53. Shaken, not Stirred:
Brazil Nuts Effect
The Question:
Take a jar of nuts of mixed sizes, shake vigorously up and down, to get a good mix. Open the jar and what do you see? A good mix? Unlikely. More likely: the heavy particles, owing to their weight, will have sunk to the bottom, the light ones will have crawled to the top.
Right?
The Paradox:
Wrong again! The big, heavy nuts are on top, the light ones at the bottom.
Repeat the experiment by placing an almond at the bottom of a jar. Then fill the jar halfway with rice. Cover the jar with one hand so nothing spills, and start shaking. Lo and behold, after a few energetic wobbles, the almond magically rises to the top.
Or do something we are all familiar with: shake a bowl of popcorn. What happens? All the small, hard kernels will migrate to the bottom, leaving the fluffy white goodies on top.
Background:
The effect seems paradoxical at first, because we are used to a different scenario: when letting a mixture of two liquids, say oil and water, stand still for a while, the heavier liquid will sink due to gravitation, thus displacing the lighter liquid towards the top.
But the situation we look at here is totally upside down
Dénouement:
The explanation can be given in two words: percolation and convection.
Whenever a shake elevates a big nut every so slightly, a small void opens up below it. Immediately, smaller nuts from the sides will tumble into the empty space below the biggie, thereby preventing the biggie from falling back into the void, and thus keeping it at the higher level. At the next shake, the big nut is again lifted a little, smaller nuts tumble into the void, preventing the biggie from settling back, and so on, until it hits the surface. There it usually remains just bouncing up and down. Sometimes it does go under, only to re-appear again a few shakes later.
Percolation – such as water dripping through coffee kernels – is the process that describes the small nuts’ migration in between the larger grains down to the bottom of the jar or bowl. Convection describes the push of the larger grains upwards toward the top of the pile.
Technical supplement:
A physical system, like the jar of nuts, or the bowl of rice with the almond, always tries to attain a state of minimum energy. This means that the center of gravity should be as low as possible. How can the center of gravity be low if the heavy nuts are on top and the less heavy on the bottow? Well, we must take a holistic view: the large Brazil nuts are heavier but around them there is a lot of air…just empty space. The small nuts, gathered at the bottom, are much more densely packed, with very little weightless air in between them. Hence, the center of gravity does, in fact, move downwards when the jar and the bowl are shaken.
***
As reasonable as the dénouement sounds, the issue is not yet fully resolved and research about the Brazil Nut Effect is still ongoing.[1] Scientists believe that there may be several more factors at play. Some suspect, for example, that the air pressure in the space between the nuts, friction, the amplitude and frequency of the vibrations, the geometry of the container may contrbiute to the effect.
And that actually makes the Brazil Nut Effect even more interesting. Because when the big nuts and the small nuts have the same densities, they remain mixed even after thorough shaking. Indeed, there may even be a Reverse Brazil Nut Effect that may occur under certain circumstances. The ratio of the densities of the big nuts versus the small nuts is one reason. And I just mentioned that the geometry of the container may play a role. Apparently, convection currents have been observed in a martini glass-shaped container that sent large grains to the bottom, keeping the little ones on top.[2]
Speaking of which, is this why James Bond, preferred his martinis “shaken, not stirred?” Probably not. However, a generation ago, a team of six researchers published a paper in the British Medical Journal showing that the antioxidant activity of shaken martinis is superior to that of stirred martinis.[3] Now, couple that with the antioxidants present in the Brazil nuts that float on top of the jar and we know why 007 managed to get out of any spat.
See also: Tea Leaves Paradox, Parrondo Paradox (movement against gravitation)
© George Szpiro, 2019
[1] For example, https://www.researchgate.net/publication/12008313_The_Reverse_Brazil_Nut_Problem_Competition_between_Percolation_and_Condensation
[2] http://guava.physics.uiuc.edu/~nigel/courses/563/Essays_2005/PDF/missel.pdf
[3] https://www.bmj.com/content/319/7225/1600.full
Corrections, comments, observations:
