The non-linear magnetization characteristics of recently developed ferrofluids complicate studies of wave dynamics and stability. A general formulation of the incompressible ferrohydrodynamics of a ferrofluid with non-linear magnetization characteristics is presented, which distinguishes clearly between effects of inhomogeneities in the fluid properties and saturation effects from non-uniform fields. The formulation makes it clear that, with uniform and non-uniform fields, the magnetic coupling with homogeneous fluids is confined to interfaces; hence, it is a convenient representation for surface interactions.

Detailed attention is given to waves and instabilities on a planar interface between ferrofluids stressed by an arbitrarily directed magnetic field. The close connexion with related work in electrohydrodynamics is cited, and the effect of the non-linear magnetization characteristics on oscillation frequencies and conditions for instability is emphasized. The effects of non-uniform fields are investigated using quasi-one-dimensional models for the imposed fields in which either a perpendicular or a tangential imposed field varies in a direction perpendicular to the interface. Three experiments are reported which support the theoretical models and emphasize the interfacial dynamics as well as the stabilizing effects of a tangential magnetic field. The resonance frequencies of ferrohydrodynamic surface waves are measured as a function of magnetization, with fields imposed first perpendicular, and second tangential, to the unperturbed interface. In a third experiment the second configuration is augmented by a gradient in the imposed magnetic field to demonstrate the stabilization of a ferrofluid surface supported against gravity over air; the ferromagnetic stabilization of a Rayleigh-Taylor instability.