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This study examines the collision dynamics of atom–atom, atom–molecule, and molecule–molecule interactions for O–O, N–N, O2–O, N2–N, O2–N, N2–O, O2–O2, N2–N2, and N2–O2 systems under thermal nonequilibrium conditions. Investigations are conducted from a molecular perspective using accurate O4, N4, and N2O2 ab initio potential energy surfaces and by performing Molecular Dynamics (MD) simulations. The scattering angle and collision cross sections for these systems are determined, forming the basis for better collision simulations. For molecular interactions, the effect of the vibrational energy on the collision cross section is shown to be significant, which in turn has a profound effect on nonequilibrium flows. In contrast, the effect of the rotational energy of the molecule is shown to have a negligible effect on the cross section. These MD-based cross sections provide a theoretically sound alternative to the existing collision models, which only consider the relative translational energy. The collision cross sections reported herein are used to calculate various transport properties, such as the viscosity coefficient, heat conductivity, and diffusion coefficients. The effect of internal energy on the collision cross sections reflects the dependence of these transport properties on the nonequilibrium degree. The Chapman–Enskog formulation is modified to calculate the transport properties as a function of the trans-rotational and vibrational temperatures, resulting in a two-temperature nonequilibrium model. The reported work is important for studying highly nonequilibrium flows, particularly hypersonic re-entry flows, using either particle methods or techniques based on the conservation laws.

Describing diatomic and polyatomic gases at high temperatures requires a deep understanding of the excitation of molecules to a higher vibrational level. We developed new second-order constitutive models for diatomic and polyatomic gases with vibrational degrees of freedom, starting from the modified Boltzmann–Curtiss kinetic equation. The closing-last balanced closure and cumulant expansion of the calortropy production associated with the Boltzmann collision term are key to the derivation of the second-order models, compatible with the second law of thermodynamics. The topology of the constitutive models showed the presence of highly nonlinear and coupled protruding or sunken regions in the compression branch. It was also shown that the vibrational mode reduces the level of nonlinearity in the topology. In addition, analysis of a strong shock structure highlighted the interplay between the second-order effects in the constitutive relations and the vibrational–translational relaxation. Finally, the analysis showed that the results of the second-order models were in better agreement with the direct simulation Monte Carlo data, when compared with the results of the first-order models, especially in the profiles and slopes of density, velocity, and vibrational temperatures.

Cross sections for the homo-nuclear atom-diatom collision induced dissociations (CIDs): N + N and O + O are calculated using Quasi-Classical Trajectory (QCT) method on ab initio Potential Energy Surfaces (PESs). A number of studies for these reactions carried out in the past focused on the CID cross section values generated using London-Eyring-Polanyi-Sato PES and seldom listed the CID cross section data. A highly accurate CASSCF-CASPT2 N and a new O global PES are used for the present QCT analysis and the CID cross section data up to 30 eV relative energy are also published. In addition, an interpolating scheme based on spectroscopic data is introduced that fits the CID cross section for the entire ro-vibrational spectrum using QCT data generated at chosen ro-vibrational levels. The rate coefficients calculated using the generated CID cross section compare satisfactorily with the existing experimental and theoretical results. The CID cross section data generated will find an application in the development of a more precise chemical reaction model for Direct Simulation Monte Carlo code simulating hypersonic re-entry flows.

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