# Albert Einstein solved the Tea Leaf paradox

The tea leaf paradox describes 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 solution first came from Albert Einstein in a 1926 paper where he used it to explain the erosion of river banks (Baer’s law).

## Explanation

The tea leaf paradox describes 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 solution first came from Albert Einstein in a 1926 paper where he used it to explain the erosion of river banks (Baer’s law)

Stirring the liquid makes it spin around the cup. In order to maintain this curved path, a centripetal force in towards the center is needed (similar to the tension in a string when spinning a bucket over your head). This is accomplished by a pressure gradient outward (higher pressure outside than inside).

However, near the bottom and outer edges the liquid is slowed by the friction against the cup. There the centripetal force is weaker and cannot overcome the pressure gradient, so these pressure differences become more important for the water flow. This is called a boundary layer or more specifically an Ekman layer.

Because of the centrifugal force, the pressure is higher along the rim than in the middle. If all the liquid rotated as a solid body, the inward (centripetal) force would match the outward (centrifugal) force from the rotation and there would be no inward or outward movement.

In a teacup, where the rotation is slower at the bottom, the pressure gradient takes over and creates an inward flow along the bottom. Higher up, the liquid flows outward instead. This secondary flow travels inward along the bottom bringing the leaves to the center, then up, out and down near the rim. The leaves are too heavy to lift upwards, so they stay in the middle. Combined with the primary rotational flow, the leaves will spiral inward along the bottom.

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