A linear analysis of interfacial instabilities of ferrofluids

Abstract

Surface motion of a magnetic fluid is studied by a linear stability analysis. When a thin horizontal magnetic-fluid layer is placed on a nonmagnetic substrate, with a vertical magnetic field applied, the surface of the ferrofluid layer can be severely corrugated, due to the normal-field instability. Based on conservation laws, it is shown that the normal-field instability of thin ferrofluid layers is a long-wave instability and that it is analogous to the interfacial mode of the thermocapillary instability in a thin horizontal layer heated from below.