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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.