- Source: Tea leaf paradox
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". The formation of secondary flows in an annular channel was theoretically treated by Joseph Valentin Boussinesq as early as in 1868. 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.
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, to understand atmospheric pressure systems, and in the process of brewing beer to separate out coagulated trub in the whirlpool.
See also
Baer–Babinet law, also known as Baer's law – Theory on the formation of rivers due to Earth's rotation
Ekman layer – Force equilibrium layer in a liquid
Secondary flow – Relatively minor flow superimposed on the primary flow by inviscid assumptions
References
External links
Highfield, Roger (14 January 2008). "Dr Roger's Home Experiments". The Daily Telegraph. Archived from the original on 9 December 2012. Retrieved 2008-12-28.
Sethi, Ricky J. (September 30, 1997). "Why do particles move towards the center of the cup instead of outer rim?". MadSci Network. Retrieved 2008-12-29.
Booker, John R. "Student Notes - Physics of Fluids - ESS 514/414" (PDF). Department of Earth and Space Sciences, University of Washington. ch. 5.8 p. 48. Retrieved 2008-12-29. See also figure 25 in figures.pdf
Stubley, Gordon D. (May 31, 2001). "Mysteries of Engineering Fluid Mechanics" (PDF). Mechanical Engineering Department, University of Waterloo. Archived from the original (PDF) on February 6, 2009. Retrieved 2008-12-29.
Einstein's 1926 article online and analyzed on BibNum (click 'Télécharger' for English) (unsecure link).