Beyond Breakfast: The Cheerios Effect, Tilting Disks, and Why Measuring it All Matters

Daniel Harris prefers Cinnamon Toast Crunch, but he’s spent a lot of time talking about Cheerios lately. And cleaning them up. The cleaning up is thanks to his 1-year-old daughter, but the talking is courtesy of his latest physics research project. Harris is a professor at Brown University who studies fluids and how they interact with solid objects. He doesn’t study breakfast cereal per se, but even cereal follows the laws of physics.

Cheerios in Milk. Credit: Photo by on Unsplash.

It turns out that one of the same physical interactions that governs the behavior of the last few Cheerios in a bowl of milk also enables water-walking insects to climb onto land and tiny particles to self-assemble into small but functional machines. The better we understand these forces, the better position we’re in to harness them in designs for next-generation robots, medical devices, environmental sensors, and other technological advances.

With this in mind, a team composed of Harris, undergraduate student Ian Ho, and former postdoc Giuseppe Pucci recently developed a new way to measure a small but important force that is key to these interactions. In a paper published last month in the American Physical Society’s journal Physics Review Letters, the team describes their technique and shares new insight on a phenomenon known as the Cheerios effect.

If you’re a cereal fan, you may have noticed that as you reach the end of your breakfast (or, in my case, late-night snack), the last few pieces of cereal don’t disperse evenly along the surface of the milk. Instead, they seem to latch onto their neighbors and form floating clusters. This is a real physical phenomenon, and it would happen even if the bowl was totally isolated from spoons and vibrations.

The effect was recognized in bubbles and other small objects long before Cheerios were invented and has intrigued scientists for decades. We now know that two Cheerios (or other small objects) resting on milk (or another liquid) are attracted to one another because of how they deform the liquid surface. Cheerios don’t just displace milk, they interact with the liquid in a way that fundamentally changes the geometry of its surface. The end result is that the Cheerios are sort of pushed together–it’s easier for them to clump together than stay dispersed. This attractive force is called the capillary force and is a result of the surface tension of the fluid.

Although the concept is well-understood, it’s proven tricky to directly measure the attractive force between two floating objects. This new design, fabricated by Ho, is based on a healthy dose of ingenuity, many prototypes, and magnetism.

The apparatus consisted of a tub of water placed inside a magnetic field. Rather than Cheerios, the objects were small 3D-printed disks. One of the disks held a magnet, the other was connected to a motor that, when activated, would move the disk by a set distance. The disk with the magnet wasn’t attached to anything but was kept in place by two vertical supports as shown in the photograph.

Photo of two disks in the experimental apparatus as they deform the surface of the liquid and attract
one another. The disk on the left has the magnet and the disk on the right is attached to the motor. Credit: Ho, et al., Physical Review Letters.

The researchers started with the disks nearly touching. Under normal circumstances, disks this close would immediately clump together, but the vertical supports restrained them. Then the researchers moved the motorized disk a predetermined distance away from its neighbor. Once there, they gradually increased the strength of the magnetic field around the bath.

The magnetic field applied a force to the magnet that directly opposed the capillary force. As the strength of this force grew, it eventually counterbalanced and then surpassed the capillary force, at which point the disk with the magnet moved off of the vertical supports as it began drifting backward, away from its neighbor. The researchers noted when this happened. Then, they simply determined the strength of the magnetic force at that point, which was equal and opposite of the capillary force, and repeated the entire process for various separation distances.

Video of an experimental run. Credit: Ho, et al., Physical Review Letters.

When the team first compared their experimental data to computer simulations, the results were disappointing. Things matched pretty well when the disks were far apart, but not at short distances. Eventually, inspiration struck and they realized that the disks in the experiment weren’t limited to moving horizontally and vertically, like the disks in the model. The real disks could also tilt.

“Once we had the idea to incorporate flexibility in our mathematical model to allow for a spontaneous tilt of the disk things matched much better,” Harris explains. “Then following this, we went back and experimentally visualized the tilt we predicted and everything fell into place.” It turns out that the disks

tilted inward as they approached one another by about 1 degree. It’s not much, but that degree had a measurable effect on the attractive force between the disks at short distances.

Using the same setup, the researchers analyzed how disk mass and diameter influenced the capillary forces in their system. They expect their results to be relevant even for systems you (hopefully) won’t find at the breakfast table, including insects and microrobots moving at air-water interfaces. Cheerios might be a fun hook, but the potential applications of the Cheerios effect extend far beyond the cereal bowl.

Kendra Redmond

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