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TitleFrom the simple reacting sphere kinetic model to the reaction-diffusion system of Maxwell-Stefan type
Author(s)Anwasia, Benjamin
Gonçalves, Patrícia
Soares, A. J.
KeywordsBoltzmann-type equations
Chemically reactive mixtures
Diffusion limit
Kinetic theory of gases
Maxwell-Stefan equations
Issue date2019
PublisherInternational Press
JournalCommunications in Mathematical Sciences
Abstract(s)In this paper we perform a formal asymptotic analysis on a kinetic model for reactive mixtures in order to derive a reaction-diffusion system of Maxwell-Stefan type. More specifically, we start from the kinetic model of simple reacting spheres for a quaternary mixture of monatomic ideal gases that undergoes a reversible chemical reaction of bimolecular type. Then, we consider a scaling describing a physical situation in which mechanical collisions play a dominant role in the evolution process, while chemical reactions are slow, and compute explicitly the production terms associated to the concentration and momentum balance equations for each species in the reactive mixture. Finally, we prove that, under the isothermal assumption, the limit equations for the scaled kinetic model is the reaction diffusion system of Maxwell-Stefan type.
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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