Dynamics of ferrofluid drop deformations under spatially uniform magnetic fields

We systematically study the shape and dynamics of a Newtonian ferrofluid drop immersed in an immiscible, Newtonian and non-magnetic viscous fluid under the action of a uniform external magnetic field. We obtain the exact equilibrium drop shapes for arbitrary ferrofluids, characterize the extent of deviations of the exact shape from the commonly assumed ellipsoidal shape, and analyse the smoothness of highly curved tips in elongated drops. We also present a comprehensive study of drop deformation for a Langevin ferrofluid. Using a computational scheme that allows fast and accurate simulations of ferrofluid drop dynamics, we show that the dynamics of drop deformation by an applied magnetic field is described up to a numerical factor by the same time scale as drop relaxation in the absence of any magnetic field. The numerical factor depends on the ratio of viscosities and the ratio of magnetic to capillary stresses, but is independent of the nature of the ferrofluid in most practical cases.