Shear Viscosity of an $N$-Component Gas Mixture using the Chapman--Enskog Method under Anisotropic Scatterings
Abstract
The analytical Chapman-Enskog formula for calculating the shear viscosity $\eta$ of a relativistic ideal gas, such as a massless quark-gluon plasma, has consistently demonstrated good agreement with the numerical results obtained using the Green-Kubo relation under both isotropic and anisotropic two-body scatterings. However, past analyses of massless, multicomponent quark-gluon plasma have focused on an effective single-component "gluon gas." The Chapman-Enskog formula for multicomponent mixtures with nonzero yet adjustable masses was previously developed for simpler cases of isotropic scatterings. This study aims to obtain the Chapman-Enskog shear viscosity formula for a massless, multicomponent mixture under general anisotropic scatterings. Since the shear viscosity depends on a linearized collision kernel, an approximation formula for the linearized collision kernel is derived under elastic and anisotropic $l+k\rightarrow l+k$ scatterings. This derived approximation agrees very well with the isotropic two-body kernels provided in previous works for both like and different species. Furthermore, for multicomponent mixtures beyond two species types, an alternative expansion method of the $N$-component Chapman-Enskog viscosity is presented. This is applied to a two-component "binary" mixture and compared with the conventional formula for binary viscosity. The agreement between the two, for interacting and noninteracting binary mixtures, varies from moderate to well.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2024
- DOI:
- 10.48550/arXiv.2406.07764
- arXiv:
- arXiv:2406.07764
- Bibcode:
- 2024arXiv240607764M
- Keywords:
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- Nuclear Theory;
- High Energy Physics - Theory;
- 81V35 (Primary);
- 82B40 (Secondary)
- E-Print:
- 29 pages (including appendices), 4 figures, 4 tables