Competition between the Bénard-Marangoni and the Rosensweig Instability in Magnetic Fluids

The linear stability analysis of a layer of magnetic fluid with deformable free surface, which is heated from below and exposed to a uniform, vertically applied magnetic field is presented. In this configuration the temperature dependence of the surface tension, the buoyancy and the focusing of the magnetic field due to surface fluctuations act as destabilising effects. We show that this system has for thin layers a stationary codimension–2–point, which can be reached for experimentally relevant values of the material parameters. We also analyse the transition from thin to thicker layers for which there is no codimension–2–point and we show how the codimension–2–point disappears. Finally we demonstrate that there is no oscillatory instability in the regions of parameter space considered here.