Coupling between stationary Marangoni and Cowley-Rosensweig instabilities in a deformable ferrofluid layer

Abstract: A horizontal thin layer of ferrofluid is bor-dered by a solid and open to an inert gas on the other side. It is submitted to a heat gradient and a weak mag-netic field, both being normal to the free deformable surface, leading to a coupling between the Marangoni phenomenon, induced by the variation of surface ten-sion along the free deformable surface and the isother-mal Cowley-Rosensweig problem, consequence of the magnetic field. The study of the steady compatibility condition shows a new pattern of stationary instability. The critical wavenumber is O( Bo), the Bond number Bo being smaller than 1, at a minima of the Marangoni number, that could be much less thus than its classical undeformable counterpart. For large wavelengthes, the Marangoni number depends on the Galileo number in contradistinction to earlier results.