Effects of spin viscosity on ferrofluid duct flow profiles in alternating and rotating magnetic fields

Previous models of plane-Poiseuille flow of ferrofluids in alternating and rotating magnetic fields are extended by including the effects of spin diffusion and planar Couette flow. Accurate modeling of this problem is required for the design of experiments to determine key parameters for previously reported anomalous forward and backward ferrofluid pumping behavior in alternating and rotating magnetic fields. The previously derived zero-spin-viscosity analysis predicted multi-valued and singular flow solutions with possible zero and negative effective magnetoviscosity. This analysis calculates analytical expressions for the translational and spin velocity profiles, vorticity profiles, volumetric flow rate, and the shear force on a moving duct surface, comparing the effects of boundary conditions of zero spin velocity and spin velocity equal to half the vorticity at the duct walls. The analysis shows that the single singularity in flow behavior corresponding to zero magnetoviscosity in the zero-spin-viscosity analysis expands to multiple possible flow singularities for the nonzero spin viscosity case. Simple representative shearing experiments are proposed to differentiate between the zero and nonzero spin viscosity solutions, to calculate the values of key viscous parameters, and to show how wall boundary conditions can be determined from shear stress measurements.