Abstract
This study is aimed to determine collision integrals for atoms interacting according to the m-6-8 and Hulburt–Hirschfelder potentials and analyze the differences between potentials. The precision of four significant digits was reached at all tested temperatures, and for high-temperature applications, six digits were calculated. The proposed method was tested on the Lennard-Jones potential and found to excellently agree with the recent high-quality data. In addition, the Hulburt–Hirschfelder potential was used for determining the collision integrals of the interaction of nitrogen atoms in the ground electronic state and compared with other known values. The calculations were performed using Mathematica computation system which can deal with singularities (so-called orbiting).
Highlights
The collision integrals are used evaluating the transport properties of gases [1]
The high-precision data for the Lennard-Jones potential were previously calculated by Kim and Monroe [14]
The collision integrals (l,s)∗ were calculated by applying the general numerical integration method using the Mathematica software at higher and lower temperatures for the Lennard-Jones, m-6-8, and Hulburt–Hirschfelder potentials
Summary
The collision integrals are used evaluating the transport properties of gases (including diffusion coefficient and thermal transport coefficient) [1]. The most basic and commonly used collision integrals are the (1,1) and (2,2) , which are called the diffusion collision integral and the viscosity collision integral, respectively. They are the first-order approximations in the Chapman-Enskog theory, while for higherorder approximations, other collision integrals are needed. Collision integrals have been used for analyzing diffusion [2] and the transport properties of equilibrium and non-equilibrium two-temperature plasmas [3,4,5,6,7] and of hypersonic flows [8,9,10], and for modeling combustion [11, 12]. Often the precision of collision integrals remains unknown [16]
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