Rosensweig instability in ferrofluids

Abstract

We propose a simple model to analyze stability of the free surface of horizontally unbound ferrofluid in a vertical magnetic field. With respect to the well known Rosensweig instability (see e.g., R.E.Rosensweig, Ferro hydrodynamics, Cambridge University Press, Cambridge (1993) and references therein) we go one step further to include into consideration coupling of surface displacements to non-magnetic degree of freedoms. We show that the coupling can lead to a considerable reduction of the critical magnetic field and as well yields to nontrivial depletion layering near the surface.