Influence of an inhomogeneous internal magnetic field on the flow dynamics of a ferrofluid between differentially rotating cylinders

The influence of a magnetic field on the dynamics of the flow of a ferrofluid in the gap between two concentric, independently rotating cylinders is investigated numerically. The Navier-Stokes equations are solved using a hybrid finite difference and Galerkin method. We show that the frequently used assumption that the internal magnetic field within a ferrofluid is equal to the external applied field is only a leading-order approximation. By accounting for the ferrofluid's magnetic susceptibility, we show that a uniform externally imposed magnetic field is modified by the presence of the ferrofluid within the annulus. The modification to the magnetic field has an r ^-2 radial dependence and a magnitude that scales with the susceptibility. For ferrofluids typically used in laboratory experiments of the type simulated in this paper, the modification to the imposed magnetic field can be substantial. This has significant consequences on the structure and stability of the basic states, as well as on the bifurcating solutions.