Torque and Bulk Flow of Ferrofluid in an Annular Gap Subjected to a Rotating Magnetic Field

Abstract

We report analysis and measurements of the torque and flow of a ferrofluid in a cylindrical annulus subjected to a rotating magnetic field perpendicular to the cylinder axis. The presence of the inner cylinder results in a nonuniform magnetic field in the annulus. An asymptotic analysis of the ferrohydrodynamic torque and flow assuming linear magnetization and neglecting the effect of couple stresses indicated that the torque should have a linear dependence on field frequency and quadratic dependence on field amplitude. To the order of approximation of the analysis, no bulk flow is expected in the annular gap between stationary cylinders. Experiments measured the torque required to restrain a polycarbonate spindle surrounded by ferrofluid in a cylindrical container and subjected to the rotating magnetic field generated by a two-pole magnetic induction motor stator, as a function of the applied field amplitude and frequency, and for various values of the geometric aspect ratios of the problem. The ultrasound velocity profile method was used to measure the azimuthal and axial velocity profiles in the ferrofluid contained in the annular gap of the apparatus. Flow measurements show the existence of a bulk azimuthal ferrofluid flow between stationary coaxial cylinders with a negligible axial velocity component. The fluid was found to corotate with the applied magnetic field. Both the torque and flow measurements showed power-of-one dependence on frequency and amplitude of the applied magnetic field. This analysis and these experiments indicate that the action of antisymmetric stresses is responsible for the torque measured on the inner cylinder, whereas the effect of body couples is likely responsible for bulk motion of the ferrofluid.