Bulk Viscosity of Interacting Hadrons

TL;DR

This paper derives approximate formulas for the bulk viscosity of interacting hadrons, highlighting its dependence on sound speed, enthalpy, and cross sections, with numerical results for a binary mixture.

Contribution

It introduces explicit expressions for bulk viscosity in terms of sound speed and interaction cross sections, using Chapman-Enskog, variational, and relaxation time methods.

Findings

Bulk viscosity depends on sound speed and interaction cross sections.

Dominant contributions come from particles with intermediate relativistic behavior.

Numerical results for a binary mixture illustrate the theoretical formulas.

Abstract

We show that first approximations to the bulk viscosity $\eta_v$ are expressible in terms of factors that depend on the sound speed $v_s$, the enthalpy, and the interaction (elastic and inelastic) cross section. The explicit dependence of $\eta_v$ on the factor $(\frac 13 - v_s^2)$ is demonstrated in the Chapman-Enskog approximation as well as the variational and relaxation time approaches. The interesting feature of bulk viscosity is that the dominant contributions at a given temperature arise from particles which are neither extremely nonrelativistic nor extremely relativistic. Numerical results for a model binary mixture are reported.