Granular Separation: The Brazil Nut Effect

As I’m sure you will have noticed, everyday phenomena is all around. There are always exceptions to every rule, and always something that science has yet to explain (looking at you, magnets). One of my absolute favourites is the Brazil Nut Effect – simply put, why do the largest nuts in a mixture always rise to the top? Surely gravity would place the larger and heavier nuts at the bottom of a mixture? This doesn’t just apply to mixed nuts, although that is where the effect is most commonly observed, it applies to any granular mixture such as granola, or a mixture of coffee beans and coffee grounds; the smaller grains are always at the bottom.

On the face of it, the answer to the question is simple: the smaller nuts fall through gaps that the larger nuts can’t fit into, filling the space beneath them and pushing the larger nuts to the top as the container is shaken. However, this is just the common sense answer, the answer that most people can accept and then move on with their lives, safe in the knowledge that a container of nuts and the physics behind it will not feature in their thoughts and dreams.

The people who CAN’T accept this answer did some research. And then even more research. Then more people who couldn’t accept the answer challenged the research with more research. And the years and years of research into the problem have produced no complete physical or mathematical theory that can fully explain why nuts behave as they do. It’s just so brilliant that this of all things remains a mystery. Get ready, we are about to get really sciencey.

There have been roughly 10 different theories proposed as the answer to this mystery, each has been studied intensively through real-life experiments and computer modelling, and each has produced significant failings and problems that prevent a proper conclusion. Currently the thinking is that the solution must be a mixture of a few different theories, or a result of the competition between them. We just don’t definitely know which ones. Or why.

One of the most familiar theories is granular convection – an idea based on the well-understood convection currents we can see when a liquid is heated: hot water rises, cold water falls, and the result is a circular current:

convection

Some experiments on a cylinder filled with large and small grains showed that a current formed as the cylinder was shaken, with the current rising up the middle of the mixture and narrower channels falling downward at the sides. The smaller grains fell down the side channels easily but the larger grains, brought to the top of the mixture by the rising central current, could not. This theory had some holes however, such as being unusually affected by changes in friction and air pressure, as well as showing a strange dependence on how dense the larger particles were. Changes in container shape and particle shape also inexplicably changed the convection currents, to the extent that the convection theory cannot be fully endorsed.

To make matters even more complicated, some researchers claim to have witnessed the Reverse Brazil Nut Effect. This is exactly what it says on the tin: under certain conditions, larger grains will fall the bottom of a mixture instead of rising to the top. Some researchers refuse to acknowledge that this reverse effect even exists. Experiments were carried out to investigate this, and provided absolutely no useful conclusion. Some experiments found that you could observe the Brazil Nut Effect in a system of shaking your cylinder, but if the shaking continued for long enough then the effect would actually reverse itself and the Reverse Brazil Nut Effect would be observed.

This picture of a container being shaken shows the Brazil Nut Effect on top (a) and the Reverse Brazil Nut Effect below (b).

reverse-effect

Another theory for the Brazil Nut Effect is based on inertia. Inertia is the resistance of any physical object to any change in its state of motion. If something is moving, it will continue to move until it is acted on by a force. So as you shake your container of mixed grains, the inertia of the larger grains as they move will cause them to break through a thin layer of smaller grains that are moving slower. When the larger grains come back down, the smaller grains will have filled in the gap they left, so the larger grains will have risen up through the container. This mechanism can even successfully explain the Reverse Brazil Nut Effect, but it makes a lot of assumptions and does not stand up to changes in the parameters of the experiment.

A third important theory that encompasses both the BNE and the RBNE (yes I got bored of typing them out, stay with me) is based on condensation, so you effectively have to imagine the different sizes of grains as different types of liquid. Then you have to do a lot of complicated maths based on molecular dynamics, and it brings us to the conclusion that the theory is based on thermodynamics and therefore has problems with competing energy and entropy, and is a bit too theoretical to be the answer to our question.

In conclusion, there is no conclusion! In the words of this incredible 12-page-long physics paper about nuts, ‘The underlying physical mechanism behind the BNE is still not well understood’. I just wanted you all to appreciate that the bag of mixed nuts sitting innocuously in your cupboard actually represents literal years of scientific research, and has frustrated physicists even to this day. I love the amount of work that scientists have put into understanding this. It’s nuts, right?

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