# Multi-velocity and multi-temperature model of the mixture of polyatomic gases issuing from kinetic theory

## TL;DR

This paper develops a multi-velocity, multi-temperature model for polyatomic gas mixtures based on kinetic theory, capturing non-conservative interactions and deriving phenomenological coefficients for extended thermodynamics.

## Contribution

It introduces a novel Euler-like balance law framework for gas mixtures that incorporates species-specific velocities and temperatures, derived from kinetic theory.

## Key findings

- Source terms for momentum and energy are explicitly computed from kinetic theory.
- Model links microscopic interactions to macroscopic thermodynamic coefficients.
- Provides a basis for extended thermodynamics in polyatomic gas mixtures.

## Abstract

In this paper, we consider Euler-like balance laws for mixture components that involve macroscopic velocities and temperatures for each different species. These laws are not conservative due to mutual interaction between species. In particular, source terms that describe the rate of change of momentum and energy of the constituents appear. These source terms are computed with the help of kinetic theory for mixtures of polyatomic gases. Moreover, if we restrict the attention to processes which occur in the neighborhood of the average velocity and temperature of the mixture, the phenomenological coefficients of extended thermodynamics can be determined from the computed source terms.