Talk:Tea leaf paradox

A fact from Tea leaf paradox appeared on Wikipedia's Main Page in the Did you know column on 3 January 2009, and was viewed approximately 6,420 times (disclaimer) (check views). The text of the entry was as follows:

Did you know... that in 1926, Albert Einstein solved the tea leaf paradox, which states that if the tea in a teacup is stirred, the tea leaves will collect in the middle rather than at the edges?

A record of the entry may be seen at Wikipedia:Recent additions/2009/January.

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Comment

Is the tornado effect of fast stirring casue by the same phenomenon? ChildofMidnight (talk) 01:11, 30 December 2008 (UTC)[reply]

I've thought about and decided the tornado is mostly centripidal force, but I wonder if the drag near the edge doesn't exagerate it. I'm getting a headache. ChildofMidnight (talk) 04:32, 30 December 2008 (UTC)[reply]

Great article!

Really great! This should go to FA. Maury Markowitz (talk) 02:07, 30 December 2008 (UTC)[reply]

Thank you very much! It would need to be quite a bit longer for FA I think. --Apoc2400 (talk) 11:44, 30 December 2008 (UTC)[reply]

Capitalization

Thank you for fixing the capitalization David Eppstein. I reverted it by mistake by editing an old version. --Apoc2400 (talk) 09:11, 31 December 2008 (UTC)[reply]

Paradox

Why is this called a paradox? I think it is the wrong use of the word. The phenomenon is caused by the laws of physics. There is no paradox. — Preceding unsigned comment added by 131.111.16.20 (talk) 20:49, 2 August 2014 (UTC)[reply]

Paradox is presumed to reflect a flaw in understanding or interpretation, and so could be considered subjective. However, given that humanity as a group seems to understand the dynamics of constrained flow well enough to explain the phenomenon, perhaps anomaly or curiosity(n.) would be better words.
--173.79.123.2 (talk) 02:50, 16 September 2014 (UTC)[reply]

The paradox is in the question "Why, when creating a centrifuge in a tea cup, do stirred tea leaves settle in the centre rather than the outside?". 79.66.204.76 (talk) 13:13, 24 March 2016 (UTC)[reply]

So thrilled to learn thay my own question posed to myself (at 75), was trally a good question, actually thought through by Prof. A. Einstein.

I suggest that the real question is - "Why, when SEEMINGLY creating a centrifuge in a tea cup, do stirred tea leaves settle in the centre rather than around the outside?"

In my now much refreshed understanding, the two dimensional diagram provided in the Article does not show the three dimensional effect of Drag all around the cup-side tea, compared with tea away between the sides and the centre-line.

The carriage of all of the tea-leaves into the centre-bottom, is caused by the currents in the tea, which spin AND spiral downwards from around the cup's rim, to rise from around the centre-bottom, while depositing the (heavier than tea-water) leaves below there at the relatively slowest centre flow.

It is not analogous to a Centrifuge's action, where the container is more like a test tube, not shaped like a tea cup.

It only becomes a seeming Paradox when the real Question is unthinkingly posed inaccurately. 106.69.217.57 (talk) 06:03, 13 February 2023 (UTC)[reply]

I agree that this is not a paradox. The word implies something more than a deviation from common expectation. Cross Reference (talk) 13:37, 26 June 2017 (UTC)[reply]

Shear force reduction?

On further reflection, I suspect the predominant forces causing these extended particles to collect at the least turbulent node is flow shear, which is least where the boundary flow speed is least, at the center of the cup.
173.79.123.2 (talk) 02:57, 16 September 2014 (UTC)[reply]

Towards a complete explanation

The explanation currently reads:

(...) friction between moving water and the cup increases water pressure, resulting in a high pressure boundary layer. (...) Therefore it is friction, between the cup and the water, that produces a centripetal force upon the mass of tea leaves.

To me it sounds misleading to say friction increases pressure. Friction between the water and the bottom of the cup slows the fluid down, which would in turn increase the pressure relative to a hypothetical inviscid scenario. I can imagine that the pressure in the bottom boundary layer (known as the Bödewadt layer according to Yeo et al 2006, APL 89, 103516) would be a bit higher, because the fluid velocity is low, but the inward pressure gradient in the cup is evidently also in the bottom boundary layer creating the famous secondary flow. I therefore wouldn't use the term high pressure BL and I don't currently see what an increased pressure across the entire bottom surface would do to explain the phenomenon.

I don't think the friction produces the force upon the tea leaves. After reading in Yeo et al 2006^[1] and on chemeurope^[2], I imagine the following. Slowly spinning fluid at the rim and fast spinning fluid in the center create a pressure gradient. On the bottom of the cup, the fluid velocity is reduced by friction and the centrifugal force diminishes. The pressure gradient overcomes the weak centrifugal force at the bottom and the resulting inward-spiraling flow creates a drag force on the tea leaves.

I wonder if the impermeability of the cup is relevant here. At the air-water interface, pressure is matched and the interface deforms, but impermeability at the bottom would prohibit deformation and thus maintain the horizontal pressure gradient?

What do you think?

SkepticalSalmon (talk) 21:09, 21 December 2021 (UTC)[reply]

I think this is completely valid remark and this is confirmed in this document (in French) : http://www.bibnum.education.fr/sites/default/files/analyse-einstein-tea.pdf .

In short, you stir the spoon and create a centrifugal rotational effect. Now, this centrifugal force creates a PARABOLOID (important word) shape of the surface. This shape makes pressure (simple total height of fluid column) higher on the side than in the center; this entails a pressure gradient on the whole fluid and this pressure gradient tends to compensate the centrifugal force.

YET ! There is a boundary layer effect (aka friction) on the bottom that slows down the centrifugal inertia but not the pressure gradient which is the highest there and so leaves which are at the bottom follow this inward pressure gradient and can even rise when the flow which reach the center at the bottom tend to go where it can (up a bit if they are light enough).

I let random wikipedia fans to correct the main page. I had a bad experience about that a long time ago and don't bother anymore. Newtoon (talk) 09:57, 23 May 2022 (UTC)[reply]

References

^ Leslie Y. Yeo, and James R. Friend, and Dian R. Arifin. "Electric tempest in a teacup: The tea leaf analogy to microfluidic blood plasma separation". {{cite web}}: Missing or empty |url= (help)CS1 maint: multiple names: authors list (link)
^ https://www.chemeurope.com/en/encyclopedia/Secondary_flow.html. {{cite web}}: Missing or empty |title= (help)

Secondary flow graphic wrong?

Isn't the secondary flow going *down* at the center and up in the outer regions? I think the graphic is wrong. Uhw (talk) 22:36, 24 September 2022 (UTC)[reply]

The tea leaves migrate to the middle, indicting that the flow is inward at the bottom, and therefore upward at the centre and downward at the outside - which would make the graphic correct. catslash (talk) 22:30, 26 September 2022 (UTC)[reply]

Explanation

The Explanation section of the article has grown and evolved to become incomprehensible. In particular it unnecessarily introduces high pressure boundary layers, flow schematics and centrifugally actuated mass. It also refers to an x-axis without defining it.

The very first version of the explanation appears to be the clearest, is concise, cites references and avoids irrelevances. Therefore, I propose to revert to this version (of the Explanation section only), and intend to do this in about a week unless there is opposition. catslash (talk) 22:34, 26 September 2022 (UTC)[reply]

Done. catslash (talk) 01:13, 22 November 2022 (UTC)[reply]

[1] Leslie Y. Yeo, and James R. Friend, and Dian R. Arifin. "Electric tempest in a teacup: The tea leaf analogy to microfluidic blood plasma separation". {{cite web}}: Missing or empty |url= (help)CS1 maint: multiple names: authors list (link)

[2] ttps://www.chemeurope.com/en/encyclopedia/Secondary_flow.html. {{cite web}}: Missing or empty |title= (help)

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