Influence of variable molecular diameter on the viscosity coefficient in the state-to-state approach

Abstract

The influence of variable diameter of vibrationally excited molecules on the shear viscosity coefficient in the state-to-state approach is studied. Three models for molecular diameters are considered: Kang-Kunc, Morse, and Tietz-Hua. On the basis of these models, diameters of N2, O2, NO molecules for different vibrational-rotational states are calculated. The Kang and Kunc model yields exponential increasing of the molecular diameter for vibrational levels higher than 10, and therefore its use is reasonable only at low temperatures. Tietz-Hua and Morse models provide similar values for diameters. It is shown that contribution of rotational excitation to the diameters of considered molecules can be neglected. For various potentials, temperatures, and both equilibrium and non-equilibrium vibrational distributions the ratio of state-to-state shear viscosity coefficient to that for the molecule in the ground state is calculated. For all cases considered, rising of molecular size with the vibrational state does not affect the viscosity coefficient; the deviation does not exceed 7%. Thus we prove the validity of the assumption that dependence of elastic collision cross section on the vibrational state can be neglected while calculating state-to-state transport coefficients. This gives justification for applying simplified algorithms for simulation of state-specific transport coefficients which reduce considerably computational resources required for the solution of modern non-equilibrium fluid dynamic problems. Refs 16. Figs 5. Tables 6.