Coupling between Stationary Marangoni and Cowley-Rosensweig Instabilities in a Deformable Ferrofluid Layer
M. Hennenberg; B. Weyssow; S. Slavtchev; and B. Scheid

doi:10.3970/fdmp.2007.003.295
Source FDMP: Fluid Dynamics & Materials Processing, Vol. 3, No. 4, pp. 295-302, 2007
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Abstract A horizontal thin layer of ferrofluid is bordered by a solid and open to an inert gas on the other side. It is submitted to a heat gradient and a weak magnetic field, both being normal to the free deformable surface, leading to a coupling between the Marangoni phenomenon, induced by the variation of surface tension along the free deformable surface and the isothermal 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 of$O(\sqrt {{\sf Bo}})$, the Bond number${\sf Bo}$ 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.
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