Tea-leaf paradox

Settled in 1926 by Albert Einstein.

James Thomson (brother of Lord Kelvin) first described the paradox in 1857 while explaining river meandering, noting that stirred tea leaves gather at the cup's center rather than its rim despite the outward centrifugal force one would naively expect. Albert Einstein revisited the problem in a short 1926 paper ostensibly about river meanders, explaining that friction against the cup's bottom slows the fluid there, weakening the centrifugal effect near the base relative to higher up, which drives a secondary top-to-bottom-to-center circulation (now understood in terms of Ekman-layer-type boundary flow) that sweeps leaves inward. The explanation is textbook fluid dynamics today and is also invoked to explain related large-scale phenomena like river meander formation.

Einstein used the same physics to explain a teacup and the shape of the world's rivers.

Explanations that circulated

• Naive intuition (and the pre-1857 assumption) that stirring should fling denser leaf particles outward by centrifugal effect, like a centrifuge, so they should end up at the rim, not the center.

References

• Die Ursache der Mäanderbildung der Flussläufe und des sogenannten Baerschen Gesetzes, A. Einstein, Die Naturwissenschaften, 1926