Brazil Nut Effect Easily Explained With Fluidization

It is not "first" and it is not "real".

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...

2004 suitable for a text horizontal brazil nut effect 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

I _said_ it would work in a vacuum by _my_ analysis.

Bret Cahill

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

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

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

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.

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.

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.

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

Dear Bret Cahill:

It doesn't always: "reverse brazil nut effect" "horizontal brazil nut effect"

David A. Smith Bret Cahill

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.

You can't explain that because large particles don't move to the top. That doesn't happen. Small particles move to the bottom. If you simply dump a uniform mix of large and small onto the floor. You end up with a more small near the bottom of the pile than the top, because the small can on average travel farther because they will fit into smaller spaces. Now move the floor down a step at a rate greater than gravity and when the pile lands again on the floor again the separation of large and small will increase because the small started out lower and also can travel lower. The big never move up they just don't move down as much. In the case of shaking they don't move up any more than the small. Neglecting air resistance a large and a small ball will be propelled upward the same amount and will move in unison until they land on something. Assuming we are talking about particles with the same density and only different in size then large particles will never "move to the top" unless there is some upward component to the shaking and with that upward component everything moves in unison upward it's only when and where they land that they behave differently. Of course, it is also matters what you use as a frame of reference. When you use a mesh to sift particles you might claim the sifter causes large particles to move upwards if your frame of reference was tied to one of the small particles.

-jim

That doesn't explain why, at the top of the stroke when all the particles impact the top of the container, the small particles don't sift upward through the interstitial spaces between the larger particles and move to the top.

The small particles actually _do_ sift past the larger particles at the top of the stroke and move upward relative to the larger particles

-- it's just not as much as they sift downward at the bottom of the stroke.

The small particles spend more time sifting downward at the bottom of the stroke than upward at the top so over the course of a cycle the net direction of the smaller particles is downward relative to the larger.

What's really interesting is how and why such a trivial to explain effect ever got to be presented as such a curious phenomenon in the first place.

Bret Cahill

That doesn't explain why, at the top of the stroke when all the particles impact the top of the container, the small particles don't sift upward through the interstitial spaces between the larger particles and move to the top.

The small particles actually _do_ sift past the larger particles at the top of the stroke and move upward relative to the larger particles

-- it's just not as much as they sift downward at the bottom of the stroke.

The small particles spend more time sifting downward at the bottom of the stroke than upward at the top so over the course of a cycle the net direction of the smaller particles is downward relative to the larger.

What's really interesting is how and why such a trivial to explain effect ever got to be presented as such a curious phenomenon in the first place.

Bret Cahill

That doesn't explain why, at the top of the stroke when all the particles impact the top of the container, the small particles don't sift upward through the interstitial spaces between the larger particles and move to the top.

The small particles actually _do_ sift past the larger particles at the top of the stroke and move upward relative to the larger particles

-- it's just not as much as they sift downward at the bottom of the stroke.

The small particles spend more time sifting downward at the bottom of the stroke than upward at the top so over the course of a cycle the net direction of the smaller particles is downward relative to the larger.

What's really interesting is how and why such a trivial to explain effect ever got to be presented as such a curious phenomenon in the first place.

Bret Cahill

That doesn't explain why, at the top of the stroke when all the particles impact the top of the container, the small particles don't sift upward through the interstitial spaces between the larger particles and move to the top.

The small particles actually _do_ sift past the larger particles at the top of the stroke and move upward relative to the larger particles

-- it's just not as much as they sift downward at the bottom of the stroke.

The small particles spend more time sifting downward at the bottom of the stroke than upward at the top so over the course of a cycle the net direction of the smaller particles is downward relative to the larger.

What's really interesting is how and why such a trivial to explain effect ever got to be presented as such a curious phenomenon in the first place.

Bret Cahill

I'm not sure it's really all that trivial.

According to the writeup at:

writeup is really quite well done, and gives references to the original scientific papers if you want to know more) the phenomonon can be really quite complex.

According to this writeup, it turns out that the "percolation" explanation (which we have been calling the "void" explanation), is true, in the sense that size segregation does indeed occur by this mechanism, but it is not nearly as important as some other mechanisms -- for instance, the particles all tend to flow up in the center, while the return downward flow is in a thin layer near the wall. The large particles can't fit in this layer, so they stay at the top. I think Uncle Al gave this explanation a while back.

Then, there are questions like: "If larger particles of the same density rise, and denser particles of the same size sink, then what is the trade-off between density and size."

Once you've got that figured out, then you can try explaining the "reverse brazil nut effect".