The capillary instability of a thin cylinder of viscous ferrofluid in a longitudinal magnetic field

Abstract The effect of a uniform magnetic field on the capillary break-up of a thin cylinder of magnetic liquid at rest, surrounded by an unbounded liquid with other coefficients of viscosity and magnetic permeability, is investigated in the linear formulation. An approximate expression is obtained for the root of the dispersion relation, describing the development of the instability when the viscosity force plays a predominant role compared with the inertia forces. Well-known forms of the roots, corresponding both to the interfaces of the immiscible liquids with different coefficients of viscosity and the interfaces of the viscous and non-viscous liquids, follow from the expression obtained as special cases. Compared with existing publications, in the latter case the next terms of the expansion in powers of the small parameter, representing the ratio of the characteristic diffusion time of the vorticity to the characteristic capillary-viscous time, are obtained.