Effect of the Variable Molecular Diameter on the Viscosity Coefficient in the State-Specific Approximation

The effect of variable diameter of vibrationally excited molecules on the shear viscosity coefficient in the state-specific approximation has been studied. Three models for molecular diameters: Kang–Kunc, Morse, and Tietz–Hua have been considered. Based on these models, diameters of N2, O2, and NO molecules for different vibrational–rotational states have been calculated. It has been shown that the Kang–Kunc model yields an exponential increase in the molecular diameter for vibrational levels above ten, so its application is only appropriate at low temperatures. Tietz–Hua and Morse models provide similar values for diameters. It has been shown that contribution of rotational excitation to the diameters of considered molecules can be neglected. For various potentials, temperatures, and equilibrium and nonequilibrium vibrational distributions, the ratio of the state-specific shear viscosity coefficient to the viscosity coefficient for a gas consisting of unexcited molecules has been calculated. In all considered cases, the effect of increasing molecule size with increasing vibrational level has virtually no effect on viscosity, with the deviation not exceeding 7%. This demonstrates the validity of the assumption that the dependence of the elastic collision cross section on the vibrational state can be ignored when calculating state-specific transport coefficients. This allows for the justified use of simplified algorithms for calculating transport coefficients in the state-specific kinetics approximation, significantly reducing computational requirements when solving nonequilibrium gas dynamics problems.