Shear viscosity of a binary mixture for a relativistic fluid at high temperature

TL;DR

This paper investigates the shear viscosity of relativistic binary mixtures at high temperature, comparing full two-component calculations with simplified models, and validates results through numerical simulations relevant to quark-gluon plasma.

Contribution

It introduces a detailed Chapman-Enskog analysis of binary mixtures' shear viscosity and compares it with numerical Boltzmann simulations, emphasizing the role of inter-species interactions.

Findings

Full shear viscosity often approximated by a weighted average of single components.

Inter-species scattering significantly affects the temperature dependence of shear viscosity.

Simplified models may not accurately capture the viscosity behavior in quark-gluon plasma.

Abstract

The determination of the shear viscosity is a central topic in various areas of modern physics. In particular, it is often necessary to evaluate the shear viscosity $\eta$ of fluids made up of more than one species, all interacting with different cross sections. Since it may be difficult to extract information on the interaction among different species, various combinations of the viscosities of the individual components are often used. We work in the Chapman-Enskog framework and investigate on binary mixtures, by comparing such single component combinations with a full 2-component formalism: we find that, in most cases, the full viscosity is well approximated by a weighted linear average of the single component viscosities, although this result is far from being general. Moreover, we validate our 2-component Chapman-Enskog results for $\eta$ by comparing them with an independent numerical simulation of the Boltzmann equation, which estimates the shear viscosity via a Green-Kubo formula, in the case of a quasi-particle system that reproduces lattice QCD thermodynamics. We see that the temperature dependence of $\eta/s$ of such system of quarks and gluons is not well described by combinations of the individual components, highlighting the importance of inter-species scattering.