to rest at the positions of zero vibrational amplitude—the nodes of the two-dimensional acoustic standing waves.
Quan Zhou and co-workers at Aalto University in Espoo, Finland, have now found that when these so-called Chladni figures form underwater, the particles gather instead at the antinodes, where the amplitude of motion is the greatest. In their experiments, when a 5-cm-square silicon plate was vibrated at its resonant frequency, 0.75-mm-diameter glass beads formed antinode patterns with fourfold symmetry. (Chladni and Faraday had also seen particles collecting at antinodes, but only when using much smaller particles; Faraday attributed this behavior to air currents that carry fine particles aloft.)
The key to this behavior is the drag force that the water imposes on the particles, which makes it harder for them to lift off the surface, compared with experiments in air. Meanwhile, the particles are driven horizontally by two forces: surface waves and gravity (because particles roll downhill as the plate flexes). It turns out that the net horizontal force averaged over a complete oscillation cycle always points toward the antinodes. Zhou draws an analogy with a ball trapped inside a long, narrow, horizontal tube. “If you hold one end of the tube and vibrate it using your wrist, the ball should move to the other end,” he says.
The particles can also be moved by plate vibrations at frequencies other than the resonant frequency. In that case, many modes of vibration are excited and the beads execute vortex-like motions that are hard to fully account for theoretically.
The researchers exploited these non-resonant motions to guide particles along predefined paths. In their system, at regular waypoints along the selected trajectory, a camera records the location of a particle or group of particles, and then the computer calculates the mixture of vibrational modes that will send it toward the next waypoint. This technique allowed the team to send a single bead through a maze on the plate surface, to guide two particles simultaneously along paths shaped like the letters L and C, and to split a cluster of particles in two. Zhou and his colleagues had previously used a similar technique to guide particles on vibrating surfaces in air using only resonant Chladni modes [1], but in the new experiments underwater, they excited the motion at non-resonant frequencies as well.
Moving small particles around remotely in a fluid medium is a challenge faced by several technologies, for example, moving and sorting living cells in biotechnology and tissue engineering, or manipulating fine powders in pharmaceutical engineering. Compared with existing particle-guiding methods, Zhou says that his team’s system has the advantage of simplicity: just a single vibration source can produce rather complicated motion because it can combine many resonant modes.
Devaraj van der Meer of the University of Twente in the Netherlands and his colleagues predicted with computer simulations that relatively large particles, like those in these latest experiments, might be made to move to antinodes [2], but he says that the effect proved elusive in experiments. Chemical engineer Leslie Yeo of RMIT University in Melbourne, Australia, is not surprised that heavy particles can be pushed to antinodes, but he still calls the manipulation method “quite neat.”
“If this technique could be scaled down a bit, it may constitute a nice tool for assembling particle structures,” adds van der Meer. “Any technique that would be able to reliably manipulate particles at small scales would be very welcome.”
This research is published in Physical Review Letters.
–Philip Ball
Philip Ball is a freelance science writer in London. His latest book is Beautiful Experiments (University of Chicago Press, 2023).
References
- Q. Zhou, V. Sariola, K. Latifi, and Ville Liimatainen, “Controlling the motion of multiple objects on a Chladni plate,” Nat. Commun. 7, 12764 (2016).
- H. J. van Gerner, M. A. van der Hoef, D. van der Meer, and K. van der Weele, “Inversion of Chladni patterns by tuning the vibrational acceleration,” Phys. Rev. E 82, 012301 (2010).