We consider a binary reacting mixture composed by a monatomic and a polyatomic gas, diffusing in a host medium, and undergoing elastic, inelastic and chemical interactions. We deduce a proper set of reaction- diffusion equations for the number densities of the two components from Boltzmann kinetic equations, in presence of a multiple time scale process. The dominant phenomenon is constituted by the elastic collision with the host medium, while other elastic collisions are less frequent; inelastic and chemical interactions are part of the slow process as well. We show that, in the diffusive limit, the total density of polyatomic constituent exhibits a cross-diffusion term. Then, we perform a preliminary Turing instability analysis in terms of macroscopic and microscopic parameters, and we investigate numerically the formation of stable patterns.

A reaction-cross-diffusion model derived from kinetic equations for gas mixtures

Martalo' G.;
2024-01-01

Abstract

We consider a binary reacting mixture composed by a monatomic and a polyatomic gas, diffusing in a host medium, and undergoing elastic, inelastic and chemical interactions. We deduce a proper set of reaction- diffusion equations for the number densities of the two components from Boltzmann kinetic equations, in presence of a multiple time scale process. The dominant phenomenon is constituted by the elastic collision with the host medium, while other elastic collisions are less frequent; inelastic and chemical interactions are part of the slow process as well. We show that, in the diffusive limit, the total density of polyatomic constituent exhibits a cross-diffusion term. Then, we perform a preliminary Turing instability analysis in terms of macroscopic and microscopic parameters, and we investigate numerically the formation of stable patterns.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11571/1511976
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