Continuum thermodynamics of chemically reacting multi-temperature fluid mixtures

Abstract

We develop a continuum-thermodynamic model for chemically reacting, multi-velocity and multi-temperature fluid mixtures. Partial balances of mass, momentum and total energy are closed using a single entropy density depending jointly on the constituent mass and nonkinetic internal-energy densities. Its partial derivatives determine the constituent temperatures and chemical potentials. For the chosen entropy flux and separately treated volume deformation, the strengthened entropy principle yields a weighted Euler relation constraining the partial thermodynamic pressures. We construct thermodynamically consistent constitutive relations for viscosity, heat conduction, Maxwell--Stefan momentum exchange, thermal relaxation and nonlinear reaction kinetics. The baseline model includes thermo-diffusion and its reciprocal coupling; a fully coupled reciprocal completion is given within the stated isotropic co-factor class. An alternative formulation couples chemical conversion and energy redistribution through specified elementary processes. We identify the material functions required for closure and admissible shifts of constituent energy zeros. An ionization network with resolved electronic levels yields Saha-type ionization relations and Boltzmann excitation ratios under the stated detailed-balance assumptions, recovering the Saha--Eggert relation at common temperature. Competing electron- and heavy-particle processes can maintain stationary populations while transferring energy between groups at different prescribed temperatures.