We investigate numerically the influence of a homogeneous magnetic field on a ferrofluid in the gap between two concentric, independently rotating cylinders. The full Navier-Stokes equations are solved with a combination of a finite difference method and a Galerkin method. Structure, dynamics, symmetry properties, bifurcation, and stability behavior of different vortex structures are investigated for axial and transversal magnetic fields, as well as combinations of them. We show that a transversal magnetic field modulates the Taylor vortex flow and the spiral vortex flow. Thus, a transversal magnetic field induces wavy structures: wavy Taylor vortex flow (wTVF) and wavy spiral vortex flow. In contrast to the classic wTVF, which is a secondarily bifurcating structure, these magnetically generated wavy Taylor vortices are pinned by the magnetic field, i.e., they are stationary and they appear via a primary forward bifurcation out of the basic state of circular Couette flow.

We report on measurements of the transverse magnetization of a ferrofluid rotating as a rigid body in a constant magnetic field, H0, applied perpendicular to the axis of rotation. The rotation of the fluid leads to a nonequilibrium situation, where the ferrofluid magnetization M and the magnetic field within the sample, H, are no longer parallel to each other. The off-axis magnetization perpendicular to H0 is measured as a function of both the applied magnetic field H0 and the angular frequency Omega. The latter ranges from a few hertz to frequencies well above a characteristic inverse Brownian relaxation time. Our experimental results strongly indicate that the transverse magnetization is caused only by a small fraction of the colloidal ferromagnetic particles. The effect of the polydispersity of the ferrofluid is discussed. Experimental results are compared to predictions based on several theoretical models. A single-time relaxation approach for the so-called effective field and a field-dependent Debye relaxation of M yield reasonably good shapes of the curves of transverse magnetization vs Omega. However, like the other models, they overestimate their magnitudes.

The gap between two concentric rotating cylinders is filled with a ferrofluid. A homogeneous magnetic field is applied parallel to the cylinder axis. The stability of the circular Couette flow is analyzed with different models that take into account the polydispersity of the ferrofluid to a varying degree. Their results are compared and their merits are discussed.

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Selected results on the spatiotemporal behaviour of equilibrium and nonequilibrium properties of ferrofluids in different magnetic fields are reviewed. They have been obtained in the project B13 Transport, response and instability behaviour of ferrofluids of the SFB 277 by experiments and by various theoretical methods ranging from purely analytical calculations to full numerical approaches.