(142cy) Spin-up Flow Experiments with Brownian Ferrofluids and the Existence of Couple Stresses

Ferrofluids are colloidal suspensions of magnetic nanoparticles with interesting fluid mechanics due to the presence of magnetic body couples and non-symmetric viscous stresses. Ferrofluid flow in a cylindrical geometry under the influence of a uniform rotating magnetic field, spin-up flow, has received much attention in the ferrohydrodynamics field since it could prove or disprove the existence of couple stresses in these fluids. Previous experiments in the spin-up geometry show qualitative agreement between the magnitude and direction of the velocity profile in the bulk and profiles predicted by the spin diffusion theory. It has been demonstrated that non-uniformities in the rotating magnetic field do not drive these flows. However, previous experiments considered ferrofluids consisting of magnetite nanoparticles at high concentrations, wherein the relaxation time could not be experimentally determined and where only a minor fraction of the particles relax by the Brownian mechanism. Additionally, measurable flows were obtained only at high magnetic fields, whereas the solution available for the ferrohydrodynamics equations was applicable for small magnetic fields. Here we consider water based ferrofluids with cobalt ferrite nanoparticles at low concentrations (< 0.01 v/v) which display the Brownian relaxation mechanism to test the ferrohydrodynamics equations, elucidate the existence of couple stress, and determine the value of the spin viscosity in these flows. We used an ultrasound technique to measure bulk velocity profiles in the spin-up geometry, varying the magnetic field intensity and frequency generated by a two pole stator winding. Additionally, torque measurements in a cylindrical geometry were considered. Results show that measured velocity profiles had rigid-body like behavior in the bulk, and no dependence in the axial direction. The magnitude of the velocity reached by these dilute Brownian ferrofluids (< 0.01 v/v), is in the same order as reported velocities using magnetite more concentrated ferrofluids (~ 0.1 v/v). Experimental velocity profiles are in quantitative agreement with the predictions of the spin diffusion theory, with a value of the spin viscosity of ~10^-8 kg m/s, two orders of magnitude larger than the value calculated with magnetite ferrofluids, and twelve orders of magnitude larger than estimated using dimensional arguments valid in the limit of infinite dilution. Additionally, the magnitudes of experimental torques are in the same order of magnitude as theoretical predictions. These results present further and conclusive evidence of the existence of couple stresses in ferrofluids and their role in driving the phenomenon of spin-up flow.