On the formal derivation of the reactive Maxwell-Stefan equations from the kinetic theory

¹ Centro de Matemática, Universidade do Minho - Braga, Portugal
² Center for Mathematical Analysis, Geometry and Dynamical Systems, IST, University of Lisbon - Lisbon, Portugal

Received: 21 November 2019
Accepted: 21 February 2020

Abstract

We study multicomponent diffusion in a gaseous mixture undergoing a reversible chemical reaction. Under isothermal and non-isothermal conditions, we extend the Maxwell-Stefan (MS) theory to the reactive system, by deriving the reactive MS equations containing additional diffusion terms resulting from the chemical reaction. We start from the simple reacting spheres (SRS) kinetic model and consider a diffusive regime, for which both mechanical collisions and chemical reactions have comparable relaxation times, which are much smaller than the characteristic times of the flow. In the corresponding hydrodynamic limit, we formally derive the reactive MS equations from the momentum equation of the species and deduce explicit expressions for the diffusion coefficients.