Binary scattering model for Lennard-Jones potential: Transport coefficients and collision integrals for non-equilibrium gas flow simulations

A Lennard-Jones (LJ) binary interaction model for dilute gases is obtained by representing the exact scattering angle as a polynomial expansion in non-dimensional collision variables. Rigorous theoretical verification of the model is performed by comparison with exact values of diffusion and viscosity cross sections and related collision integrals. The collision quantities given by the polynomial approximation model agree within 3.5% with those of the exact LJ scattering. The proposed model is compared in detail with the generalized soft sphere (GSS) model which is the closest in terms of fidelity among existing direct simulation Monte Carlo collision models. The GSS model's performance for the collision integral used in the first approximate of viscosity coefficient is comparable to the proposed model for most reduced temperatures. However, other collision integrals deviate significantly, even at moderate reduced temperatures. The high fidelity of the proposed model at low reduced temperatures enables non-equilibrium simulations of gases with deep LJ potential well such as metallic vapors. The model is based on the scattering angle as opposed to viscosity or diffusion coefficients and provides a direct link to molecular dynamics simulations.