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Q & A: anti-centrifuge?

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Most recent answer: 12/31/2012
Q:
After gaining a good understanding of how a centrifuge works, this leaves me stumped. Put a handful of sand in a bucket of water. Slosh it around in a circle until you have a good vortex going. Then let it sit. Why does the more dense sand gather in the center, and not the outside edge?
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- Andrew Watt (age 39)
Jacksonville, Fl
A:
That's a great question.

The only plausible explanation [but now, see below] I've seen runs as follows.  The water is nearly stationary near the middle of the bucket. Any sand that happens to be there can fall quietly to the bottom. Near the edges, the flow can be fast enough to stir things up, so that the sand there doesn't settle until it happens to get closer to the middle..

If this explanation is right, for a very slowly swirling bucket, with smooth flow (no turbulence, no stirring) there should be some normal centrifugal effect and not this reverse effect. Since nothing would be stirred I guess you'd do the measurement by sprinkling the sand in from the top.

Let us know how it comes out, because we really aren't sure about this.

Mike W.
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(published on 06/04/2009)

Follow-Up #1: sand in water bucket

Q:
You have a topic/question entitled anti-centrifuge which found after I asked a similar question. I just found an answer on Robert Krampf's website(http://thehappyscientist.com) His answer goes as follows (but I am wondering if it makes sense).I simply don't know. If you would review it and if it makes sense confirm and explain it (especially his pressure references)a little better I would appreciate it. Last time, I left you with a challenge. We put a little sand into a glass of water and stirred it. Instead of moving to the outside edge, as we might expect, the sand gathered in the center of the glass. I left you with the challenge of telling me why. Congratulations! Several of you got the right answer, and several more got it at least partially right. So, why does the sand do that? Lets investigate by stirring the water again. As you stir the water, notice what happens to its surface. The water rises along the edges of the glass, and a depression forms in the center. The faster you stir, the higher it gets at the edges, and the lower the depression gets in the center. This change in the surface is caused by inertia. The moving water will try to continue moving in the same direction, forcing it against the side of the glass. That increases the water pressure there, and forces the water up the side of the glass. The highest water pressure will be along the sides of the glass, and the lowest water pressure will be in the center. Keep stirring, but look at the sand instead of the water. While you are stirring, the sand is suspended in the water, and is flung outwards, as you would expect. It is only when the grains of sand fall to the bottom that they move towards the center. Now, think about what is different at the bottom of the glass. The bottom of the glass, right? That water is touching the solid, stationary surface of the bottom of the glass, instead of being surrounded by moving liquid. The water tends to stick to that stationary surface, producing a layer water at the very bottom of the glass that spins more slowly than the rest of the water. Now we have a layer of water at the very bottom that is spinning slower. Because it is moving slower, it has less inertia pushing it outwards, which gives us a thin layer of water with lower pressure along the bottom. So we have high pressure along the sides of the glass, except at the very bottom, which has low pressure. The water flows from high pressure to lower pressure, moving inward along the bottom towards the center, carrying any sand that is resting on the bottom with it. Once it reaches the center, the water moves upwards to the low pressure area in the center of the glass. The sand is left behind, piled up in the center. I'll leave you with something to think about. What could you do to cause the sand to move from the center and form a ring around the outside of the bottom? Have a wonder-filled week.
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- Kimball Clark
Gallipolis, OH USA
A:
This is quite a different explanation than the one we'd seen before. For the time being, I'll just put it up here as something we can all think about. It has important elements that were missing from our previous answer.
Something may be missing from this explanation too.  I suspect that it's important that the outer walls are not turning, so the outer edge of the water isn't turning fast, which probably creates a net flow outward in the rapidly spinning top, which helps drive an inward flow at the bottom.

Experimentally, it would be good to get water stirred in a glass, then put a few drops of dye in to see whether this flow pattern (out near the top, in toward the bottom) really is there.

Mike W.


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(published on 08/24/2009)

Follow-Up #2: particle settling data

Q:
In your most recent post you mentioned that it would be good to put some dye in the water and see what the water flow actually is. I tried it and I think I have at least part of the answer. I hydrated some of those plastic crystals that soak up huge amounts of water. Some times they're sold under the name of water jelly crystals. I put a fair amount of blue food coloring in the water the plastic soaked up. The hydrated plastic chunks became a very visible blue and they are only slightly more dense than water. I got a large bowl of water circulating by stirring vigorously. Then I dropped a couple pieces of the plastic in and what I saw was that the plastic pretty much stayed at the radius where it was inserted. I also saw that the water near the center was circulating much faster than the water farther from the center. This actually makes sense since the bowl is not moving and it is slowing the water down. This velocity distribution is not what you would get in a centrifuge where the outer wall is the faster part and follows the relationship that the velocity is proportional to distance from the center. In the water it is the reverse of this, but I don't know if it is a linear (or simple inverse) relationship or not. So the water in a circulating bowl or beaker is not like a centrifuge and thus does not show centrifugal behaviour. Lastly as the water speed became very slow the plastic pieces gradually moved down to the bottom of the bowl where they really slowed down. It looked like they were dragging on the bottom and then they moved toward the center where they continued to spin for a short while. Why they moved to center at the end I do not claim to fully understand, but I can clearly see that one cannot expect centrifugal behavior. It may be that near the bottom when the fluid is moving very slowly that the pressure in the center is slightly smaller because the water is still moving a litter faster there.
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- Kimball Clark
Gallipolis, OH USA
A:
Thanks for this careful and very well-reported set of observations. Now that you have this great set-up there may be some useful follow-ups.

I wonder what would happen to particles  added later, around when the ones along the bottom are gathering in the middle. Is something else flowing outward? Or is there just net inward flow as the raised rim of the top surface (caused by the spinning) settles down to level?

Mike W.
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(published on 09/13/2009)

Follow-Up #3: more tea

Q:
I found an article that quotes Einstein as answering this question. The article was written about storms and describing the pattern of of wind in cyclones, hurricanes etc. It talked about a boundary layer (a cylindrical layer) outside of which the motion is not centrifugal and inside this layer it is centrifugal. It described the motion of the sand (or in this article tea leaves) as the result of two competing effects: the centrifugal force outward and the Coriolis force inward. Inevitably as the water slows down the Coriolis force wins out and the sand (or tea leaves) move into the center.
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- Kimball Clark
Gallipolis, OH
A:
I am not sure I follow the role of the Coriolis force here, probably just because I haven't thought enough about it.

Summarizing, I think this is the picture you've taught us:

Looking toward the top, the middle part is spinning, driving water out to the edges. However, near the edge, it's spinning less due to the walls, so the level there is too high. That leads to downward flow. The flow goes toward the bottom, where there's very little spinning at all. There, the pressure difference between the middle and edge drives flow in toward the middle. Of course the continuity of the flow then drives the circulation up in the middle. 

So sand or tea that makes it to the bottom is just dragged in toward the middle. Makes sense.

Mike W.
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(published on 11/12/2010)

Follow-Up #4: Einstein and tea leaves

Q:
It appears that Einstein answered the question why tea leaves gather in the center of the cup, back in 1926, and The Physics Teacher Vol. 48, May 2010 revisits this answer and goes on to elaborate about pressure systems in the Atmosphere. The Title is "Einstein's Teas Leaves and Pressure Systems in the Atmosphere". Basically Einstein explained that the friction between the bottom of the cup and the water reduces the centrifugal force at the bottom. So the centrifugal force is larger at heights significantly higher. This causes water to flow towards the sides at the top which then flows down the sides and at the bottom of the cup it flows towards the center. A circulation loop. This circulation sweeps the material on the bottom into the center.
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- Kimball Clark (age 53)
Gallipolis, OH 45631
A:
Thanks, sorry we missed seeing this when it first came in.

It's been a very enlightening exchange.

Mike W.
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(published on 07/15/2010)

Follow-Up #5: particles settling in a bucket

Q:
When a circular vessel (containing water and insoluble particles of various sizes) is stirred the larger particles move towards the centre and settle there. Bigger particles are surrounded by smaller, with most of the finest at the perifery of the central deposit. One might expect centrifugal force to throw particles outwards towards the walls of the container, and that they should settle there instead of all 'gavitating' towards the centre.Something to do with the speed of the water passing the 'inner' and 'outer' surface of each particle, resulting in a spin which moves each particle further towards the centre perhaps? Larger particles would presumably experience a greater differential across their diameter and thus be more influenced by the effect?
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- Brian Duckitt (age 73)
Durban, Natal, South Africa
A:
Brian- We've marked this as a follow-up to an old exchange. We haven't thought about what happens to particles of different sizes, but maybe this old series will get you started toward an answer.

Mike W.
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(published on 12/19/2011)

Follow-Up #6: dirt swirls toward center

Q:
How come when we swirl water in the bathtub or the pool, all of the dirt goes to the center of the pool, yet when the washing machine spins, all the clothes fly to the outside? (Mama knew centrifugal force on the washing machine, but was stumped about the pool). Thanks for your help!
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- Nathanael (age 3.5)
West chester, oh, USA
A:
It happens we've had a great exchange on this very question. See above.

Mike W.
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(published on 12/31/2012)

Follow-up on this answer.