# Brazil Nut Effect Easily Explained With Fluidization

This is the first real explanation of why larger particles rise to the top when you shake a container filled with different sized particles
all of the same density.
Actually it's almost trivial. They made an easy problem more complicated than what it is.
When the container rises, it flings all the particles up to the top and when it falls it flings all the particles down to the bottom.
The accelleration on the nuts at the bottom is the accelleration of the can plus the accelleration of gravity. At the top, however, it's the accelleration of the can minus gravity so the nuts spend more time packed on the bottom than packed on the top.
During the flight up and down the larger particles will have a higher mass/drag ratio than the smaller particles. Mass ~ D^3 and drag ~ D^2. The drag is from the air-particle fluid but a "drag" may also come from the particles scattered in a vacuum.
The larger will blast right past the smaller ones when moving from one end to the other.
Basically the smaller particles act as a fluid when in transit with the larger ones passing through that "fluid."
This happens in both directions.
The difference is on the way down the smaller particles pack earlier and longer than at the top and cease to be like a fluid. The larger particles cannot make much headway in a packed bed.
The small particles may pack at the top as well but not as long as at the bottom so the big particles will rise relative to the small on each shake.
Bret Cahill
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It is not "first" and it is not "real". http://arxiv.org/PS_cache/cond-mat/pdf/0510/0510115v2.pdf ... note that the Brazil nut effect occurs even in vacuum, which sinks your explanation.

Maybe they tried to actually produce quantitative results?

Doesn't follow, since the impluse could be greater at the bottom.

Filling gas is not required for either the "Brazil nut effect" or the "reverse Brazil nut effect". No gas, no drag. It does have an effect, but...

http://www.freepatentsonline.com/EP1432508.html ... 2004 http://inls.ucsd.edu/~lev/papers/gran_patterns.pdf ... suitable for a text http://newton.ex.ac.uk/aip/physnews.653.html ... horizontal brazil nut effect http://jfi.uchicago.edu/~jaeger/granular2/Brazilnut.html ... first reported in the 1930s. References as early as 1998.
What I want to know is could this effect work in a star to preferentially lift larger nucleii to the surface.
David A. Smith
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I _said_ it would work in a vacuum by _my_ analysis.
Bret Cahill
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wrote:

nuclei Brazil nuts are the same density, whereas atomic nuts are not. This is why the stony-ory planets are on the inside and the isy-wispy planets are on the outside.
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Bret Cahill wrote:

I have heard a different explanation:
For a particles to drop down a level, there must be a void underneath the particle, and the void must be large enough for the particle to fit into.
Since, in a randomly shaken container of particles, the odds of finding a small void are greater than the odds of finding a large void, the smaller particles are able to descend more often than the larger particles.
Olin Perry Norton
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wrote:

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Why wouldn't that also be true on the way up?
Any explanation must acknowledge that gravity and the force moving the container are not the same on the top as on the bottom and that the bed resides on the bottom longer than on the top, if at all.
If you don't admit that then what happens on the way up will be the same as on the way down and there's no reason for the large particle to gravitate in any direction.
Bret Cahill
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Bret Cahill wrote:

The particles fall because of gravity.
If there is a void underneath the particle large enough for the particle to fall into, it falls because of gravity.

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Bret Cahill wrote:

The particles fall because of gravity.
If there is a void underneath the particle large enough for the particle to fall into, it falls because of gravity.

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http://www.nature.com/nature/journal/v429/n6990/full/429352b.html
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Dumbass, what will watter or sand do in the same cann?
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They need to be kept separate, in different canns.
Bret Cahill
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I tried three phase fluidization -- liquid, particles, gas -- which has heat transfer coefficients that approach those of condensation but I could never figure out a way to keep the two heavier phases from sloshing to one side of the cylinder.
Bret Cahill
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A more concise and clear restatement of the above:
Due to gravity the small particles spend more time over the course of a cycle packed at the bottom than the top where they spend more time dispersed.
The larger particle cannot plow down through the packed bed at the bottom but it can make headway up through the small dispersed particles above it whenever it has a higher velocity.
Random verticle velocity is why it works in a vacuum.
Bret Cahill
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This is just the void theory with different words. Two masses cannot occupy the same space. Any particle will go down if it can (void beneath it) due to gravity. The larger particle can't plow down through the packed bed at the bottom because there's no void for it. It can go up through the dispersed particles because it can push up and make its own void.
Shaking just generates a random void distribution in the system, which the smaller particles preferentially fill.
Tom.
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True but it doesn't explain why the larger particles move to the top.

Why doesn't the large particle beat the smallers ones to the bottom?

Because the particles act like a fluid.

There are voids in both packed beds and dispersed beds but they aren't 100% random when shaking a can of particles.
Over the course of the cycle more particles will tend to be packed at the bottom than the top.

Why don't the particles fill the same at the top and bottom?
No matter the analysis the explanation must mention that gravity packs the smaller particles at the bottom.
Bret Cahill
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Dear Bret Cahill:
...

It doesn't always: "reverse brazil nut effect" "horizontal brazil nut effect"
David A. Smith Bret Cahill
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Sure it does. Small voids are more common than large ones, so a small particle is more likely to move than a large one. Gravity biases the motion in one direction, so the small particles can move down more easily than the large ones.

A large particle can't enter a small void. In order for a large particle to go down, you need a large void under it.

Well, no. The two things that really define a fluid are infinite strain under constant shear and the ability to transmit pressure. The small particles can "flow" in a sense, but they don't transmit pressure. The situation is more like rarified gas dynamics.

Since they do depend on local geometry, you're correct that they're not 100% random. But I'm not sure that's important for this effect. Shaking creates voids. Small particles can move into a void more easily than large ones. Gravity makes all the particles want to move down into an available void. Therefore the small particles end up at the bottom.

Gravity. The particles all want to be at the bottom. The smaller ones just have an easier time getting there.

Yep. So far, I think your theory and the void theory are really the same physics, just semantically different.
Tom.
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The BN effect doesn't require any theory other than basic Newtonian mechanics.
Fluidization has been studied for over 70 years and even that isn't really necessary. It was just the path that led me to the answer.
. . .

I don't have a theory. All I did was apply Newton's laws in the most conventional mundane manner.

In that case the really interesting question becomes:
How did such a trivial easy-to-explain effect ever get presented as such a baffling curiousity of science in the first place?
Bret Cahill