Tea leaf paradox
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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".[2] The formation of secondary flows in an annular channel was theoretically treated by Joseph Valentin Boussinesq as early as in 1868.[3] The migration of near-bottom particles in river-bend flows was experimentally investigated by A. Ya. Milovich in 1913.[1] 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.[4][5]
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.[5]
Applications
The phenomenon has been used to develop a new technique to separate red blood cells from blood plasma,[6][7] to understand atmospheric pressure systems,[8] and in the process of brewing beer to separate out coagulated trub in the whirlpool.[9]
See also
References
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- ↑ a b His results are cited in: Script error: No such module "Citation/CS1". Reprinted in: Script error: No such module "citation/CS1".
- ↑ James Thomson, On the grand currents of atmospheric circulation (1857). Collected Papers in Physics and Engineering, Cambridge Univ., 1912, 144–148. DjVu file.
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- ↑ a b Script error: No such module "Citation/CS1". 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.
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External links
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- Script error: No such module "citation/CS1". See also figure 25 in figures.pdf
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- Einstein's 1926 article online and analyzed on BibNum (click 'Télécharger' for English) (unsecure link).