Accurate predictions for the viscosities of several liquid transition metals, plus barium and strontium
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I. INTRODUCTION
THE viscosity of liquid metals is a very important property since it has a great influence on many metallurgical manufacturing processes, such as the fluid flow in a vessel, metallic glass formation, and so forth. Consequently, there has been much interest in the viscosity of almost all liquid metallic elements. Even so, experimental data for the viscosity of liquid metallic elements are relatively scanty. The recent development of containerless levitation techniques has made thermophysical property measurements of liquid high-melting-point metals possible.[1,2,3] The viscosities of several liquid high-melting-point metals have been measured in the last few years using containerless techniques.[4] However, viscosity measurements for a number of transition, chemically reactive, and high-vapor-pressure metals are extremely difficult experimentally. As such, the development of reliable, universal models for predicting liquid metal viscosities is needed. Accordingly, the authors recently presented appropriate models to reliably predict the viscosities of pure liquid metals.[5] In this article, using the new models, the authors predict values for the viscosity of several liquid transition metals, plus barium and strontium. None of these liquid metals have been measured experimentally. Finally, newly recommended data for previous metals[5] are collected for the experimental viscosities of pure liquid metals. II. THE ESSENTIAL OUTLINE OF THE AUTHORS’ MODELS AND EVALUATION OF THE MODELS’ PERFORMANCES Recently, the authors presented two models for accurate viscosity predictions of pure liquid metals: one is based on the Andrade equation for the melting-point viscosity, and the other is based on a relationship between viscosity and surface tension of a liquid metal in terms TAKAMICHI IIDA, Visiting Professor, is with McGill University, and is Emeritus Professor with Osaka University, 2-1, Yamadaoka, Suita, Osaka 565-0871, Japan. RODERICK GUTHRIE, MacDonald Professor of Metallurgy, MIHAIELA ISAC, Research Manager, and NAGENDRA TRIPATHI, Postdoctoral Fellow, are with the McGill Metals Processing Centre, McGill University, Montreal, QC, Canada H3A 2B2. Contact e-mail: [email protected] Manuscript submitted September 19, 2005. METALLURGICAL AND MATERIALS TRANSACTIONS B
of the new parameter j T recently introduced by the authors.[5] A. Model Based on the Andrade Equation The “Andrade-type” equation for the melting-point viscosity mm is given by[6–13] mm % CA
(MTm)1/2 Vm2/3
[1]
where CA is called the Andrade coefficient, M is the atomic mass, and Vm is the molar volume at the metal’s melting point Tm. As Born and Green stated,[7] the Andrade derivation was an ingenious dimensional consideration, in which the value for the proportionality factor CA requires experimental or theoretical determination. The average value for the proportionality factor CA, found by dividing experimental viscosity values mm by the value of (MTm)1/2 V#2/3 for the various liquid metm als for which data are available, is 1.80 $ 10#7 J
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