Spin-up flow in ferrofluids: a toy model

It is now more than 50 years since the first observation of ferrofluid spin-up by a rotating magnetic field by the author and R. Moskowitz. The ferrofluid rotated in direction opposite to that of the applied field. The intervening years have seen multiple unsuccessful attempts to explain this phenomenon. A clue was experimentally discovered by J. Popplewell and the author in 1987; rotation direction depends on shape of the ferrofluid meniscus. That notion is studied in further detail in the present work which describes tangential stress generated on the meniscus surface and an analytical expression for torque is developed. Increasing spin rate in smaller diameter vessels is rationalized. In addition, a physical picture of spin-up is introduced.