Electrical activity of the Hartmann layers relative to surface viscous shearing in an annular magnetohydrodynamic flow. - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Physics of Fluids Année : 2014

Electrical activity of the Hartmann layers relative to surface viscous shearing in an annular magnetohydrodynamic flow.

Résumé

As a first step towards two-phase magnetohydrodynamics (MHD), this paper addresses an original analytical coupling between surface rheology, e. g., a gradually oxidizing liquid metal surface, ruled by the Boussinesq number B-o, and a supporting annular MHD flow, ruled by the Hartmann number H-a, in the general layout of a classical annular deep-channel viscometer, as developed by Mannheimer and Schechter [J. Colloid Interface Sci. 32, 195-211 (1970)]. Using a matched asymptotic expansion based on the small parameter 1/H-a, we can express the surface velocity as a coupling variable in the jump momentum balance at the liquid surface. By solving the latter through the determination of the Green's function, the whole flow can be analytically calculated. A modified Boussinesq number, (B) over tilde (o), is produced as a new non-dimensional parameter that provides the balance between surface viscous shearing and the Lorentz force. It is shown that the (B) over tilde (o) number drives the electrical activation of the Hartmann layers, heavily modifying the MHD flow topology and leading to the emergence of the Lorentz force, for which interaction with the flow is not classical. Finally, the evolution laws given in this study allow the determination of scaling laws for an original experimental protocol, which would make it possible to accurately determine the surface shear viscosity of a liquid metal with respect to the quality of the ambient atmosphere. (C) 2014 AIP Publishing LLC.

Domaines

Matériaux
Fichier non déposé

Dates et versions

hal-01053449 , version 1 (31-07-2014)

Identifiants

Citer

J. Delacroix, L. Davoust. Electrical activity of the Hartmann layers relative to surface viscous shearing in an annular magnetohydrodynamic flow.. Physics of Fluids, 2014, 26 (3), ⟨10.1063/1.4869327⟩. ⟨hal-01053449⟩
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