miriam_e | a vortex pulls to the center

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Why, when you stir a cup of tea, do the tea leaves all move to a neat pile in the center? Why doesn't it simply mix everything up and distribute the leaves evenly throughout the volume?

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From:

superchikka.livejournal.com

In order for it to be evenly distributed, you'd need essentially random dispersion of the leaves. This would only happen if there were no forces acting on the leaves (gravity, temperature gradients, you stirring teh tea). To mimic randomness, if you stir every which way, the waves form each direction would cancel each other out, but still causing motion in the tea. Therefore, the leaves are set in motion, but in so many directions (except likely upwards unless you shook the teacup!) that there is not much order.

This answer was wholly useless and most likely scientifically incorrect. I'm a biologist, not a physicist. :)

From:

miriam-e.livejournal.com

I really want to know.

Thanks for the thoughts. It has given me a direction to think along.

I've always been fascinated by turbulence. It can capitalise on very simple ways to use chaos to mix fluids and produce a fairly random-looking result. Stirring a cup of tea doesn't do that though.

I wouldn't be surprised if it shuffled the tea leaves evenly over the bottom of the cup. Likewise, I wouldn't raise my eyebrows if the stirring sent all the heavier-than-the-fluid leaves to the edge of the cup, as you might expect centrifugal forces to do. But neither of these happens. They get piled in the center.

I'm sure there is a simple explanation... but I'm stumped.

Incidentally, being a biologist you've heard of this:
Big fleas have little fleas
upon their backs to bite them,
and little fleas have lesser fleas,
and so ad infinitum.

But have you heard of this variant?
(Ode to Turbulent Flow)
Big whirls have little whirls
Which feed on their velocity,
And little whirls have lesser whirls
And so on, to viscosity.

From:

superchikka.livejournal.com

I've been thikning aobut it more:

I think the leaves stay in vortex, instead of flying out in centrifugal motion, is because the water and the cup is exerting an oppostie force. unlike in a centrifuge, where the whole mug is spun around in one circle perpendicular to the mug itself, in this case the water is moving but the mug is not. The spoon provides a consistent circular force, but vectors only work in straight lines. as the spoon circles, it exerts a bunch of tangents to the circle on the water - picture a cartoon run that's been given a twist so that teh rays are now tangents instead of perpendicular. so the water is moving toward the cup in this tangent, and the cup applies an equal force back on the water, forcing it back into the path of the spoon (or something like that).
Now the tea leaves. these are particles whose motion is under the control of 2 forces: the vortex of tea, and gravity. I think since the water is so much denser than floaty leaves, they exert less force on the water, but according to one (i can't remember which number, but each force has an equal and oppostie force) of newton's laws of motion, that means the water exerts less force on teh leaves, too.
I had a brainwave while I was jsut brushing my teeth now before bed, but I forget the rest. It was kind of vague.

I hope these raw thoughts help you out some.

How about doing some experiments?

a) Tape your much to a lazy suzan, and spin it at aobut the same speed in the same direction as you stir the tea. any changes? What about when the mug is spun in opposite direction of the spoon? I would predict counter-spinning would concentrate the leaves even more, but maybe not.
b) Try stirring a mug with something heavy, like ball bearings or beads. Don't touch them with your spoon, just use it to setthe current of water in motion. is there a different effect? the downwards migration by gravity is not a factor in this case.

I am in the middle of studying for a midterm, so can't experiment myslef, but if you do do these, please tell me how they go!

I have not head of the turbulent flow one.

You knwo, there is a math joke like that, how sprinters should never finish a race, becaus they have to finish half of it, then half of half of it, and so on, and so on, and you can go on halving infinitely and you can never reach infinity.

From:

miriam-e.livejournal.com

I have a feeling it might all be due to the way the fluid circulates. If the fluid moves inward along the bottom of the cup and spirals upwards then that would push the leaves along, piling them up on each other in the center. I notice that the center of the top of the cup of fluid is lower than the edges so if the fluid is rising from the center at the bottom, it isn't going all the way to the top. There might be something like the atmospheric circulation on Earth. I can imagine the top and bottom of the cup being like mirror images of each other, with fluid circulating in at the top and at the bottom of the cup, and about halfway up the cup it moves outward. I drew a quick sketch -- a picture works so much better than words. As you suggest, I'll try an experiment. If this is how it circulates it should make possible a simple test. I need to think on it. Perhaps a clear glass and a small amount of very fine sand that is suspended in the liquid, might work...

Then, of course, is the next question: why would it circulate like that rather than the reverse, or some other pattern?

The infinitely running sprinters is an example of Zeno's Paradox, actually a family of paradoxes that all use the same concept. They come from ancient Greek times. I think I first read about it in Douglas Hofstadter's amazing book "Godel Escher Bach". He plays with a lot of wonderful, crazy concepts in that book.