Using Molecular Simulation to Compute Transport Coefficients of Molecular Gases

TL;DR

This paper introduces a simple numerical scheme to compute transport coefficients of molecular gases, providing results that align well with existing theories and extending to complex molecules like nitrogen dimers and n-octane.

Contribution

A new approximate numerical method for calculating transport properties of molecular gases, applicable to complex molecules and providing lower bounds consistent with Chapman-Enskog results.

Findings

Results agree with Chapman-Enskog for simple molecules

Method provides estimates for nitrogen dimer where no analytical results exist

Good predictions for diffusivity and viscosity of n-octane

Abstract

The existing kinetic theory of gases is based on an analytical approach that becomes intractable for all but the simplest molecules. Here we propose a simple numerical scheme to compute the transport properties of molecular gases in the limit of infinite dilution. The approach that we propose is approximate, but our results for the diffusivity $D$, the viscosity $\eta$ and the thermal conductivity $\lambda$ of hard spheres, Lennard-Jones particles and rough hard spheres, agree well with the standard (lowest order) Chapman-Enskog results. We also present results for a Lennard-Jones-dimer model for nitrogen, for which no analytical results are available. In the case of poly-atomic molecules (we consider n-octane), our method remains simple and gives good predictions for the diffusivity and the viscosity. Computing the thermal conductivity of poly-atomic molecules requires an approximate treatment of their quantized internal modes. We show that a well-known approximation that relates $\lambda$ to $D$ and $\eta$, yields good results. We note that our approach should yield a lower limit to the exact value of $D$, $\eta$ and $\lambda$. Interestingly, the most sophisticated (higher-order) Chapman-Enskog results for rough hard spheres seem to violate this bound.