(418bl) Ferrofluid Flow in a Channel Induced By a Rotating Magnetic Field

Ferrofluids are a clear example of structured fluids; whose rheological behavior is influenced by forces of magnetic polarization. Additionally, these fluids are characterized by an antysimmetric stress tensor when they are under the action of a rotating magnetic field. This work has been motivated by the experimental evidence of the surface flow of a ferrofluid driven by a rotating magnetic field in a circular channel of square cross section. In this work a numerical solution for this particular geometry is obtained, which considers the effect of diffusion of the internal angular momentum of the ferrofluid particles; which is described by the tensor "couple stresses" and quantified by a phenomenological coefficient "spin viscosity". In order to obtain a numerical solution, this study considered the interfacial balances for linear and internal angular momentum obtained for Chaves and Rinaldi as boundary conditions at interface ferrofluid-air. Additionally, a numerical solution for the ferrofluid flow in a duct with a square cross section is also obtained. The numerical solutions obtained showed that the ferrofluid flow in a duct is generated only in case that the existence of the internal angular momentum diffusion is assumed (“spin viscosity”). As for the results of the channel, in the event of “spin viscosity” zero, it is possible to generate ferrofluid flow of superficial character because of discontinuity of "couple stresses" and antisymmetric stresses through the ferrofluid-air interface. Moreover, it was found that the channel flow magnitude is greater when the parameter of flow “spin viscosity” was at nonzero: this can be explained because of the combined action between the mechanism of flow volumetric and surface. Finally, for the same conditions of intensity and frequency of the applied magnetic field, the magnitude of the flow in the channel was found to be higher than the magnitude of the flow in the duct.