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

Question

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?

Answer 1

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, or section 2 in this PD). 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.

Answer 2

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.