Cluster–Associate Model for the Viscosity of Sodium Fluoride in Comparison with the Frenkel Model

• Published in: Russian metallurgy Metally Vol. 2021; no. 2; pp. 176 - 180
• Main Authors: Makasheva, A. M., Malyshev, V. P.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01-02-2021; Springer Nature B.V
• Subjects: Chemistry and Materials Science; Clusters; Computational fluid dynamics; Fluid flow; Fluorides; Materials Science; Mathematical analysis; Mathematical models; Metallic Materials; Sodium fluoride; Structural hierarchy; Temperature dependence; Viscosity; Boltzmann distribution; cluster; chaotic particles; dynamic viscosity; associate; sodium fluoride
• ISSN: 0036-0295; 1555-6255; 1531-8648
• DOI: 10.1134/S0036029521020154

The aim of this work is to find the temperature dependence of the dynamic viscosity for sodium fluoride. The relevance of the research is associated with insufficient knowledge of the nature of viscous state and fluid flow, the variety of the temperature dependences of viscosity, the fragmentary and narrow experimental determination of this characteristic, and the inability to display it in the full temperature range of the liquid state (especially for melts). The scientific novelty of the work consists in displaying the temperature dependence of viscosity by a cluster–associate probabilistic mathematical model, the hierarchical structure of which is adequate to the physical nature of the aggregation of particles without taking into account their specific structure but with allowance for the change in the degree of their association with increasing temperature. Calculations are performed using a new cluster–associate equation derived in terms of the concept of chaotic particles. The calculations are carried out in the temperature range from the melting to the boiling temperature. The degree of cluster association is shown to decrease with increasing temperature; on average, an associate consists of 3–4 clusters. The cluster–associate model is compared with the Frenkel equation in logarithmic coordinates. The approximation is carried out by two linear dependences intersecting at 1500 K. A high coefficient of correlation between the Frenkel and cluster–associate models indicates a functional character of the relation and mutual correspondence and complementarity of these models.