Why Do Tea Leaves Gather at the Centre of a Stirred Cup?

Stir loose-leaf tea, then let the motion subside, and the leaves often collect at the centre of the cup’s bottom. Rotation seems as though it should fling material outwards, so why does the opposite happen?

The rotating surface sits slightly higher at the wall than at the centre. This produces an inward pressure gradient that supplies the centripetal acceleration needed for circular motion. Away from the bottom, where the water rotates relatively quickly, that pressure gradient roughly matches the required acceleration. Near the bottom, however, viscous friction slows the water while the pressure gradient remains. The bottom layer is therefore driven inwards more strongly than its reduced speed requires.

Water cannot accumulate indefinitely at the centre. It rises there, flows outwards nearer the surface, and descends along the wall, forming a secondary circulation superimposed on the main rotation. Tea leaves first settle under gravity and are then swept towards the centre by the inward flow along the bottom. They are not defeating a single outward “centrifugal force”; they are being transported by a three-dimensional current.

In 1926, Einstein used this teacup flow to explain sediment transport around river bends. The cup shows why a simple-looking rotation can hide another current created by friction at a boundary.

https://arxiv.org/abs/2305.09528