# Laboratoire de Mécanique des Fluides et d’Acoustique - UMR 5509

LMFA - UMR 5509
Laboratoire de Mécanique des Fluides et d’Acoustique
Lyon
France

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Article dans C. R. Mécanique (2016)

## Influence of a magnetic field on the stability of a binary fluid with Soret effect

Mokhtar Ben Sassi, Slim Kaddeche, Ali Abdennadher, Daniel Henry, Hamda Ben Hadid & Abdelkader Mojtabi

The effect of both magnitude and orientation of a uniform magnetic field on the critical transition occurring within an electrically conducting binary fluid layer, stratified in temperature and concentration, taking into account the Soret effect, is investigated numerically. For such a configuration, the results show that the critical thresholds corresponding to an arbitrary orientated magnetic field can be derived from those obtained for a vertical magnetic field and that the axes of the marginal cells are aligned with the horizontal component of the magnetic field. Moreover, an analytical study is conducted to investigate the impact of the magnetic field on long-wavelength instabilities. The effect of the magnetic field on such instabilities reveals a new phenomenon consisting in major changes of the unstable modes that lose their unicellular nature to regain their multi-roll characteristic, as it is the case without magnetic field for $\psi<\psi_{\ell_0}=131Le\,/(34-131\,Le)$. For a binary fluid characterized by a Lewis number $Le$ and a separation factor $\psi>\psi_{\ell_0}$, the value of the Hartmann number $Ha_\ell(\Psi,Le)$ corresponding to that transition responsible for a significant change in mass and heat transfer can be determined from the analytical relations derived in this work.
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