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Vortex in liquid collects particles in center

Why when you mix a cup of tea with a teaspoon, tea-craps collect in the center of cup, instead of goes near the walls?

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Identical question : physics.stackexchange.com/q/3244 –  Georg Apr 20 '11 at 13:58
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marked as duplicate by Mark Eichenlaub, Georg, mbq Apr 21 '11 at 21:44

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A rotating fluid roughly observes a $v=r\omega$ law where $v$ is the velocity of a fluid element or anything moving with the fluid element, $r$ is the distance from the centre and $\omega$ is the roughly constant angular rotation rate.

So if a large particle like a tea leaf residue is found in the fluid, it should rotate at a speed $v$, given a particular distance. However, such large particles will be more suspect to frictional forces by the viscous tea that reduce the velocity of the particle very quickly. So in order to satisfy $v=r\omega$, it has to collect at the centre of the cup once its velocity is completely reduced to zero.

There is yet another reason why such a particle should float to the centre, but I suspect it has a much smaller contribution. In the rotating frame, there is a centrifugal force acting outward on the large particle. Let's ignore Coriolis forces and look at the effect of only this centrifugal force. Now locally, in a small region around this particle, this is analogous to a gravitational field acting along the surface of the fluid outward to the edge of the cup (the Equivalence Principle). You'd expect the particle to move towards the edge then, but remember that this tea leaf particle is less dense than tea (it floats) and so it should feel a force opposite in direction to the imaginary gravitational field (the centrifugal force), just like a tea leaf particle in a stationary fluid should float upwards against a real vertical gravitational field.

This sort of behaviour is counter-intuitive, but it is actually observed in centrifuges where the suspended particles are less dense than the fluid -- they collect in the center. If you want to check this for yourself without a centrifuge (or if you suspect that friction has a greater role in this), take a helium balloon into a train and you will observe that when the train brakes, while you move forward because of the non-inertial force, the balloon actually inclines backwards! (If the braking is long enough for the air to settle and there are no air currents in the cabin -- agreed, it's not the easiest thing to test)

See here for a more detailed explanation of the balloon example : http://physics101.wordpress.com/2008/11/30/balloons-and-accelerations/

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So you mean centrifugal force has no effect here? because we can see this for other massive particles like sugar. –  Abolfazl Apr 20 '11 at 13:44
See my addendum :) I might be wrong about which is the larger contribution and would like to hear from others. –  dbrane Apr 20 '11 at 13:45
All this was debated already here! It ended up with Einstein as the origin of that "paradox". physics.stackexchange.com/questions/3244/… –  Georg Apr 20 '11 at 13:57
Ah, didn't see that. Will check it out. –  dbrane Apr 20 '11 at 14:08
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The previous life of this question gave an explanation based upon slowing convection, caused by the frictional slowing of the fluid, (slower at the edges), which seems a reasonable possibility. In that case fluid flow is needed because the surface of the fluid is changing because of decreasing angular velocity.

I wonder if surface tension might be involved as well (or instead). Surface tension is modified by the curvature of the surface, and our surface does have curvature that varies as a function of radius. Could this be driving small hydrophobic particles towards the center? However, I think the phenomena is also seen in large ocean votices, with logs caught on the surface, and these objects would be too large to be affected by surface tension gradients.

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This is straightforward silly! 1st tea leafs after some minutes of soak are not hydrophobic, not at all! But even when one assumes some hydrophobic particles "for fun", the only thing that will happen not in accordance to the observations on tea leaves will be that the hydrophobic particles will clinge to the surface (= air!) if they happen to get there during the stirring action. Reality is of course, that such particles would refuse to be stirred "down" just from begin. –  Georg Apr 21 '11 at 17:05
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