How a rotating magnetic field causes ferrofluid to rotate

The article explores the various mechanisms by which a rotating magnetic field causes to rotate a magnetic fluid contained in a cylinder (the so-called spin-up of ferrofluids). It is shown first that the generally accepted theory of spin diffusion cannot explain this phenomenon due to the extremely low spin viscosity η′: Our calculations give η′∼10-14gcm/s which is 11 orders of magnitude less than the most optimistic estimates. Then we develop a theory linking the rotation of a free surface layer to the shape of the meniscus. The latter, equally as the strength and frequency of the rotating field, determines both the direction and the magnitude of the fluid velocity. However, the magnetic torque created on the curved surface of the liquid captures only a thin subsurface layer and does not cause rotation in the volume. As for the volumetric flow, we associate it with the release of heat in microvortices that arise around rotating magnetic particles. In a vertical cylinder, such heating forms a parabolic temperature profile, which makes the magnetization of the fluid spatially inhomogeneous. As shown, this is sufficient to induce an observable bulk flow of the ferrofluid. The influence of natural convection on this spin-up flow is also investigated. In conclusion, it is shown that the stress tensor of a magnetic fluid can always be brought to a symmetric form.