Have you ever opened a new box of cereal to find that most of the tasty bits have risen to the top?

As a kid, this feels like hitting the jackpot. But those among us with a more developed sense of delayed gratification might be interested in  redistributing the marshmallows to save some for later.

A quick little shake of the box should do the trick, right? Well, actually, that’s the worst thing you can do. See, mixed in among those hearts, stars, and horseshoes, there’s a surprising amount of physics going on in your box of cereal.

Here’s why things sometimes unmix themselves. [intro] Your cereal ended up neatly sorted into its component parts precisely because of all the shaking and jostling that occurred as the box was transported from the cereal factory to your cupboard. When a mixture of small pieces — such as sand, sugar, or cereal — is shaken at low speeds, the largest pieces of the mixture will make their way to the top, sorting the mixture by size. Even if the bigger pieces are denser than the smaller ones, they’ll still rise to the top.

Physicists have a name for this: the Brazil nut effect. Canned nut enthusiasts might be familiar with the experience of opening a brand new tin only to find all the Brazil nuts at the top and the peanuts on the bottom. This nutty problem began troubling physicists in the 1930s.

Similar self-sorting effects were also a problem for industrial powders, like the powders used for metallurgy, pharmaceuticals, and paint pigments. So understanding this issue was important to more than just the nut industry. Yet it wasn’t until the 1990s that physicists discovered some satisfying explanations for the Brazil nut effect.

Let’s say we have a mix of  purple and green particles, with the purple ones being  three times as big as the green. As the mixture jostles, the large purple particles bounce up, leaving gaps big enough for the smaller green particles to fill. For a while this was considered to be the full explanation, but computer simulations and experiments have revealed another layer that contributes to the Brazil nut effect.

Friction with the walls of the container pulls the outer layer of small particles toward the bottom of the container. Eventually they make their way back to the center of the column where they gradually rise to the top. The circular flow of  particles, driven by friction, sets up convection cells.

You might have experienced them the last time you boiled water for pasta. In a pot of water, a central heat source drives hot water to the surface. The hot water flows toward the edges of the pot, losing heat along the way.

The cooler water sinks along the edges of the pot, only to be reheated by the heat source, starting the cycle over again. For our purple and green particles, convection is instead driven by friction. It lifts all particles to the surface, but the purple particles are too large to be dragged back down along the edges, so they get stranded on top.

These experiments studied perfectly spherical particles of different sizes – not lumpy or oblong particles like nuts or cereal. In 2021 researchers tackled a more real world scenario by taking x-rays of a vibrating tin of nuts. Imagine being that person at a cocktail party.

What do you do for a living? Well, I’me working on a project where we X-ray cans of nuts. Is that like some kind of art project…?

The x-rays revealed that irregular particle shapes — like in the case of fancy nuts or cereal pieces — self-sort even more aggressively. The Brazil nuts jostle into  a vertical orientation, then the peanuts migrate down, pushing the Brazil nuts to the top. But if vibration-induced size segregation wasn’t weird enough to ponder over breakfast, there’s also a reverse Brazil nut effect.

And yeah, that’s the actual name for it Physicists are super creative. In the reverse Brazil nut effect, vibrations cause the largest pieces of a mixture to fall to the bottom. If a mixture is vibrated really fast, it can become fluidized, meaning it begins to act like a fluid.

But, put down the cereal box these vibrations are faster than you’d be able to achieve on your own — fluidization requires vibration frequencies upwards of 20 Hertz, or 20 shakes per second. At these high frequencies, the particles jostle so much that they are no longer in contact. This lack of friction means they bounce around independently, similar to the freeform movement  of molecules in a fluid.

And since the mixture is acting like a fluid, our expectations about fluids apply here. The densest particles slip through the “fluid” to the bottom of the mixture – they sink. So we have these two different scenarios.

Slow shaking causes large particles to rise to the top, and fast shaking causes dense particles to sink to the bottom. That implies the existence of a happy middle Goldilocks point, called the transition frequency. At the transition frequency, the mixture shouldn’t segregate at all.

Researchers have found that by alternating between low frequencies and the transition frequency, they could repeatedly sort and recombine a mixture of  different-sized particles. And these results led to huge developments for the industrial transportation and mixing of granular media – that is, stuff made up of small particles. Any production process that relies on granular components — such as baking mixes, plant fertilizers, medicinal powders, or, yes, breakfast cereals — was plagued by these mixing problems.

But the effects of the Brazil nut effect can be mitigated in several ways. First, whenever possible, the particles in a mixture can be made the same size. The Brazil nut effect only applies to mixtures of  differently-sized particles, so your cereal is less likely to sort itself if the marshmallows are the same size as the oat pieces.

Secondly, reducing friction in hoppers and tubes can prevent the formation of convection cells in the mixture. This can be done by changing the shape of storage containers, or making the walls smooth and slippery. Finally, mixing machines can be tuned to vibrate at  the transition frequency that ensures even distribution of large particles.

So when it comes to your cereal box, you could either experimentally find exactly the right frequency that results in complete mixing… or you could turn the box upside and give it a few good shakes to jostle the marshmallows back into the bulk of the cereal. And if you use this knowledge to guarantee yourself a bowl of all marshmallows… well, we won’t tell your housemates. [ outro ]