Tea leaf paradox explained

In fluid dynamics, the tea leaf paradox is a phenomenon where tea leaves in a cup of tea migrate to the center and bottom of the cup after being stirred rather than being forced to the edges of the cup, as would be expected in a spiral centrifuge.

The correct physical explanation of the paradox was for the first time given by James Thomson in 1857. He correctly connected the appearance of secondary flow (both Earth atmosphere and tea cup) with ″friction on the bottom″.[1] The formation of secondary flows in an annular channel was theoretically treated by Joseph Valentin Boussinesq as early as in 1868.[2] The migration of near-bottom particles in river-bend flows was experimentally investigated by A. Ya. Milovich in 1913. The solution first came from Albert Einstein in a 1926 paper in which he explained the erosion of river banks, and repudiated Baer's law.[3] [4]

Explanation

The stirring makes the water spin in the cup, causing a centrifugal force outwards. Near the bottom however, the water is slowed by friction. Thus the centrifugal force is weaker near the bottom than higher up, leading to a secondary circular (helical) flow that goes outwards at the top, down along the outer edge, inwards along the bottom, bringing the leaves to the center, and then up again.

Applications

The phenomenon has been used to develop a new technique to separate red blood cells from blood plasma,[5] [6] to understand atmospheric pressure systems,[7] and in the process of brewing beer to separate out coagulated trub in the whirlpool.[8]

External links

Notes and References

  1. James Thomson, On the grand currents of atmospheric circulation (1857). Collected Papers in Physics and Engineering, Cambridge Univ., 1912, 144-148 djvu file
  2. Boussinesq J.. Joseph Valentin Boussinesq. 1868. Mémoire sur l'influence des frottements dans les mouvements réguliers des fluides. https://web.archive.org/web/20220317085525/http://portail.mathdoc.fr/JMPA/PDF/JMPA_1868_2_13_A17_0.pdf. dead. March 17, 2022. Journal de mathématiques pures et appliquées . 2e Série. 13. 377–424.
  3. Bowker. Kent A.. 1988. Albert Einstein and Meandering Rivers. Earth Science History. 1. 1. 45 . 10.17704/eshi.7.1.yk72n55q84qxu5n6 . 1988ESHis...7...45B . 2008-12-28.
  4. Einstein. Albert. March 1926. Die Ursache der Mäanderbildung der Flußläufe und des sogenannten Baerschen Gesetzes. Die Naturwissenschaften. Springer. Berlin / Heidelberg. 14. 223–4. 10.1007/BF01510300. 1926NW.....14..223E. 11 . 39899416. English translation: The Cause of the Formation of Meanders in the Courses of Rivers and of the So-Called Baer's Law, accessed 2017-12-12.
  5. Arifin. Dian R.. Leslie Y. Yeo. James R. Friend. 20 December 2006. Microfluidic blood plasma separation via bulk electrohydrodynamic flows. Biomicrofluidics. American Institute of Physics. 1. 1. 014103 (CID). 10.1063/1.2409629. 2008-12-28. 19693352. 2709949. https://archive.today/20121209001530/http://link.aip.org/link/?BIOMGB/1/14103/1. 9 December 2012.
  6. News: Einstein's tea-leaves inspire new gadget. Pincock. Stephen. 17 January 2007. ABC Online. 2008-12-28.
  7. Einstein's Tea Leaves and Pressure Systems in the Atmosphere. Tandon. Amit. Marshall, John . The Physics Teacher. 2010. 48. 5. 292–295. 10.1119/1.3393055. 2010PhTea..48..292T. free. 1721.1/118473. free.
  8. Book: Bamforth, Charles W.. Beer: tap into the art and science of brewing. limited. 2nd. Oxford University Press. 2003. 978-0-19-515479-5. 56.

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