[Physics] Why do tea leaves go to the center of the cup

Question

When I stir my tea with a spoon, I observe that the tea leaves all eventually concentrate in the center of the cup. Clearly they go against the centrifugal force. Why?

Yet when I put the cup in the center of the rotating platter of my gramophone turntable, the tea leaves concentrate at the edge following the centrifugal force.

The surface of the tea is concave with the depth lower in the center in both cases. Thus the pressure in the center cannot be higher than at the edge. The tea leaves drown, so they are heavier than water and should not move to where pressure is lower.

So why do the tea leaves move to the center?

In response to the possible duplicate, the earlier question does not include the case of a rotating turntable and therefore has a lesser scope. In addition, the method of stiring is different, so the question is not a duplicate. Finally, the earlier question does not have a complete correct answer, but only a reference to the Elkman layer for a further research. Thus my question is not at all addressed earlier from any angle. The second link also does not address the case of the rotating turntable, explaining where, how, and why the leaves would collect in this case.

Answer 1

When I steer my tea with a spoon, I observe that the tea leaves all eventually concentrate in the centre of the cup. Clearly, they go against the centrifugal force. Why?

When you are stirring the tea in your cup you are trying to give rotational motion to the fluid layers but the layers in contact with the cup surfaces remain at zero speeds. The velocity gradient radially (as the viscous drag between the layers reduces the speed) picks up the leaves but it can not maintain the circular path in absence of required centripetal acceleration and slowly collects at the centre.

For moving along with the fluid they need necessary centripetal force and that is not being provided by the layers of fluid.

Yet when I put the cup in the centre of the rotating platter of my gramophone turntable, the tea leaves concentrate at the edge following the centrifugal force.

When you are rotating the cup filled with tea and leaves on a turntable- slowly the layers of fluid will pick up the speed and then drag the tea leaves to rotate along with layers of liquid but as its heavier than the liquid media , it again searches for required centripetal force and gets back to the rim of the cup, where it can rotate with centripetal force provided by the reaction of the surface. Its a centrifuge action.

There is an interesting discussion of the same event-the first part of stirring which is being quoted for added insight. the reference gives diagram of action when stirring.

Added a quote- for further explanation.

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 fictitious (inertial) centrifugal 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.[6]

The inertial centrifugal force due to the bulk rotation of the liquid results in the development of an outward pressure gradient within the liquid, where the pressure is higher along the rim than in the middle. This manifests itself as the formation of a concave liquid-air interface. This pressure gradient provides the necessary centripetal forces for circular motion when summed over the entirety of the rotating liquid.

However, within the boundary layers where fluid rotation is slowed by friction and viscous effects, the centripetal force due to pressure gradient is dominant over the inertial forces from rotation, and creates an inward secondary flow within the boundary layer. The flow converges at the bottom of the teacup (where the tea leaves are observed to gather) and flows upwards to the surface. Higher up, the liquid flow meets the surface and flows outwards. The leaves are too heavy to lift upwards and remain in the middle. Combined with the primary rotational flow, the leaves will be observed to spiral inwards along the bottom of the teacup.[5] https://en.wikipedia.org/wiki/Tea_leaf_paradox