Flow of immiscible ferrofluids in a planar gap in a rotating magnetic field

Abstract

Analytical solutions are obtained for the steady, fully developed flow of two layers of immiscible ferrofluids of different thicknesses between two parallel plates. Interfacial linear and internal angular momentum balance relations are derived for the case when there is a ferrofluid-ferrofluid interface to obtain the translational and spin velocity profiles in the gap. As expected for the limit of low applied field amplitude, the magnitude of the translational velocity is directly proportional to the frequency of the applied magnetic field and to the square of the magnetic field amplitude. Expressions for the velocity profiles are obtained for the zero spin viscosity and non-zero spin viscosity cases and the effect of applied pressure gradient on the flows is studied. The spin velocity in both ferrofluid phases is in the direction of the rotating magnetic field, except for cases of extreme applied pressure gradients for which the fluid vorticity opposes the spin. We find that for the case of non-zero spin viscosity, flow reversals are predicted using representative ferrofluid property values and field conditions. The unique predictions of the solution with non-zero spin viscosity could be used to experimentally test the existence of couple stresses in ferrofluids and the validity of previously reported values of the so-called spin viscosity.