Analysis of flows of ferrofluids under simple shear

We analyze the nature of steady solutions of a sheared ferrofluid between two parallel boundaries and subject to an applied magnetic field H perpendicular to the boundaries. Making no a priori assumption about the magnitude of spin, we find solutions numerically for the velocity and spin fields under the combined pressure gradient and boundary flow forcing. The numerical technique is valid for arbitrary spin viscosity, and by approaching asymptotically small values we explore the impact of the spin boundary conditions on the flow. When the imposed magnetic field is time independent, its effect on the flow is dissipative, but spatially varying fields still permit control of the velocity profile, including the breaking of its midplane symmetry. Time dependent or rotating perpendicular fields can drive the flow and allow more complete flow control, as illustrated in a simple numerical experiment that approximates plug flow.