Simulation of non-linear flow density in transition state from the mathematical model of the diffusion of metal anions through a flat sheet supported liquid membrane

A mathematical model is developed for the carrier facilitated transport of metal ions through a flat sheet support liquid membrane (FSSLM) in transition state from Fick’s second law. From this model, and from Fick’s first law, the flow density is derived as a non-linear concentration gradient. Both...

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Autores: Benzal, Ma. Graciela, Kumar, Aditya, Sastre Requena, Ana María|||0000-0002-6586-8113, Delshams Valdés, Amadeu|||0000-0003-4134-8882
Tipo de recurso: artículo
Fecha de publicación:2003
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/924
Acceso en línea:https://hdl.handle.net/2117/924
Access Level:acceso abierto
Palabra clave:Parabolic partial differential equations
Fluid mechanics
Natural sciences
Diffusion of metal anions
Non-linear flow density
Equacions en derivades parcials
Difusió
Convecció (Física)
Fluxos (Sistemes dinàmics diferenciables)
Fisiologia
Medicina
Classificació AMS::76 Fluid mechanics::76R Diffusion and convection
Classificació AMS::35 Partial differential equations::35K Parabolic equations and systems
Classificació AMS::76 Fluid mechanics::76S05 Flows in porous media
filtration
seepage
Classificació AMS::92 Biology and other natural sciences::92C Physiological, cellular and medical topics
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repository_id_str
spelling Simulation of non-linear flow density in transition state from the mathematical model of the diffusion of metal anions through a flat sheet supported liquid membraneBenzal, Ma. GracielaKumar, AdityaSastre Requena, Ana María|||0000-0002-6586-8113Delshams Valdés, Amadeu|||0000-0003-4134-8882Parabolic partial differential equationsFluid mechanicsNatural sciencesDiffusion of metal anionsNon-linear flow densityEquacions en derivades parcialsDifusióConvecció (Física)Fluxos (Sistemes dinàmics diferenciables)FisiologiaMedicinaClassificació AMS::76 Fluid mechanics::76R Diffusion and convectionClassificació AMS::35 Partial differential equations::35K Parabolic equations and systemsClassificació AMS::76 Fluid mechanics::76S05 Flows in porous mediafiltrationseepageClassificació AMS::92 Biology and other natural sciences::92C Physiological, cellular and medical topicsA mathematical model is developed for the carrier facilitated transport of metal ions through a flat sheet support liquid membrane (FSSLM) in transition state from Fick’s second law. From this model, and from Fick’s first law, the flow density is derived as a non-linear concentration gradient. Both expressions, concentration and flow density, depend on the thickness of the membrane and on time. Since the rate constant plays an important role in the model, it is considered as the parameter that controls the system and an equation for it is obtained. This equation explains the velocity of the co-transport process. The proposed model takes into account the species co-transported together with the metal ions. An equation for the number of moles of this species is obtained as a function of the metal species. The concentration gradient of this species explains the behaviour of pH in the feed phase during the process. The model is tested against experimental data corresponding to the transport of metal anions in acidic solution and it is shown that the co-transport process is reproduced with high accuracy.Peer Reviewed20032003-01-0120072007-05-07journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/924reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/9242026-05-27T15:37:01Z
dc.title.none.fl_str_mv Simulation of non-linear flow density in transition state from the mathematical model of the diffusion of metal anions through a flat sheet supported liquid membrane
title Simulation of non-linear flow density in transition state from the mathematical model of the diffusion of metal anions through a flat sheet supported liquid membrane
spellingShingle Simulation of non-linear flow density in transition state from the mathematical model of the diffusion of metal anions through a flat sheet supported liquid membrane
Benzal, Ma. Graciela
Parabolic partial differential equations
Fluid mechanics
Natural sciences
Diffusion of metal anions
Non-linear flow density
Equacions en derivades parcials
Difusió
Convecció (Física)
Fluxos (Sistemes dinàmics diferenciables)
Fisiologia
Medicina
Classificació AMS::76 Fluid mechanics::76R Diffusion and convection
Classificació AMS::35 Partial differential equations::35K Parabolic equations and systems
Classificació AMS::76 Fluid mechanics::76S05 Flows in porous media
filtration
seepage
Classificació AMS::92 Biology and other natural sciences::92C Physiological, cellular and medical topics
title_short Simulation of non-linear flow density in transition state from the mathematical model of the diffusion of metal anions through a flat sheet supported liquid membrane
title_full Simulation of non-linear flow density in transition state from the mathematical model of the diffusion of metal anions through a flat sheet supported liquid membrane
title_fullStr Simulation of non-linear flow density in transition state from the mathematical model of the diffusion of metal anions through a flat sheet supported liquid membrane
title_full_unstemmed Simulation of non-linear flow density in transition state from the mathematical model of the diffusion of metal anions through a flat sheet supported liquid membrane
title_sort Simulation of non-linear flow density in transition state from the mathematical model of the diffusion of metal anions through a flat sheet supported liquid membrane
dc.creator.none.fl_str_mv Benzal, Ma. Graciela
Kumar, Aditya
Sastre Requena, Ana María|||0000-0002-6586-8113
Delshams Valdés, Amadeu|||0000-0003-4134-8882
author Benzal, Ma. Graciela
author_facet Benzal, Ma. Graciela
Kumar, Aditya
Sastre Requena, Ana María|||0000-0002-6586-8113
Delshams Valdés, Amadeu|||0000-0003-4134-8882
author_role author
author2 Kumar, Aditya
Sastre Requena, Ana María|||0000-0002-6586-8113
Delshams Valdés, Amadeu|||0000-0003-4134-8882
author2_role author
author
author
dc.subject.none.fl_str_mv Parabolic partial differential equations
Fluid mechanics
Natural sciences
Diffusion of metal anions
Non-linear flow density
Equacions en derivades parcials
Difusió
Convecció (Física)
Fluxos (Sistemes dinàmics diferenciables)
Fisiologia
Medicina
Classificació AMS::76 Fluid mechanics::76R Diffusion and convection
Classificació AMS::35 Partial differential equations::35K Parabolic equations and systems
Classificació AMS::76 Fluid mechanics::76S05 Flows in porous media
filtration
seepage
Classificació AMS::92 Biology and other natural sciences::92C Physiological, cellular and medical topics
topic Parabolic partial differential equations
Fluid mechanics
Natural sciences
Diffusion of metal anions
Non-linear flow density
Equacions en derivades parcials
Difusió
Convecció (Física)
Fluxos (Sistemes dinàmics diferenciables)
Fisiologia
Medicina
Classificació AMS::76 Fluid mechanics::76R Diffusion and convection
Classificació AMS::35 Partial differential equations::35K Parabolic equations and systems
Classificació AMS::76 Fluid mechanics::76S05 Flows in porous media
filtration
seepage
Classificació AMS::92 Biology and other natural sciences::92C Physiological, cellular and medical topics
description A mathematical model is developed for the carrier facilitated transport of metal ions through a flat sheet support liquid membrane (FSSLM) in transition state from Fick’s second law. From this model, and from Fick’s first law, the flow density is derived as a non-linear concentration gradient. Both expressions, concentration and flow density, depend on the thickness of the membrane and on time. Since the rate constant plays an important role in the model, it is considered as the parameter that controls the system and an equation for it is obtained. This equation explains the velocity of the co-transport process. The proposed model takes into account the species co-transported together with the metal ions. An equation for the number of moles of this species is obtained as a function of the metal species. The concentration gradient of this species explains the behaviour of pH in the feed phase during the process. The model is tested against experimental data corresponding to the transport of metal anions in acidic solution and it is shown that the co-transport process is reproduced with high accuracy.
publishDate 2003
dc.date.none.fl_str_mv 2003
2003-01-01
2007
2007-05-07
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/924
url https://hdl.handle.net/2117/924
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300724

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