Stirring tea with floating leaves

[Himal kharel]

I recently noticed that when a cup of tea was stirred, the floating leaves collect at center of cup rather than outer rim. Can anyone explain this?

 

[xts]

That's a great question I can't find a simple answer!
It must be caused by tea flow in the cup, which is not uniform (there is a friction between tea and the cup, causing the tea to rotate at centre with higher speed than at the rim).
But I am not able to present any calculations justifying the phonomenon you've noticed.

You may make the similar experiment: put a cup on a gramophone plate (so not only tea, but also the cup rotate) - in such scenario floating leaves are scattered uniformly on the surface.

 

[obafgkmrns]

Try this experiment: Fill a round bowl with water and stir. Wait a few moments for the worst turbulence to dissipate. Drop a bit of food coloring halfway between the center and rim. What happens to the food coloring?

 

[turbo]

@OP, you have stumbled onto the mechanism used by paper mills to clean pulp (difference in density) using centrifugal cleaners to separate pulp and water from contaminants. Typical centrifugal cleaners have a tangential inlet at the top that spins the mixture. Denser materials hug the walls of the cleaner cone, and are rejected at an outlet at the narrow end of the cone.

It is sometimes desirable to remove lighter materials from the mix, so again, the separation is done on the basis of density and the lighter materials are rejected. This is important for applications in which using recycled materials for papermaking can result in contamination by adhesives, waxes, etc. Here is a paper written about the more conventional uses of centrifugal cleaners (taking denser contaminants out, like sand, dirt, etc.)

http://www.coveyconsulting.com.au/Documents/FRIM centrifugal cleaners.pdf

 

[Bill_K]

I don't see the similarity. The discussion on centrifugal cleaners is about the settling rate of suspended particles, not the congregation of floating ones.

 

[turbo]

I don't see the similarity. The discussion on centrifugal cleaners is about the settling rate of suspended particles, not the congregation of floating ones.

The cleaners designed to remove light-density materials are often referred to generically as "reverse cleaners" since the light material at the center of the vortex is rejected and heavier materials from the outside of the vortex are accepted into the clean pulp stream.

Google on hydroclone for examples.

 

[xts]

As Bill_K said, hydrocyclones (http://en.wikipedia.org/wiki/Hydrocyclone) separate fractions within mass of the fluid.

Here we have quite different case: grouping of objects floating on the surface.

Those objects (in the first approximation) lay on the equipotentional surface. The grouping mechanism must be related to tea circulation: down in the centre, up near the rim, caused by friction between rotating tea and the cup in rest. However, I can't see simple mechanism leading to such circulation (actually - the intuition tells something opposite...)

 

[lluke9]

I don't know if it really is something as simple as this... but isn't this just a centripetal acceleration thing?
I have the feeling that I'm missing something big.

Edit (again):
I mean, I was thinking that the water creates something of a funnel, and the water molecules below that kind of support the water molecules above them as they are "pushed" to the edges of the cup.

Then the leaf naturally floats down this funnel shape due to gravity.

I'm not sure, is this what you guys are talking about?

(sorry turbo, I saw your post right after I revised mine, hehe)

 

[turbo]

Is that what this "hydroclone" thing is based on? The leaf is more dense, so the tea doesn't "push" much on the leaf?

The leaf is less dense than the liquid tea. That's why it is floating.

 

[A.T.]

http://en.wikipedia.org/wiki/Tea_leaf_paradox
http://en.wikipedia.org/wiki/Secondary_flow
http://www-paoc.mit.edu/paoc/papers/Einstein'sTeaLeavesTPT.pdf

 

[A.T.]

The leaf is less dense than the liquid tea. That's why it is floating.

The phenomenon described by the OP works best, when the leaves have already sunk to the bottom. The secondary flow takes them from the bottom into the center. Contrary to what you claim, It is NOT a centrifugal separation effect. Look at the links I posted.

If the leaves are still floating on the surface it is quite ambiguous: Some end up at the wall due to the secondary flow, some are stuck together due to surface tension and stay in the vortex dent in the center. But I assume by "floating" the OP meant floating within the tea, not on the surface.

 

[xts]

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

[URL]http://upload.wikimedia.org/wikipedia/commons/7/77/Tea_leaf_Paradox_Illustration.svg[/URL]
That is an explanation why sunken leaves collect in the centre of bottom.
But (as I understand OP) the question was: why leaves floating on the surface also group in the middle of cup? (The same you may see with foam on cappuccino)
Einstein's explanation for the bottom leaves grouping implies that surface ones should be taken to the rim. But they group also! So there must be another mechanism, stronger than Einstein's circulation.

 

[A.T.]

Einstein's explanation for the bottom leaves grouping implies that surface ones should be taken to the rim. But they group also! So there must be another mechanism, stronger than Einstein's circulation.

Some of the surface leaves go to the rim. But others are sticking together due to surface tension. They form a compound with internal forces (just like the foam) which prevents individual leaves form moving outwards.

 

[xts]

They form a compound with internal forces (just like the foam) which prevents individual leaves form moving outwards.

That is a plausible explanation.
One question remains (and, honestly, I am not sure if I know how to make appropriate calculations...) - why the 'floating isle' of straws or foam stays in the centre rather than drift towards the rim with Einstein's stream? At the first guess position in the centre should be unstable due to Einstein's circulation.

 

[A.T.]

One question remains (and, honestly, I am not sure if I know how to make appropriate calculations...) - why the 'floating isle' of straws or foam stays in the centre rather than drift towards the rim with Einstein's stream? At the first guess position in the centre should be unstable due to Einstein's circulation.

Some potential reasons:

- The horizontal component of the secondary flow in the middle of the surface it is rather weak or zero. Only the outer elements of the floating isle are affected.

- Moving the isle out of the middle over the spinning surface requires increasing its velocity. The leaves might have only little inertia, but they form a "skin" with the water molecules on the very surface. (In the rotating frame you would say the Coriolis force makes the isle go in circles instead of going to the rim)

- Moving the isle over the spinning surface requires differential accelerations of it's parts. Due to the their interconnection this might cause them move slower than the spinning water underneath, that determines the shape of the surface. So they cannot climb out of the equipotential dent.

 

[NascentOxygen]

Explained by Mr Einstein. http://people.ucalgary.ca/~kmuldrew/river.html"

 

[xts]

Some potential reasons...

The first argument is false. Considering Einstein's circulation the centre is an unstable equilibrium point - infinitesimal shift from it increases drift force in the same direction.

The second - I may agree only conditionally. The same argumantation applies equally to a molecule of tea - and those are in equilibrium on such a surface, so floating leaves are affected the same. That's a case of a boat on a Earth ocean (not falling from an equatorial bulge)
It may be, however, some second order effect: the "floating isle" of tea leaves form a rigid body, which size cannot be neglected - maybe such forces on the outer part are not sufficient to pull the leaves floating closer to the centre.

Third argument - seems plausible. However I don't feel brave enough to calculate it...

 

[Himal kharel]

What if we put objects same density as water instead of tea leaves?

 

[Himal kharel]

I am just a high school student. Can you explain this in simple language?

 

[DrStupid]

[URL]http://upload.wikimedia.org/wikipedia/commons/7/77/Tea_leaf_Paradox_Illustration.svg[/URL]
That is an explanation why sunken leaves collect in the centre of bottom.

Due to surface tension and interaction with air the rotation is also decelerated at the surface. This should result in an additional vortex in opposite direction.

 

[xts]

What if we put objects same density as water instead of tea leaves?
I am just a high school student. Can you explain this in simple language?

Density of the objects matter only to that if they float on the surface or sink.
Einstein explained why objects a bit heavier than water (i.e. sinking to the bottom) gather in the centre of the cup.
But other effect is that objects on the surface also gather in the centre of the surface - and it is something I can't explain so simply as Einstein did with leaves at the bottom of the cup.
Objects of exactly the same density as water (tea) should follow circulation streams not only at the bottom or surface, but in the whole volume. If you love English customs that much or you are ready to sacrifice a cup of tea: you may try to add some milk to a cup of tea and watch its path.

Due to surface tension and interaction with air the rotation is also decelerated at the surface. This should result in an additional vortex in opposite direction.

Yeah. that seems reasonable. Maybe not the air friction, but rather some leaves/foam sticking to the rim with their VanDerWaals' forces, thus forming additional friction at the surface layer. So we would have then circulation: rim->centre at bottom, rim->centre (but slower) at the surface, centre->rim in the mid depth.

OK. Let me waste few cups of tea dropping milk to it, maybe I'll be able to spot the circulation at the surface...

EDIT>>
I really like English culture... Tea with milk is just an exception!

 

[xts]

I must admit DrStupid was right - that effect is seen even if there are no leaves/foam sticking to the rim.

Experiment: cylindrical tall glass (6cm in diameter, 12cm tall) of water (I was too greedy to waste good tea), stirred.
Drop of milk injected using a syringe with long needle.

If the drop is left on the surface, it goes to the centre, sinks there, goes 2cm or so deep, there it goes towards rim.

If the drop is injected neer the bootom, it goes to the centre, climbs to 5cm or so, there goes to the rim. The effect is much stronger (speed is 5 times or so bigger) than for drops left on the surface.

In the medium area there is a barely noticeable movement towards the rim.

 

[A.T.]

Thanks for doing the experiment xts. Here is a similar one, but the vessel & air are rotating at the same speed as the water. It is interesting what happens then at the surface:

https://www.physicsforums.com/showthread.php?t=423984