Influence of a magnetic field on the Soret-effect-dominated thermal convection in ferrofluids

We investigate theoretically the influence of a magnetic field on the growth of convective rolls in a slab of ferrofluid subject to a vertical temperature gradient. Due to the pronounced Soret effect of these materials in combination with a considerable solutal expansion, a dynamic description as a binary mixture is appropriate. We first derive a comprehensive set of magnetic field effects in the statics and dynamics of binary mixtures. Among those, the two prominent ones, the Kelvin force and magnetophoresis, are studied in detail with respect to their influence on the thermal convection behavior. The main difference from the case without an external field rests in the importance of the boundary layers, which influence the bulk problem through the magnetic boundary conditions. We discuss an analytical approximate solution and compare it with a numerical multimode expansion.