Transport coefficients of helium-neon mixtures at low density computed from <i>ab initio</i> potentials

Sharipov, Felix; Benites, Victor J.

doi:10.1063/1.5001711

Cited by 32 publications

(37 citation statements)

References 35 publications

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“…It has been verified that these transport coefficients obtained by the DSMC method are in agreement within 0.1% difference with those reported in Ref. [19] over the temperature range considered in the present paper. The matrices of deflection angle with classical scattering have been calculated by the method described in Ref.…”

Section: Deflection Angle and Total Cross-sectionsupporting

confidence: 91%

“…The DCS is calculated according to both quantum [19,20] and classical mechanics [17,48]. Due to the complexity of calculating the DCS from the ab initio potentials, the deflection angles for a series of discrete relative velocities g i have been pre-calculated as two-dimensional matrices for each type of collision pairs (He-He, He-Ne, and Ne-Ne) with both classical and quantum scattering.…”

Section: Deflection Angle and Total Cross-sectionmentioning

confidence: 99%

“…They have been successfully applied in the DSMC method by a simple efficient technique [16][17][18]. In particular, DSMC based on ab initio potentials with quantum-scattering [19] has been also developed to handle the quantum effects in the low-weight gas molecular collisions e.g., 3 He, 4 He, hydrogen, and neon [20][21][22]. It is found the quantum effects are nonnegligible for the transport of single-component light-weight gases when the temperature is lower than 300 K.…”

Section: Introductionmentioning

confidence: 99%

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

Zhu

Zhang

et al. 2019

International Journal of Heat and Mass Transfer

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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 dsmc-Foam+ 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.

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Section: Deflection Angle and Total Cross-sectionsupporting

confidence: 91%

Section: Deflection Angle and Total Cross-sectionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Zhu

Zhang

et al. 2019

International Journal of Heat and Mass Transfer

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“…Finally, we pointed that the established accurate FSM to solving the quantum Boltzmann collision operator are ready to be used to calculate the transport coefficients of noble gases based on the ab initio potentials [41,42]. Also, the FSM can be used to assess the accuracy of quantum kinetic models [43,44,45].…”

Section: Discussionmentioning

confidence: 99%

A fast spectral method for the Uehling-Uhlenbeck equation for quantum gas mixtures: Homogeneous relaxation and transport coefficients

2019

Journal of Computational Physics

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A fast spectral method (FSM) is developed to solve the Uehling-Uhlenbeck equation for quantum gas mixtures with generalized differential cross-sections. The computational cost of the proposed FSM is O(M dv−1 N dv +1 log N), where d v is the dimension of the problem, M dv −1 is the number of discrete solid angles, and N is the number of frequency nodes in each direction. Spatially-homogeneous relaxation problems are used to demonstrate that the FSM conserves mass and momentum/energy to the machine and spectral accuracy, respectively. Based on the variational principle, transport coefficients such as the shear viscosity, thermal conductivity, and diffusion are calculated by the FSM, which compare well with analytical solutions. Then, we apply the FSM to find the accurate transport coefficients through an iterative scheme for the linearized quantum Boltzmann equation. The shear viscosity and thermal conductivity of the three-dimensional quantum Fermi and Bose gases interacting through hard-sphere potential are calculated. For Fermi gas, the relative difference between the accurate and variational transport coefficients increases with the fugacity; for Bose gas, the relative difference in the thermal conductivity has similar behavior as the gas moves from the classical to the degenerate limits, but that in the shear viscosity decreases. Finally, the shear viscosity and diffusion coefficient have also been calculated for a two-dimensional equal-mole mixture of Fermi gases. When the molecular mass of the two components are the same, our numerical results agree well with the variational solution. However, when the molecular mass ratio is not one, large discrepancies between the accurate and variational results are observed; our results are reliable because (i) the method relies on no assumption and (ii) the ratio between shear viscosity and entropy density satisfies the minimum bound predicted by the string theory.

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“…αβ Π (i) α + υ The dependence of the differential cross section σ on the energy E and deflection angle χ is determined by the potential of interatomic potential. In case of ab initio and Lennard-Jones potentials, the quantity σ(E, χ) is calculated numerically using the quantum theory to interatomic collision [24,51]. Then, the Ω…”

Section: Appendix a Collision Termmentioning

confidence: 99%

Sublimation and deposition in gaseous mixtures

Polikarpov

Graur

Sharipov

2020

International Journal of Heat and Mass Transfer

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The sublimation and deposition behaviors of the Helium-Argon mixture is analyzed numerically in the temperature range where Helium is only in gaseous state while Argon can sublimate and deposit on its own solid phase. The Mc-Cormack model is implemented to model the Boltzmann collision term. Three kinds of potential are used for simulation of the intermolecular collisions: Hard Sphere, Lennard-Jones potential, and ab initio. The matrices of the kinetic coefficients have been obtained for different values of the rarefaction parameters and molar fraction of non-sublimating gas. The influence of the intermolecular potential on the kinetic coefficients as well as on the gas macroscopic profiles has been analyzed.

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Transport coefficients of helium-neon mixtures at low density computed from ab initio potentials

Cited by 32 publications

References 35 publications

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

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

A fast spectral method for the Uehling-Uhlenbeck equation for quantum gas mixtures: Homogeneous relaxation and transport coefficients

Sublimation and deposition in gaseous mixtures

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