Spin-up of ferrofluids: The impact of the spin viscosity and the Langevin function

The spin-up of ferrofluids (rotational motion of a magnetic fluid induced by a rotating magnetic field) is examined computationally. Key questions are the impact of the spin viscosity, a mildly non-uniform magnetic field, and the importance of the Langevin magnetization equation. Comsol Multiphysics is used with boundary layer meshes to capture the effect when the spin viscosity is small. The effect of the spin viscosity is examined as it affects the critical magnetic field for non-rotational flow to occur and the magnitude of the rotational velocity and torque. Comparisons are made for the effect of magnetic field when using the Langevin magnetization equation and a linear equation. The equations for flow, magnetic field, and spin velocity are solved in two dimensions as a representation of a long cylinder with the magnetic field oriented perpendicular to the axis of the cylinder and rotated about that axis. Solutions are obtained for spin viscosities as low as 5.8 10-14 kg m s-1.