A kinetic model for chemical reactions without barriers : transport coefficients and eigenmodes

Detalhes bibliográficos
Autor(a) principal: Alves, Giselle M.
Data de Publicação: 2011
Outros Autores: Marques Júnior, Wilson, Soares, A. J., Kremer, Gilberto M.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: https://hdl.handle.net/1822/13477
Resumo: The kinetic model of the Boltzmann equation proposed in the work of Kremer and Soares 2009 for a binary mixture undergoing chemical reactions of symmetric type which occur without activation energy is revisited here, with the aim of investigating in detail the transport properties of the reactive mixture and the influence of the reaction process on the transport coefficients. Accordingly, the non-equilibrium solution of the Boltzmann equation is determined through an expansion in Sonine polynomials up to the first order, using the Chapman-Enskog method, in a chemical regime for which the reaction process is close to its final equilibrium state. The non-equilibrium deviations are explicitly calculated for what concerns the thermal-diffusion ratio and coefficients of shear viscosity, diffusion and thermal conductivity. The theoretical and formal analysis developed in the present paper is complemented with some numerical simulations performed for different concentrations of reactants and products of the reaction as well as for both exothermic and endothermic chemical processes. The results reveal that chemical reactions without energy barrier can induce an appreciable influence on the transport properties of the mixture. Oppositely to the case of reactions with activation energy, the coefficients of shear viscosity and thermal conductivity become larger than those of an inert mixture when the reactions are exothermic. An application of the non-barrier model and its detailed transport picture is included in this paper, in order to investigate the dynamics of the local perturbations on the constituent number densities, and velocity and temperature of the whole mixture, induced by spontaneous internal fluctuations. It is shown that for the longitudinal disturbances there exist two hydrodynamic sound modes, one purely diffusive hydrodynamic mode and one kinetic mode.
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spelling A kinetic model for chemical reactions without barriers : transport coefficients and eigenmodesKinetic theory of gases and liquidsBoltzmann equationTransport processesChemical kineticsHeat transfer (theory)Chemically reactive flowstransport processes/heat transfer (theory)Science & TechnologyThe kinetic model of the Boltzmann equation proposed in the work of Kremer and Soares 2009 for a binary mixture undergoing chemical reactions of symmetric type which occur without activation energy is revisited here, with the aim of investigating in detail the transport properties of the reactive mixture and the influence of the reaction process on the transport coefficients. Accordingly, the non-equilibrium solution of the Boltzmann equation is determined through an expansion in Sonine polynomials up to the first order, using the Chapman-Enskog method, in a chemical regime for which the reaction process is close to its final equilibrium state. The non-equilibrium deviations are explicitly calculated for what concerns the thermal-diffusion ratio and coefficients of shear viscosity, diffusion and thermal conductivity. The theoretical and formal analysis developed in the present paper is complemented with some numerical simulations performed for different concentrations of reactants and products of the reaction as well as for both exothermic and endothermic chemical processes. The results reveal that chemical reactions without energy barrier can induce an appreciable influence on the transport properties of the mixture. Oppositely to the case of reactions with activation energy, the coefficients of shear viscosity and thermal conductivity become larger than those of an inert mixture when the reactions are exothermic. An application of the non-barrier model and its detailed transport picture is included in this paper, in order to investigate the dynamics of the local perturbations on the constituent number densities, and velocity and temperature of the whole mixture, induced by spontaneous internal fluctuations. It is shown that for the longitudinal disturbances there exist two hydrodynamic sound modes, one purely diffusive hydrodynamic mode and one kinetic mode.This paper is partially supported by the Brazilian Research Council (CNPq), by Minho University Mathematics Centre (CMAT-FCT) and by Project FCT-PTDC/MAT/68615/2006.IOP PublishingUniversidade do MinhoAlves, Giselle M.Marques Júnior, WilsonSoares, A. J.Kremer, Gilberto M.2011-032011-03-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/1822/13477eng1742-546810.1088/1742-5468/2011/03/P03014The original publication is available at http://iopscience.iop.org/1742-5468/2011/03/P03014info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-21T12:43:49Zoai:repositorium.sdum.uminho.pt:1822/13477Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:41:22.636326Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv A kinetic model for chemical reactions without barriers : transport coefficients and eigenmodes
title A kinetic model for chemical reactions without barriers : transport coefficients and eigenmodes
spellingShingle A kinetic model for chemical reactions without barriers : transport coefficients and eigenmodes
Alves, Giselle M.
Kinetic theory of gases and liquids
Boltzmann equation
Transport processes
Chemical kinetics
Heat transfer (theory)
Chemically reactive flows
transport processes/heat transfer (theory)
Science & Technology
title_short A kinetic model for chemical reactions without barriers : transport coefficients and eigenmodes
title_full A kinetic model for chemical reactions without barriers : transport coefficients and eigenmodes
title_fullStr A kinetic model for chemical reactions without barriers : transport coefficients and eigenmodes
title_full_unstemmed A kinetic model for chemical reactions without barriers : transport coefficients and eigenmodes
title_sort A kinetic model for chemical reactions without barriers : transport coefficients and eigenmodes
author Alves, Giselle M.
author_facet Alves, Giselle M.
Marques Júnior, Wilson
Soares, A. J.
Kremer, Gilberto M.
author_role author
author2 Marques Júnior, Wilson
Soares, A. J.
Kremer, Gilberto M.
author2_role author
author
author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Alves, Giselle M.
Marques Júnior, Wilson
Soares, A. J.
Kremer, Gilberto M.
dc.subject.por.fl_str_mv Kinetic theory of gases and liquids
Boltzmann equation
Transport processes
Chemical kinetics
Heat transfer (theory)
Chemically reactive flows
transport processes/heat transfer (theory)
Science & Technology
topic Kinetic theory of gases and liquids
Boltzmann equation
Transport processes
Chemical kinetics
Heat transfer (theory)
Chemically reactive flows
transport processes/heat transfer (theory)
Science & Technology
description The kinetic model of the Boltzmann equation proposed in the work of Kremer and Soares 2009 for a binary mixture undergoing chemical reactions of symmetric type which occur without activation energy is revisited here, with the aim of investigating in detail the transport properties of the reactive mixture and the influence of the reaction process on the transport coefficients. Accordingly, the non-equilibrium solution of the Boltzmann equation is determined through an expansion in Sonine polynomials up to the first order, using the Chapman-Enskog method, in a chemical regime for which the reaction process is close to its final equilibrium state. The non-equilibrium deviations are explicitly calculated for what concerns the thermal-diffusion ratio and coefficients of shear viscosity, diffusion and thermal conductivity. The theoretical and formal analysis developed in the present paper is complemented with some numerical simulations performed for different concentrations of reactants and products of the reaction as well as for both exothermic and endothermic chemical processes. The results reveal that chemical reactions without energy barrier can induce an appreciable influence on the transport properties of the mixture. Oppositely to the case of reactions with activation energy, the coefficients of shear viscosity and thermal conductivity become larger than those of an inert mixture when the reactions are exothermic. An application of the non-barrier model and its detailed transport picture is included in this paper, in order to investigate the dynamics of the local perturbations on the constituent number densities, and velocity and temperature of the whole mixture, induced by spontaneous internal fluctuations. It is shown that for the longitudinal disturbances there exist two hydrodynamic sound modes, one purely diffusive hydrodynamic mode and one kinetic mode.
publishDate 2011
dc.date.none.fl_str_mv 2011-03
2011-03-01T00:00:00Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://hdl.handle.net/1822/13477
url https://hdl.handle.net/1822/13477
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1742-5468
10.1088/1742-5468/2011/03/P03014
The original publication is available at http://iopscience.iop.org/1742-5468/2011/03/P03014
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv IOP Publishing
publisher.none.fl_str_mv IOP Publishing
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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