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 Bo, and a supporting annular MHD flow, ruled by the Hartmann number Ha, 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/Ha, 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, \documentclass[12pt]{minimal}\begin{document}$\tilde{B_o}$\end{document}Bõ, 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 \documentclass[12pt]{minimal}\begin{document}$\tilde{B_o}$\end{document}Bõ 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.
Thermophysical properties of liquid metal alloys play a crucial role in the variety of processes. Present work reports experimental investigations of two new transformation induced plasticity (TRIP) steels. A classical maximum bubble pressure technique is successfully used to measure surface tension and density of the liquid TRIP‐steel samples in the temperatures range of 1500–1800 °C. Experiments are performed in two different measurement cells from TU Freiberg and Commissariat a l'Energie Atomique (CEA), Cadarache. Capillaries are made of zirconia partially stabilized with yttrium oxide, and the samples are molten in Al2O3 crucibles. Measurements are conducted under the argon atmosphere. Surface tension of the investigated samples rises up to 1700 °C and further remains the same. Density of the new steels obtained in this study is in good agreement with the previously reported values for Fe–Cr alloys with similar Cr content. Density of the alloy is estimated as 875 488–11 885 × T (±218.85 kg m−3) for a 15%Cr alloy and 796 042–06 897 × T (±199 kg m−3) for a 19%Cr alloy.
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