Ab initio calculation of rarefied flows of helium-neon mixture: classical vs quantum scatterings

In order to faithfully simulate rarefied gas flows of light-weight molecules at cryogenic temperatures down to several kelvins, the Boltzmann equation with the differential cross section calculated from the realistic intermolecular potential should be applied. In the present work, the direct simulation Monte Carlo (DSMC) method with ab initio intermolecular potentials is first implemented into the open-source software dsmcFoam+ for the simulation of general rarefied gas flows. Then, Fourier and Couette flows of the helium-neon mixture are studied for the temperature ranging from 10 K to 2000 K, where the differential cross sections calculated from both classical and quantum mechanics have been used. Our simulation results show that the quantum scattering effects on the heat flux and shear stress are non-negligible when the equilibrium temperature is lower than 500 K. Also, for the Fourier flow, the mole fraction distributions calculated from the quantum scattering are significantly different from those of classical scattering.