A spinning top submerged in a liquid can make a striking fractal structure.
Fractals are patterns and structures that repeat themselves at smaller scales when zoomed in. and at the Massachusetts Institute of Technology were studying how one liquid breaks up into droplets when it is mixed into another and unexpectedly discovered a new kind of liquid fractal.
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Their original experiment consisted of adding liquids to a tank of glycerine in which a spinning top was immersed. Because of the shape of the top, the added liquid and glycerine swirl together in a more complex way than, say, mixing tea and milk with a spoon.
Keshavarz and Geri wanted to see whether using the spinning top for mixing would make the added liquid fragment, or break into individual droplets, and what the sizes of such droplets might be.
Because it can be hard to see droplets of one liquid in another, they decided to use a substance that would make the droplets easier to count and measure. When they poured this elastomer into the tank, it got caught in the glycerine swirling around the spinning top. With each spin, the elastomer stretched around the top in thinner and thinner loops. Eventually, it broke into many droplets, each of which solidified into a bead within minutes.
The researchers wanted to measure the sizes of these beads and count them, so they removed the top and let buoyant forces push the beads to the glycerine surface. Keshavarz says that, one day, they let the beads rise overnight and what they saw in the morning surprised them.
鈥淭hey formed a really intricate, beautiful fractal structure,鈥� he says. His and Geri鈥檚 video of the process won the at the annual meeting of the American Physical Society鈥檚 Division of Fluid Dynamics in Indianapolis, Indiana, in November.
They repeated the experiment a few times and worked out that the fractal pattern forms because beads of different sizes rise to the surface at different speeds. Larger beads rise the fastest and arrive at the surface first. Smaller beads then rise more slowly, reach the surface and attach to the larger beads in certain patterns because of the Cheerios effect 鈥� a phenomenon where objects arrange themselves in particular ways to minimise the distortion of a liquid鈥檚 surface. Even smaller beads then arrive at the surface, and the attaching process keeps repeating, thus creating a self-similar, or fractal, pattern.
at Grenoble Alpes University in France says that this mixing process differs from the more common kinds of mixing that produce many identical droplets that get evenly distributed throughout.
Consequently, using a spinning top to mix could be used to assemble elastomer structures that have pieces of different sizes without having to connect them one at a time, says at Princeton University.
However, predicting details of a fractal structure that specific liquids and spinning speeds would make would be very challenging, says at the University of California, Santa Barbara. Writing down equations that predict how glycerine swirls around the spinning top is already difficult, he says.
