Dissipation process of binary mixture gas in thermally relativistic flow

TL;DR

This paper investigates the dissipation process of binary mixture gases in relativistic flows, focusing on diffusion flux characteristics, comparing relativistic Boltzmann equation results with NSF approximations, and emphasizing the importance of particle four flow for accuracy.

Contribution

It provides a detailed analysis of diffusion flux in relativistic binary gases, highlighting limitations of NSF approximation and proposing the use of particle four flow for precise calculation.

Findings

Diffusion flux near walls differs significantly from NSF approximation.

Diffusion flux inside shock wave aligns with NSF approximation.

Accurate diffusion flux calculation requires particle four flow.

Abstract

In this paper, we discuss dissipation process of the binary mixture gas in the thermally relativistic flow \textcolor{red}{by focusing on the characteristics of the diffusion flux}. As an analytical object, we consider the relativistic rarefied-shock layer problem around the triangle prism. Numerical results of the diffusion flux are compared with the Navier-Stokes-Fourier (NSF) order approximation of the diffusion flux, which is calculated using the diffusion and thermal-diffusion coefficients by Kox \textit{et al}. [Physica A, 84, 1, pp.165-174 (1976)]. In the case of the uniform flow with the small Lorentz contraction, the diffusion flux, which is obtained by calculating the relativistic Boltzmann equation, is roughly approximated by the NSF order approximation inside the shock wave, whereas the diffusion flux in the vicinity of the wall is markedly different from the NSF order approximation. The magnitude of the diffusion flux, which is obtained by calculating the relativistic Boltzmann equation, is similar to that of the NSF order approximation inside the shock wave, unlike the pressure deviator, dynamic pressure and heat flux, even when the Lorentz contraction in the uniform flow becomes large, because the diffusion flux does not depend on the generic Knudsen number from its definition in Eckart's frame. \textcolor{red}{Finally, the author concludes that the accurate diffusion flux must be calculated from the particle four flow, which is formulated using the four velocity distinguished by each species of particles.