Viscosity Modeling With the Thermodynamic Dimension Theory: Application to Argon fluid

This study extends the recently introduced theory for predicting fluid viscosity by focusing on the thermodynamic dimension (DT) and its relationship to the effective intermolecular potential, Ueff (r, T). The DT describes the degree of freedom in fluid–particle interactions, ranging from three in solids to zero in perfect gases (0 ≤ DT ≤ 3). The DT of fluid varies between these limits depending on temperature and pressure. Unlike traditional models, this method views a fluid as a mix of free particles and temporary clusters (t-clusters), with viscosity resulting from gaseous and solid-like interactions. Viscosity is the sum of dilute gas viscosity and viscosity caused by intermolecular interactions. The theory uses explicit thermodynamic relations to link the Ueff (r, T) to the fluid's equation of state (EoS), giving a unified approach that connects the viscosity equation to the EoS. Argon fluid serves as a case study to demonstrate the model's correctness. The model accurately predicts viscosity throughout a temperature range of 100–1000 K and pressures up to 1000 MPa, with average absolute relative deviations less than 2%. The model's accuracy and computational efficiency enable it to be applied to other simple fluids while upholding the corresponding states principle. These results demonstrate how this theory may be used to unify quantum and classical thermodynamics viewpoints, providing a new framework for understanding and predicting fluid behavior under a variety of circumstances. Because of its accuracy and computational simplicity, the method shows promise for use in fluid mechanics and thermophysical modeling.