Estimation of viscosity of ternary-metallic melts
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INTRODUCTION
VISCOSITY
of high-temperature metallurgical melts is an important property that influences metallurgical processes in many aspects. The knowledge of metallic melts and slag viscosity is essential in understanding the kinetics of reactions relevant to process metallurgy as well as to processes such as casting and welding. For examples, the rise of gas bubbles through metallic melts depends on its viscosity; the rate of impurities transferring from a metallic melt to a slag is affected by the viscosity of both slag and metallic melt. However, the amount of viscosity data is far from satisfactory for the needs of today’s technology, although a number of experimental measurements have been carried out. To meet the requirement of viscosity data, modeling the viscosity of complex melts has received the attention of many scientists over the past decades.[1–9] Eyring,[1] Moelwyn-Hughes,[2] Hirai,[3] Kucharski,[4,5] Sichen et al.,[6] Zhang and Jahanshahi,[7] Weymann,[8] and Seetharaman and Sichen[9] have reported the model to predict the viscosities of metallic and ionic melts. But, progress has been limited because of the lack of the fundamental viscosity data. Among the viscosity models, Moelwyn-Hughes[2] and Seetharaman and Sichen[9] suggested that the estimation of the viscosity of complex melts can be done by using thermodynamic data (Gibbs free energy or enthalpy of mixing). In view of the fact that the thermodynamic data of multicomponent melts are relatively more available than are the data of viscosity, a thermodynamic approach is desirable. In addition, geometric models[10,11] have been successfully applied in estimating thermodynamic properties of multicomponent melts from binary melts. This article issues a new model that combines Seetharamn’s viscosity model and Chou’s geometric-thermodynamic model to estimate the viscosity of ternary-metallic melts. Some calculations, along with the analyses, experiments and discussions, have been carried out. II. MODEL OF VISCOSITY ESTIMATION The viscosity of metallic and ionic melts can be expressed by the equation[1]
⫽
hN ⌬G* exp M RT
冢 冣
where h is Planck’s constant (6.626 ⫻ 10⫺34 J ⭈ s), N is Avagadro’s number (6.022 ⫻ 1023 mol⫺1), is the density of the melts (kg/m3), M is the molecular weight (kg ⭈ mol⫺1), ⌬G* is the Gibbs free energy of activation per mol (J ⭈ mol⫺1), R is the gas constant (8.314 J ⭈ mol⫺1 ⭈ K⫺1), and T is the temperature (K). Thus, the unit of the viscosity is Pa ⭈ s. In the case of a unary system, the Gibbs free energy of activation can be expressed as ⌬G* ⫽ a ⫹ bT ⫹ cT ln T ⫹ ⭈⭈⭈
METALLURGICAL AND MATERIALS TRANSACTIONS A
[2]
In the case of high-order melts, M, , and ⌬G* of the melts can be calculated by the following equations: M ⫽ 兺xi Mi
⫽ 兺xi Mi
冒兺
x i M i / i
[3] [4]
⌬G* ⫽ 兺x i ⌬G i* ⫹ ⌬G*mix
[5]
⌬G* ⫽ 兺xi⌬Gi* ⫹ ⌬Gmix ⫹ 3RTx1x2
[6]
where xi , Mi , i , and ⌬G* i represent the mol fraction, molecular weight (or atomic mass), the density, and Gibbs activation energy of component i. The term ⌬G* mix is the vis
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