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

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.