Dissipative hydrodynamics for multi-component systems

TL;DR

This paper derives second-order dissipative hydrodynamic equations for multi-component systems, validating them against kinetic results and exploring how inter-species interactions influence shear viscosity over time.

Contribution

It introduces a new derivation of hydrodynamic equations for multi-component systems using the entropy principle and examines the impact of inter-species interactions on shear viscosity.

Findings

Hydrodynamic equations agree with kinetic transport results.

Shear viscosity depends on cross sections and partial densities.

Inter-species interactions cause time-dependent shear viscosity.

Abstract

Second-order dissipative hydrodynamic equations for each component of a multi-component system are derived using the entropy principle. Comparison of the solutions with kinetic transport results demonstrates validity of the obtained equations. We demonstrate how the shear viscosity of the total system can be calculated in terms of the involved cross sections and partial densities. Presence of the inter-species interactions leads to a characteristic time-dependence of the shear viscosity of the mixture, which also means that the shear viscosity of a mixture cannot be calculated using the Green-Kubo formalism the way it has been done recently. This finding is of interest for understanding of the shear viscosity of a quark-gluon-plasme extracted from comparisons of hydrodynamic simulations with experimental results from RHIC and LHC.