The paradox of tea is a paper published by Einstein in 1926, which describes the phenomenon that tea leaves will swim to the center of the cup bottom after being stirred, instead of being pushed to the edge of the cup bottom by spiral centrifugal force as expected.

scientific explanation

Stir the liquid to make it rotate in the cup, resulting in outward centrifugation. The liquid near the outside of the bottom slows down due to the friction of the cup wall, where the centrifugal force is weakened, so the pressure difference has a greater effect on the water flow than the centrifugal force. This is called the boundary layer, or more precisely the Ekman layer.

Due to centrifugal phenomenon, the force along the edge is greater than that in the middle. If all liquids rotate as solids, the internal centripetal force is related to the external (centripetal force) and the rotation speed, so there is no inward or outward movement.

In a teacup, the bottom rotates slowly, resulting in a pressure gradient and an inward wave flow along the bottom. Up, the liquid flows outside. The second wave flows inward along the bottom, collecting the tea leaves outside the edge to the center. Because the weight of tea can't rise, it stays at the bottom center. Combined with the first rotating wave, these tea leaves will spiral inward along the bottom.

It can be applied to the floating motion in ocean currents.

Secondary and secondary flow

In fluid mechanics, the concept of secondary flow is defined as follows: if the flow along the boundary is displaced parallel to the boundary due to lateral pressure, the fluid layer near the boundary is displaced more than the fluid layer far away from the boundary because of its lower velocity, thus causing the secondary flow to be superimposed on the mainstream.

The secondary flow refers to the water flow that is parallel to the boundary and superimposed on the main flow. One flow (mainstream) causes another flow of different nature. For example, the flow on the cross section perpendicular to the axis direction of the main flow in the pipe flow is the secondary flow; Other flows, such as separated flow and vortex, will also cause corresponding secondary flow.