Low Rm magnetohydrodynamics as a means of measuring the surface shear viscosity of a liquid metal: A first attempt on Galinstan

Abstract

This paper introduces an experimental apparatus which generates the end-driven annular flow of a liquid metal pervaded by a uniform magnetic field. Unlike past viscometers involving an annular channel with particular values of the depth-to-width ratio, the present experiment enables us to drive the viscous shear at the surface of an annular liquid metal bath put in rotation. The magnetic interaction parameter N and the Boussinesq number related to the surface shear viscosity can be monitored from the magnitude of the applied magnetic field; the latter being set large enough for avoiding artefacts related to centrifugation and surface dilatation. This essential feature is obtained due to the ability of the magnetic field to set dimensionality of the annular flow in the channel between 2D-1/2 (swirling flow) and 2D axisymmetric (extinction of the overturning flow if N is large enough). By tracking the azimuthal velocity of tracers seeded along the oxidised surface of liquid Galinstan, an estimate for the surface shear viscosity of a liquid metal can be given.

Between no slip and free slip: A new boundary condition for the surface hydrodynamics of a molten metal

“…By first considering the classical model of a Newtonian interface (n = 1), a value of the Boussinesq number as high as Bo = 1500 permits to explain both the low intensity of the surface flow and the evolution of the velocity field with the Hartmann number. This value corresponds to a surface shear viscosity of η s = 1.12 kg.s −1 , which is found here much higher than the one measured by Delacroix et al for partially oxidized Galinstan [11]. As a result, the residual oxide layer formed on the surface of melted A356 aluminum alloy is found extremely viscous with a considerable impact upon the supporting flow.…”

“…Because no such data seem available in the literature devoted to aluminum alloys, the focus is first given to the surface shear viscosity, making use of an annular MHD surface viscometer (MaDip experiment), recently developed at the SIMaP/EPM laboratory [11]. The classical configuration of the annular viscometer, historically designed by Mannheimer and Schechter [12] in 1970s, is considered by many authors for the determination of the surface shear viscosity of a liquid sample covered by surfactants such as carboxylic acids or protein monolayers [13,14,15,16,17].…”

“…An accurate measurement of the surface velocity field, as performed via the introduction of tracers along the interface, allows the shear surface viscosity to be identified by comparison with the Mannheimer and Schechter analytical solution [18]. Quite recently, the addition of a uniform vertical magnetic field has been proved particularly relevant for the characterisation of an electrically conductive liquid metal also subjected to oxidation [11]. The interaction between a static magnetic field and the annular flow induces loops of electrical current densities, which affect in return the flow due to the Lorentz force.…”

“…Delacroix & Davoust to study Galinstan, a liquid metal at room temperature that is recognised to be sensitive to oxidation process [11]. Here, the challenge was to develop a surface viscometer experiment capable of 1) withstanding the high temperature of molten aluminum and 2) taking into account the chemical and geometrical requirements imposed by the oxidation reaction and the electromagnet gap.…”