Skip to main content
Log in

Determination of Viscosity and Surface Tension for CaO–SiO2–CaF2 Slags

  • Published:
Journal of Solution Chemistry Aims and scope Submit manuscript

Abstract

Determination of the physicochemical properties of solutions is important for industrial applications. Geometrical models, specifically the “mass triangle model” and a new model, have been utilized to calculate the viscosity and surface tension of CaO–SiO2–CaF2 slags based on the corresponding ternary system boundary data within the partially soluble region. The two models are validated with available experimental data in terms of viscosity and surface tension. Results reveal that the models are capable of estimating the physicochemical properties of the ternary system with limited solubility with high accuracy. The new model predicts the viscosity better, but the mass triangle model may perform better for the surface tension predictions. It is expected that these two solution models could be applied to the calculation of physicochemical properties of more ternary systems with limited solubility, especially when the systems are with high melting points or/and volatile components and/or easily oxidized or reduced components.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Chou, K.C.: A general solution model for predicting ternary thermodynamic properties. Calphad 19, 315–325 (1995)

    Article  CAS  Google Scholar 

  2. Wang, X.D., Bao, H., Li, W.C.: Estimation of viscosity of ternary-metallic melts. Metall. Mater. Trans. 33A, 3201–3204 (2002)

    Article  CAS  Google Scholar 

  3. Arslan, H.: Analytical determination of partial and integral properties of the six components systems Ni–Cr–Co–Al–Mo–Ti and their subsystems. Phys. B: Condens. Matter 438, 48–52 (2014)

    Article  CAS  Google Scholar 

  4. Scatchard, G.: Solutions of nonelectrolytes. Annu. Rev. Phys. Chem. 3, 259–274 (1952)

    Article  CAS  Google Scholar 

  5. Scatchard, G., Ticknor, L.B., Goates, J.R., McCartney, E.R.: Heats of mixing in some non-electrolyte solutions. J. Am. Chem. Soc. 74, 3721–3724 (1952)

    Article  CAS  Google Scholar 

  6. Scatchard, G., Ticknor, L.B.: Vapor–liquid equilibrium. IX. The methanol–carbon tetrachloride–benzene system. J. Am. Chem. Soc. 74, 3724–3729 (1952)

    Article  CAS  Google Scholar 

  7. Kohler, F.: Estimation of the thermodynamic data for a ternary system from the corresponding binary systems. Monatsh. Chem. 91, 738–740 (1960)

    Article  CAS  Google Scholar 

  8. Bonnier, E., Caboz, R.: Sur l'estimation de l'enthalpie libre de mélange de certains alliages métalliques liquides ternaires. C. R. Hebd. Seances Acad. Sci. 250, 527–529 (1960)

    CAS  Google Scholar 

  9. Tsao, C.C., Smith, J.M.: Heat of mixing of liquids. “Applied thermodynamics”. Chem. Eng. Prog. Symp. Ser. 49, 107–117 (1953)

    CAS  Google Scholar 

  10. Chou, K.C.: Application of phenomenological theory to chemical metallurgy. ISIJ Int. 58, 785–791 (2018)

    Article  CAS  Google Scholar 

  11. Hillert, M.: Empirical methods of predicting and representing thermodynamic properties of ternary solution phases. Calphad 4, 1–12 (1980)

    Article  CAS  Google Scholar 

  12. Chou, K.C., Chang, Y.A.: A study of ternary geometrical models. Ber. Bunsenges. Phys. Chem. 93, 735–741 (2010)

    Article  Google Scholar 

  13. Arslan, H., Dogan, A.: Determination of surface tension of liquid ternary Ni–Cu–Fe and sub-binary alloys. Philos. Mag. 99, 1206–1224 (2019)

    Article  CAS  Google Scholar 

  14. Colinet, C.: Estimation des grandeurs thermodynamiques des alliages ternaries. University of Grenoble, France (1967)

    Google Scholar 

  15. Muggianu, Y.M., Gambino, M., Bros, J.P.: Enthalpies of formation of liquid alloy bismuth–gallium–tin at 723 K. Choice of an analytical representation of integral and partial excess functions of mixing. J. Chim. Phys. 72, 83–88 (1975)

    Article  CAS  Google Scholar 

  16. Lück, R., Gerling, U., Predel, B.: Interpolation algorithms for thermodynamic functions of mixtures in multicomponent systems from binary boundary systems. Z. Metallkd. 77, 442–446 (1986)

    Google Scholar 

  17. Chou, K.C.: A new solution model for predicting ternary thermodynamic properties. Calphad 11, 293–300 (1987)

    Article  CAS  Google Scholar 

  18. Toop, G.W.: Predicting ternary activities using binary data. Trans. Metall. Soc. AIME 233, 850–855 (1965)

    CAS  Google Scholar 

  19. Chou, K.C., Li, W.C., Li, F.S., He, M.G.: Formalism of new ternary model expressed in terms of binary regular-solution type parameters. Calphad 20, 395–406 (1996)

    Article  CAS  Google Scholar 

  20. Gomidželović, L., Živković, D., Balanović, L., Manasijevic, D.: Ternary Au-Ga-Sb system: calculation of thermodynamic properties using general solution model. Rare Met. 35, 262–268 (2016)

    Article  Google Scholar 

  21. Gomidželović, L., Kostov, A., Živković, D., Krstić, V.: Analytic approach to alloys thermodynamics: ternary Cu–Ga–Ni system. Mater. Res. 19, 1026–1032 (2016)

    Article  Google Scholar 

  22. Živković, D., Grgurić, T.H., Gojić, M., Ćubela, D., Šimišić, Z.S., Kostov, A., Kožuh, S.: Calculation of thermodynamic properties of Cu––(Ag, Au) shape memory alloy systems. Trans. Indian Inst. Met. 67, 285–289 (2014)

    Article  Google Scholar 

  23. Maniani, M.E., Chaar, R.M., Moudane, M.E., Sabbar, A.: Comparative study of thermodynamic predicting methods applied to the Au–In–Zn ternary system. Mater. Environ. Sci. 5, 2045–2051 (2014)

    Google Scholar 

  24. Zhang, G.H., Chou, K.C.: General formalism for new generation geometrical model: application to the thermodynamics of liquid mixtures. J. Solution Chem. 39, 1200–1212 (2010)

    Article  CAS  Google Scholar 

  25. Chou, K.C., Wei, S.K.: A new generation solution model for predicting thermodynamic properties of a multicomponent system from binaries. Metall. Mater. Trans. 28B, 439–445 (1997)

    Article  CAS  Google Scholar 

  26. Chou, K.C., Zhong, X.M., Xu, K.D.: Calculation of physicochemical properties in a ternary system with miscibility gap. Metall. Mater. Trans. 35B, 715–720 (2004)

    Article  CAS  Google Scholar 

  27. Chou, K.C., Yu, Z.G.: Calculation of the physicochemical properties for ternary solution with limited solubility. Ceram. Int. 44, 20955–20960 (2018)

    Article  CAS  Google Scholar 

  28. Živković, D., Du, Y., Talijan, N., Kostov, A., Balanović, L.: Calculation of thermodynamic properties in liquid phase for ternary Al–Ni–Zn alloys. Trans. Nonferrous Met. Soc. China 22, 3059–3065 (2012)

    Article  Google Scholar 

  29. Wang, L.J., Chou, K.C., Seetharaman, S.: A comparison of traditional geometrical models and mass triangle model in calculating the surface tensions of ternary sulphide melts. Calphad 32, 49–55 (2008)

    Article  CAS  Google Scholar 

  30. Yu, Z.G., Leng, H.Y., Wang, L.J., Chou, K.C.: Computational study on various properties of CaO–Al2O3–SiO2 mold flux. Ceram. Int. 45, 7180–7187 (2019)

    Article  CAS  Google Scholar 

  31. Yu, Z.G., Luo, Q., Zhang, J.Y., Chou, K.C.: An insight into the viscosity prediction of ternary alloys with limited solubility. Philos. Mag. 99, 2408–2423 (2019)

    Article  CAS  Google Scholar 

  32. Yu, Z.G., Leng, H.Y., Luo, Q., Zhang, J.Y., Chou, K.C.: Geometrical modelling of the physicochemical properties of CaO–Al2O3–CaF2 slag at 1873 K. Ceram. Int. 46, 8075–8081 (2020)

    Article  CAS  Google Scholar 

  33. Shahbazian, F., Sichen, D., Mills, K.C., Seetharaman, S.: Experimental studies of viscosities of some CaO–CaF2–SiO2 slags. Ironmak. Steelmak. 26, 193–199 (1999)

    Article  CAS  Google Scholar 

  34. Park, J.H., Min, D.J., Song, H.S.: The effect of CaF2 on the viscosities and structures of CaO–SiO2(–MgO)–CaF2 slags. Metall. Mater. Trans. 33B, 723–729 (2002)

    Article  CAS  Google Scholar 

  35. Herty, C.H., Hartgen, F.A., Frear, G.L., Royer, M.B.: Temperature-viscosity measurement in the systems CaO–SiO2 and CaO–SiO2–CaF2. U. S. Bur. Mines Rep. Invest. R.I. 3232, 1–31 (1934)

    Google Scholar 

  36. Okabe, Y., Tajima, I., Ito, K.: Thermodynamics of chromium oxides in CaO–SiO2–CaF2 slag. Metall. Mater. Trans. 29B, 131–136 (1998)

    Article  CAS  Google Scholar 

  37. Shiraishi, Y., Saitô, T.: The viscositys of CaO–SiO2–alkaline earth fluoride systems (on the viscosity of molten slags, (I)). Nippon Kinzoku Gakki 29, 614–622 (1965)

    CAS  Google Scholar 

  38. Ejima, A., Shimoji, M.: Effect of alkali and alkaline-earth fluorides on surface tension of molten calcium silicates. Trans. Faraday Soc. 66, 99–106 (1970)

    Article  CAS  Google Scholar 

  39. Wang, C., Zhang, J.L., Liu, Z.J., Jiao, K.X., Wang, G.W., Yang, J.Q., Chou, K.C.: Effect of chlorine on the viscosities and structures of CaO–SiO2–CaCl2 slags. Metall. Mater. Trans. 48B, 328–334 (2017)

    Article  Google Scholar 

Download references

Acknowledgements

This work was financially supported by the China Postdoctoral Science Foundation (No. 2018M631339), the Fundamental Research Funds for the Central Universities (No. FRF-TP-18-008A1) and the Key Program of the National Natural Science Foundation of China (No. 51734002).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Kuo-Chih Chou.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, C., Chou, KC. & Yu, ZG. Determination of Viscosity and Surface Tension for CaO–SiO2–CaF2 Slags. J Solution Chem 49, 863–874 (2020). https://doi.org/10.1007/s10953-020-00998-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10953-020-00998-w

Keywords

Navigation