Hi,

I was asked a question yesterday which I could not answer -

Why do the tea leaves in my cup of tea go into the middle of the cup when stirred? The leaves are heavier than water (as they sink), so shouldn't they go to the outside by centrifugal forces?

Any ideas?

Thanks,

Glenn

The rotation sets up a radial pressure gradient in the cup - the pressure increases as you go further out from the center. In the bulk of the rotating tea this pressure gradient is exactly balanced by the centrifugal force and there is no net flow in the radial direction.

However, at the bottom of the cup the wall slows down the tea and in this boundary layer the rotational velocity is lower than in the bulk above. Hence also the centrifugal force is lower. The pressure gradient is the same as above though and this will drive a flow into the center of the cup (the fluid then goes up along the centerline).

When the tea-leaves sink down to this boundary layer at the bottom they will be convected with it into the center. You might also see some of them following the stream up along the centerline a bit, but often gravity holds them down and makes them gather up in a small pile in the center.

The existence of the secondary flow motion ( in this case, the motion of the flow on the radial plane normal to the circular motion of the main flow) is a very important issue in many turbomachinery applications. The secondary flow motion tends to move the low speed boundary layer flow into a much larger area and thus creates much higher loss (outside its original wall boundary layer region). Turbine blade design with shapes to modify the 3-D pressure field and thus reduces the creation, promotion of secondary flow loss is an area of current interest. A new tea cup design with reduced secondary flow motion ?

Did you ever notice the game those leaves are playing? They go to the middle, then return, then again go to the middle, and so on several times, until finally set down in the center. If, now, you consider in more detail that secondary flow (see Larsson's mesage) you will discover that it consists of fluid layers moving to and from the center (Coriolis forces, of course). And if you estimate the thickness of the boundary layer you will find that it is comparabale with the size of the leaves, and that as the rotation velocity decreases, the layer thickness grows, so that the leaves of a given size are in fact in a fluid moving toward and from the center, alternatively. I checked it assuming that the bottom rotates too, but a bit slower then the fluid. In this case the solution can be found explicitly. I have a collection of such examples, I call them fluid flow mechanisms, and would be gratefull for any additions to my collection.

Sergei Chernyshenko (another e-mail: sergei@chernyshenko.dnttm.rssi.ru, use any)

Thanks all,

A cup of tea will never be the same again. I shall stir with renewed vigour next time.

Glenn