Why does the sugar move towards the centre of the cup when you stir it?

I found this one fascinating. The ekman pumping doesn't explain it. According to Wikipedia the Ekman pumping is a property of the spherical earth and the imaginary coriolis forces that apply over the large distances of the air stream.

It is a 90 degree shift of the motion of particles compared to the direction of the wind and that 90 degree shift is opposite in the northern and southern hemisphere.

Now I don't claim to know the answer, and perhaps I will be making a fool of myself, but I think the answer given about boundary layers is close.

At the bottom of the cup all the water moves slowly because it is slowed by the surface of the mug.

Higher up the water is moving at a much higher speed so its outward pressure ( centrifugal force) is higher than the outwards pressure at the bottom. ( lower speed lower centrifugal force)

The result is that there will be flow downwards along the outside wall of the mug.

And of course if fluid is moving downwards somewhere then it must be moving upwards somewhere else. i.e the middle of the mug.

Hence there is a flow of fluid. Down the outside, across the bottom to the middle, up the centre, then outwards to the walls.

And as it moves toward the middle at the bottom then the heavier items are dragged to the middle also by the pure friction of the water moving over them. They would flow with the current.

From there they are too heavy to rise much. But it would explain the little pile that is formed. Higher in the middle. i.e some upward force keeping it in a pile rather than letting it form a flat "puddle" in the middle.

Now if we stirred it faster then particles that aren't too heavy should be transported upwards. Perhaps we can see the tea leaves circulate if we are fast enough?

but think about the rest.

The dissolved sugar at the bottom somehow sweetens the whole mug. So the dissolved particles which are light must have been transported upwards.

This is consistent with the above explanation.

Now if we took lighter particles. Perhaps sawdust? Then we should not only see them move to the middle but from there we should be able to see them rise and form currents similar to convection currents.

I am going to test this. I have pondered this problem before but never taken the time to truly understand it.

Fascinating.

Of course there are other ideas to test but I don't think they are right.

If heavy things move to the middle for other reasons than the above description then things lighter than the water should move to the outside. But I don't think that this happens.

First you look the Cup, you will see that when you stir the sugar, sugar move towards outside until the centrifugal force decrease. When we stop stirring, the centrifugal force decreases and the sugar comes toward centre.

Ekman pumping

As spinning fluid spins down in the cup under the action of viscosity, boundary layers are formed at the bottom and sidewalls of the cup. One of the net results of a boundary layer is that slow moving fluid within the layer is pumped out into the faster moving fluid outside the layer (effectively growing the thickness of the layer of slower moving fluid.)

The net circulation pattern that results from the Ekman pumping is for the fluid at the bottom of the cup to move towards the axis of rotation and then be pumped vertically up the axis of symmetry.

Any particles entrained in this circulation pattern (like tea leaves or sugar) will move towards the center of the cup and form a little pile there.

Einstein trumps!

It turns out that Einstein did a paper on this in 1926. Well, not on sugar, but tea leaves, but it is the same theme.

Here's a link to Wikipedia

http://en.wikipedia.org/wiki/Tea_leaf_paradox

There is indeed an Ekman layer involved.