A Model for Estimation of Viscosities of Complex Metallic and Ionic Melts
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I.
INTRODUCTION
V I S C O S I T Y is an important property to be considered in dealing with fluid flow behavior and in understanding the kinetics of reactions of relevance to process metallurgy. For example, the rise of gas bubbles through metallic melts depends on the viscosity of the bath. Similarly, the rate of transfer of impurities like S and P from metal to slag is affected by slag viscosities. In the simulation of the metallurgical process, it is often required to extrapolate available experimental data over wide composition and temperature ranges for metallic as well as slag systems. The need for a computer model that enables the estimation of viscosities of complex systems at relevant conditions has long been felt. Modeling of viscosities of complex melts has been receiving the attention of scientists, especially in the past 3 decades. The approach to modeling can be classified into two types, viz., the fundamental molecular approach and the semitheoretical procedure. The former type of theories are particularly of relevance to liquid metals in view of their monatomic nature. But most of the theories existing today are still under development and hardly meet the technological requirements. On the other hand, the semitheoretical or empirical procedures seem to give somewhat satisfactory results, t~-13~ In the case of metallic melts, the most commonly used equation was proposed by Andrade.C61 He suggested that the viscosity of a metallic melt could be described by the following equation: r / V 1/3 =
A exp ( C / v T )
[I]
where r/is viscosity in poise, v is specific volume, and T is temperature in kelvin. The two constants A and C can be obtained by conducting the viscosity measurements at different temperatures for the same melt. Although this equation has been used in many studies and has been proven to be successful, the shortcoming of this approach is that different sets of A and C have to be determined for different compositions. In the case of complex systems, it cannot provide a whole description of the viscosity in the system. DU SICHEN and J. BYGDI~N, Research Associates, and S. SEETHARAMAN, Professor, are with the Division of Theoretical Metallurgy, Royal Institute of Technology, S-100 44 Stockholm, Sweden. Manuscript submitted March 31, 1993. METALLURGICAL AND MATERIALS TRANSACTIONS B
In some cases, system-specific equations to describe viscosity of metallic melts have also been proposed for different systems. For example, Thresh and Crawley, tTJ from their experimental results, suggested a linear equation, 7]alloy = r/pbXp b ~I_ r/snXs n
[II]
for calculating the viscosities of Pb-Sn liquid alloys. In this equation, X stands for mole fraction. Ganesan et al. Iz~ proposed a rcgrcssion equation, r/aUoy = ao + alC + a2C 2
[III]
in their studies for the viscosity of the AI-Cu system, where ao, al, and a: are constants at a certain temperature. The constant C is weight percent of Cu. As the equations like [1I] and [III] are characterized by the systems involved, the applicability of the same t
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