Cluster-associated viscosity model and methods for determining its parameters

Abstract

A detailed development of a hierarchical cluster-associate mathematical viscosity model is shown. The model is based on the equilibrium Boltzmann’s distribution and, therefore, is regarded as a chaosensitive property of a fluid inherent in it not only in motion but also at rest. In this model, the key characteristics are chaotic thermal barriers at the melting and boiling points, in connection with which the behavior of a liquid is determined by the action of three energy classes of particles – crystal-mobile, liquid-mobile, and vapor-mobile. An important single indicator in the new model depends on temperature and makes sense of the degree of association of clusters of crystal-mobile particles. The assignment of the activation energy of the viscous flow of melts determined by the Frenkel’s equation to the degree of cluster association gives a constant value commensurate with the binding energy of the van der Waals particle attractive forces. On this basis, the authors hypothesized that a viscous flow occurs due to the destruction of cluster associates while preserving the clusters themselves. To adapt the cluster-associate model to experimental data, certain data processing techniques have been developed to identify unknown model parameters. All calculations are illustrated on liquid lithium and have shown their high adequacy. Also added is a method for processing viscosity data using the entire set of viscosity data while maintaining two reference points and processing the rest to determine the degree of aggregation of associates.