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This note introduces the linear stability of a ferrofluid thick layer  submitted to gravity and to a normal magnetic field. The compatibility condition  is derived taking into account the Rayleigh–Taylor instability and the Marangoni  one. The pure normal deformation is analytically solved and these results can be  extended to explain the heat conducting case.

Linear Marangoni and Rayleigh-Taylor instabilities of a ferrofluid thick layer in a vertical magnetic field