Viscosity of Heterogeneous Silicate Melts: A Non-Newtonian Model
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I.
INTRODUCTION
VISCOSITY of heterogeneous silicate melts (containing solid crystals) has long been investigated to support the understanding of natural processes, e.g. volcano eruption[1,2] and control the industrial production, e.g. iron and steelmaking.[3] Enormous efforts have been made to develop a mathematic model allowing viscosity estimation without the costly and time-consuming experimental measurement. The most widely used viscosity equation for suspension system is the Einstein-Roscoe (ER)[4] equation. Kondratiev and Jak[5] validated the applicability of the ER equation with a large experimental data set in the Al2O3-CaO-‘‘FeO’’SiO2 slag with solid fraction up to 30 vol pct. They underlined the effect of solid fraction and liquid viscosity, however, the effect of particle shape and shear rate were neglected. Wright et al.[6,7] observed the shear rate-dependent behavior in the calcium ferrite slags and calcium alumino-silicate slags containing spinel particles, but no model was proposed to calculate the non-Newtonian behavior. Later work by Wu et al.,[8] Xu et al.[9] and Zhen et al.[10] all employed the ER equation in calculating solid-bearing slag viscosity by fitting the parameters in this equation to the measured data. Consequently, the values of the parameters varied at lot. One of the main reasons is that they neglected the influence of particle shape (Xu et al.,[9] Wu et al.[8]) or approximated the non-spherical particles as spheres
ZHUANGZHUANG LIU, BART BLANPAIN, and MUXING GUO are with the Department of Materials Engineering, KU Leuven, Kasteelpark Arenberg 44 box 2450, 3001 Leuven, Belgium. Contact e-mails: [email protected] and [email protected] Manuscript submitted May 11, 2017.
METALLURGICAL AND MATERIALS TRANSACTIONS B
(Zhen et al.[10]). In reality, however, the heterogeneous silicate melt systems contain solid particles of different sizes and shapes. And it has been experimentally observed that solid particles’ shape can influence the viscosity of melts significantly.[6,7] Furthermore, although non-Newtonian behavior has been observed in solid-containing slags and it is found the Newtonian assumption is only valid at dilute limit, i.e., solid fraction
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