# Analysis of correlation between viscosity Arrhenius parameters: Extension to ternary liquid mixtures

## DOI:

https://doi.org/10.13171/mjc65/0171114633rhk## Abstract

The study of viscosity-temperature dependence is important for the design and the optimization of several industrial processes and products. In this context, an interesting equation is recently proposed for pure solvents correlating the two parameters of the viscosity Arrhenius-type equation, as knowing the activation energy (Ea) and the pre-exponential factor (As), allowing the simplification of the viscosity Arrhenius equation to become an expression depending on only one parameter instead of two. The present work investigates the validity of the simplified Arrhenius-type equation for ternary fluids mixtures. The extension of the proposed equation to ternary liquid mixtures is very important since it simplifies the estimation of viscous behavior and the ensuing calculations. Using statistical methods and 114 experimental data from the literature on viscosity for 5 ternary liquid mixtures over different temperature ranges at atmospheric pressure, we found that the validation of the proposed equation depends significantly on the density of liquids and is validated only for 4 studied ternary liquid mixtures. This result opens the way to investigate the sensitivity of the equation’s parameters for more specific mixtures.## References

- N. Ouerfelli, M. Bouaziz, J.V. Herráez, Treatment of Herráez Equation Correlating Viscosity in Binary Liquid Mixtures exhibiting strictly monotonous distribution, Phys. Chem. Liq. 2013, 51, 55-74.

- J.V. Herráez, R. Belda, O. Diez, M. Herráez, An Equation for the Correlation of Viscosities of Binary Mixtures, J. Solution Chem. 2008, 37, 233-248.

- J.B. Irving, NEL Report Numbers 630 and 631, National Engineering Laboratory, East Kilbride: Glasgow, 1977.

- S.W. Benson, Thermochemical Kinetics, 2nd ed. Wiley: New York, 1976.

- J.A. Dean, Handbook of Organic Chemistry, McGraw-Hill: New York, 1987.

- S. Glasstone, K.L. Laidler, H. Eyring, The theory of rate rocess, McGraw-Hill: New York, 1941.

- H. Eyring, Viscosity, plasticity, and diffusion as examples of absolute reaction rates, J. Chem. Phys. 1936, 4, 283-291.

- H. Eyring, J.O. Hirschfeldern, The theory of the liquid state, J. Phys. Chem. 1937, 41, 249-257.

- H. Eyring and M.S. John, Significant Liquid Structure, Wiley: New York, 1969.

- P.T. Cummings, D.J. Evans, Non-equilibrium molecular dynamics approaches to transport properties and non-Newtonian fluid, Ind. Eng. Chem. Res. 1992, 31, 1237-1252.

- J.G. Kirkwood, F.P. Buff, M.S. Green, The statistical mechanical theory of transport processes. III. The coefficients of shear and bulk viscosity of liquids, J. Chem. Phys. 1949, 17, 988-994.

- J. De. Guzman, Relation between fluidity and heat of fusion, Anales Soc. Espan. Fis. Quim. 1913, 11, 353-362.

- C.R. Duhne, Viscosity-temperature correlations for liquids, Chem. Eng. 1979, 86, 83-91.

- D.S. Viswanath, G. Natarajan, Databook on Viscosity of Liquids, Hemisphere: New York, 1989.

- N.V.K. Dutt, D.H.L. Prasad, Representation of the Temperature Dependence of the Viscosity of Pure Liquids, Private Communication, Chemical Engineering Division, Indian Institute of Chemical Technology: Hyderabad, 2004.

- R.C. Reid, J.M. Prausnitz, B.E. Poling, Properties of Gases and Liquids, McGraw-Hill: New York, 4th Ed., 1987.

- H. Vogel, Das Temperatur-abhängigkeitsgesetz der Viskosität von Flüssigkeiten, Physik Z. 1921, 22, 645-646.

- G.S. Fulcher, Analysis of Recent Measurements of the Viscosity of Glasses, J. Am. Ceram. Soc. 1925, 8, 339-355.

- G. Tammann, W. Hesse, Abhängigkeit der Viscosität von der Temperature bieunterkühlten Flüssigkeiten, Z. Anorg. Allg. Chem. 1926, 156, 245-251.

- Jr. E. Goletz, D. Tassios, An Antoine type equation for liquid viscosity dependency to temperature, Chem. Proc. Des. Dev. 1977, 16, 75-79.

- T.E. Thorpe, J.W. Rodger, Bakerian Lecture: On the Relations between the Viscosity (Internal Friction) of Liquids and Their Chemical Nature, Phil. Trans. 1895, 185, 397-710.

- L.A. Girifalco, Temperature dependence of viscosity and its relation to vapor pressure for associated liquids, J. Chem. Phys. 1955, 23, 2446-2447.

- D.S. Viswanath, T.K. Ghosh, G.H.L. Prasad, N.V.K. Dutt, K.Y. Rani, Viscosity of Liquids. Theory, Estimation, Experiment, and Data, Springer: Dordrecht, The Netherlands, 2007.

- T.E. Daubert, R.P. Danner, Physical and Thermodynamic Properties of Pure Chemicals-Data Compilation Design Institute for Physical Properties Data, AIChE, Taylor and Francis: Washington DC, 1989-1994.

- R.H. Kacem, N. Ouerfelli. J.V. Herráez, M. Guettari, H. Hamda, M. Dallel, Contribution to modeling the viscosity Arrhenius type-equation for some solvents by statistical correlation analysis, Fluid Phase Equilibr. 2014, 383,11-20.

- B. B. Gurung, M. N. Roy, Study of densities, viscosity deviations, and isentropic compressibilities of ternary liquid mixtures of water and ethane-1,2-diol with some monoalcohols at various temperatures, Phys. Chem. Liq. 2007, 45, 331-343.

- A. Rodríguez, A.B. Pereiro, J. Canosa, J. Tojo, Dynamic viscosities of the ternary liquid mixtures (dimethyl carbonate + methanol + ethanol) and (dimethyl carbonate + methanol + hexane) at several temperatures, J. Chem. Thermodyn. 2006, 38, 505-519.

- R.H. Kacem, N. Ouerfelli and J.V. Herráez, Viscosity Arrhenius Parameters Correlation: Extension from Pure to Binary Liquid Mixtures, Phys. Chem. Liq. 2015, 53, 776-784.

- R.H. Kacem, N.O. Alzamil and N. Ouerfelli, Sensitivity of viscosity Arrhenius parameters to polarity of liquids, Russian J. Phys. Chem. A. 2017, 91, 1654-1659.

- R.H. Kacem, N. Al-Omair, M. Alkhaldi, A.A. Al-Arfaj and N. Ouerfelli, Sensitivity of viscosity Arrhenius-type equation to density of liquids, Asian J. Chem. 2016, 28, 2407-2410.

- A.A. Al-Arfaj, R. H. Kacem, L. Snoussi, N.Vrinceanu, M. A. Alkhaldi, N. O. Alzamel and N. Ouerfelli, Correlation Analysis of the viscosity Arrhenius-type equations parameters for some binary liquids mixtures, Mediterr. J. Chem. 2017, 6(2), 23-32.

- Wonacott T.H.& Wonacott R.J. Introductory Statistics, 5th edition, John Wiley, 1990.

- F. Wilcoxon, Individual comparisons by ranking methods, Biom. Bull. 1945, 1, 80-83.

## Downloads

## Published

## Issue

## Section

## License

Authors who publish with this journal agree to the following terms:- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (SeeÂ The Effect of Open Access).