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Stationary thermocapillary instability in a thin ferrofluid layer submitted to a weak magnetic field

par Hennenberg, Marcel ;Slavtchev, Slavtcho;Weyssow, Boris ;Scheid, Benoît
Référence (1-6 septembre 2006: SUNNY BEACH Resort BULGARIA), 11th Workshop on transport phenomena in two-phase flow
Publication Publié, 2006

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Résumé :

We study the thermocapillary instability in a thin horizontal ferrofluid layer with a deformable free surface. The magnetic liquid is submitted to a weak magnetic field and a thermal gradient, both normal to the layer boundaries. Two different types of instability may occur in the liquid. In the isothermal case, static Rosensweig instability may exit due to the magnetic force acting on the free surface. When the layer is heated, variations in the surface tension along the liquid-gas surface, due to temperature gradients, induce Marangoni convection in the bulk. In the present paper, we study the necessary conditions for the appearance of both instabilities for the non-inductive case. The linear stability analysis is applied in the case of stationary perturbations and the compatibility condition is obtained in two equivalent analytical forms representing either the Marangoni number or the magnetic Bond number as a function of the wavenumber. Previous results from other authors for thermocapillary instability in a ferrofluid layer are revised and corrected.