What forces are at work causing sand to migrate to the centre of a spinning bucket of water? [duplicate]

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A bucket is filled with water and a handful of sand. The water is then spun. Why and what forces are in play which cause the sand particles to congregate in the centre of the bucket?

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marked as duplicate by Chris White, Waffle's Crazy Peanut, Manishearth♦Jul 3 '13 at 6:32

Wait, the sand doesn't collect in the centre, does it? It is pushed outwards! – mikhailcazi Jun 25 '13 at 14:01
From my observations as the water spins and yes as it slows the sand appears to move towards the centre. – Charles Hendry Jun 25 '13 at 14:12
@mikhailcazi you should try the experiment. – Nathaniel Jun 25 '13 at 15:14
@Nathaniel I think I will ;) – mikhailcazi Jun 25 '13 at 15:20
possible duplicate of Vortex in liquid collects particles in center – FraSchelle Jun 29 '13 at 16:39

As far as I know:

The sand only piles up at the center when the spinning is slowing down.

As the spinning slows down, water flows from the edge areas to the center to gradually restore the horizontal surface, adding circular motion of water to this it will result in a spiral motion of water inwards, which steers the dust towards the center.

There might other factors too, eg. the Bernoulli effect: the water may move faster at the center as it's slowed down at the edges due to friction. So the particles are sucked in by the faster current.

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The problem was solved by a certain Albert Einstein, who is probably not unknown to users of this web site. Actually he also calculated the viscosity of particle dispersions (Einstein (1906). A. Ann. Phys. 19: 289 - not on the net!). Presumably he only did special relativity after getting bored with fluid dynamics.

Anyhow, it's because the motion of the liquid around the cup causes a flow along the bottom of the cup towards the centre and then upwards. The sand is carried by this current so it collects at the centre. If you swirl the container rapidly you should be able to see the sand being carried upwards a short distance before its weight pulls it back down.

In the body of the fluid there is a pressure gradient along the line from the centre to the edge of the cup. This gradient is maintained by the variation is speed of the fluid flow from the centre to the edge i.e. high flow rate at the edge and low in the centre. However at the bottom of the cup the friction with the base of the cup slows the film of water close to the base. Because the flow rate is reduced by the friction it cannot balance the pressure gradient, and the result is a flow towards the centre at the base of the cup. As the flowing fluid reaches the centre it flows upwards then out towards the edge of the cup again. This is what causes the circulation shown in the picture.

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''A. Ann. Phys. 19: 289 - not on the net!'' - This is a state that I would like to see changed. – Captain Giraffe Jun 25 '13 at 18:11
Well, I don't know how good your german is - but here's a link: physik.uni-augsburg.de/theo1/hanggi/History/… – Wojciech Morawiec Jun 25 '13 at 20:14
@CaptainGiraffe Google the English translation, "A New Determination of Molecular Dimensions." For instance, a pdf comes up here – Chris White Jun 25 '13 at 21:40
@WojciechMorawiec, @ Chris. Scholars and gentlemen! I am impressed. Saving as if it was my own grandfather. – Captain Giraffe Jun 25 '13 at 23:05
Thanks for the explanation – Charles Hendry Jun 26 '13 at 9:46