Numerical simulation of mass transfer in circulating drops

Autores
Ubal, Sebastian; Harrison, C. H.; Grassia, P.; Korchinsky, W. J.
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Numerical simulations of mass transfer are performed for a circulating liquid drop with applications in liquid–liquid extraction. Simulation parameters are chosen for a multi-component ternary system acetone–methanol–benzene. The drop circulation pattern is estimated via a truncated Galerkin representation of the drop streamfunction. Fickian diffusivities for multi-component mass transfer are obtained via Maxwell–Stefan theory with thermodynamic corrections. The advection–diffusion equations governing mass transfer are solved via two distinct numerical methods: a finite difference scheme (using the alternating direction implicit method) and a finite element scheme. Good agreement was obtained between both schemes. Simulation results are presented for a Reynolds number (Re=30) and for a selection of Peclet numbers (Pe=100, 1000 and 10 000, thereby giving insight into the effects of increasing Peclet number). The numerical simulations of the full advection–diffusion equations are compared against predictions of a rigid drop model (i.e. without circulation) and also against predictions of a semi-analytical boundary layer model developed by Uribe-Ramirez and Korchinsky. Results for bulk mass fractions reveal that the rigid drop model predictions evolve too slowly, while the boundary layer model predictions evolve much more quickly than the numerical simulations. Advection–diffusion simulation results for the evolution of mass fractions at selected individual locations in the drop show that points on streamlines nearest to the drop surface and/or drop axis evolve fastest, while those closest to the drop internal stagnation point evolve slowest. Corroborated by contour plots of component concentrations throughout the drop at selected times, this supports a picture whereby mass fractions become roughly uniform along individual streamlines, but mass is transferred diffusively from streamline to streamline.
Fil: Ubal, Sebastian. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química (i); Argentina
Fil: Harrison, C. H.. University Of Manchester; Reino Unido
Fil: Grassia, P.. University Of Manchester; Reino Unido
Fil: Korchinsky, W. J.. University Of Manchester; Reino Unido
Materia
Mass Transfer
Circulating Drop Model
Convective Transport
High Peclet Number
Cross-Stream Diffusion
Boundary Layers
Mathematical Modelling
Numerical Analysis
Simulation
Liquid-Liquid Extraction
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/13698

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network_name_str CONICET Digital (CONICET)
spelling Numerical simulation of mass transfer in circulating dropsUbal, SebastianHarrison, C. H.Grassia, P.Korchinsky, W. J.Mass TransferCirculating Drop ModelConvective TransportHigh Peclet NumberCross-Stream DiffusionBoundary LayersMathematical ModellingNumerical AnalysisSimulationLiquid-Liquid Extractionhttps://purl.org/becyt/ford/2.4https://purl.org/becyt/ford/2Numerical simulations of mass transfer are performed for a circulating liquid drop with applications in liquid–liquid extraction. Simulation parameters are chosen for a multi-component ternary system acetone–methanol–benzene. The drop circulation pattern is estimated via a truncated Galerkin representation of the drop streamfunction. Fickian diffusivities for multi-component mass transfer are obtained via Maxwell–Stefan theory with thermodynamic corrections. The advection–diffusion equations governing mass transfer are solved via two distinct numerical methods: a finite difference scheme (using the alternating direction implicit method) and a finite element scheme. Good agreement was obtained between both schemes. Simulation results are presented for a Reynolds number (Re=30) and for a selection of Peclet numbers (Pe=100, 1000 and 10 000, thereby giving insight into the effects of increasing Peclet number). The numerical simulations of the full advection–diffusion equations are compared against predictions of a rigid drop model (i.e. without circulation) and also against predictions of a semi-analytical boundary layer model developed by Uribe-Ramirez and Korchinsky. Results for bulk mass fractions reveal that the rigid drop model predictions evolve too slowly, while the boundary layer model predictions evolve much more quickly than the numerical simulations. Advection–diffusion simulation results for the evolution of mass fractions at selected individual locations in the drop show that points on streamlines nearest to the drop surface and/or drop axis evolve fastest, while those closest to the drop internal stagnation point evolve slowest. Corroborated by contour plots of component concentrations throughout the drop at selected times, this supports a picture whereby mass fractions become roughly uniform along individual streamlines, but mass is transferred diffusively from streamline to streamline.Fil: Ubal, Sebastian. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química (i); ArgentinaFil: Harrison, C. H.. University Of Manchester; Reino UnidoFil: Grassia, P.. University Of Manchester; Reino UnidoFil: Korchinsky, W. J.. University Of Manchester; Reino UnidoElsevier2010-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/13698Ubal, Sebastian; Harrison, C. H.; Grassia, P.; Korchinsky, W. J.; Numerical simulation of mass transfer in circulating drops; Elsevier; Chemical Engineering Science; 65; 10; 5-2010; 2934-29560009-2509enginfo:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0009250910000382info:eu-repo/semantics/altIdentifier/doi/10.1016/j.ces.2010.01.021info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T14:54:49Zoai:ri.conicet.gov.ar:11336/13698instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-15 14:54:49.295CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Numerical simulation of mass transfer in circulating drops
title Numerical simulation of mass transfer in circulating drops
spellingShingle Numerical simulation of mass transfer in circulating drops
Ubal, Sebastian
Mass Transfer
Circulating Drop Model
Convective Transport
High Peclet Number
Cross-Stream Diffusion
Boundary Layers
Mathematical Modelling
Numerical Analysis
Simulation
Liquid-Liquid Extraction
title_short Numerical simulation of mass transfer in circulating drops
title_full Numerical simulation of mass transfer in circulating drops
title_fullStr Numerical simulation of mass transfer in circulating drops
title_full_unstemmed Numerical simulation of mass transfer in circulating drops
title_sort Numerical simulation of mass transfer in circulating drops
dc.creator.none.fl_str_mv Ubal, Sebastian
Harrison, C. H.
Grassia, P.
Korchinsky, W. J.
author Ubal, Sebastian
author_facet Ubal, Sebastian
Harrison, C. H.
Grassia, P.
Korchinsky, W. J.
author_role author
author2 Harrison, C. H.
Grassia, P.
Korchinsky, W. J.
author2_role author
author
author
dc.subject.none.fl_str_mv Mass Transfer
Circulating Drop Model
Convective Transport
High Peclet Number
Cross-Stream Diffusion
Boundary Layers
Mathematical Modelling
Numerical Analysis
Simulation
Liquid-Liquid Extraction
topic Mass Transfer
Circulating Drop Model
Convective Transport
High Peclet Number
Cross-Stream Diffusion
Boundary Layers
Mathematical Modelling
Numerical Analysis
Simulation
Liquid-Liquid Extraction
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.4
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv Numerical simulations of mass transfer are performed for a circulating liquid drop with applications in liquid–liquid extraction. Simulation parameters are chosen for a multi-component ternary system acetone–methanol–benzene. The drop circulation pattern is estimated via a truncated Galerkin representation of the drop streamfunction. Fickian diffusivities for multi-component mass transfer are obtained via Maxwell–Stefan theory with thermodynamic corrections. The advection–diffusion equations governing mass transfer are solved via two distinct numerical methods: a finite difference scheme (using the alternating direction implicit method) and a finite element scheme. Good agreement was obtained between both schemes. Simulation results are presented for a Reynolds number (Re=30) and for a selection of Peclet numbers (Pe=100, 1000 and 10 000, thereby giving insight into the effects of increasing Peclet number). The numerical simulations of the full advection–diffusion equations are compared against predictions of a rigid drop model (i.e. without circulation) and also against predictions of a semi-analytical boundary layer model developed by Uribe-Ramirez and Korchinsky. Results for bulk mass fractions reveal that the rigid drop model predictions evolve too slowly, while the boundary layer model predictions evolve much more quickly than the numerical simulations. Advection–diffusion simulation results for the evolution of mass fractions at selected individual locations in the drop show that points on streamlines nearest to the drop surface and/or drop axis evolve fastest, while those closest to the drop internal stagnation point evolve slowest. Corroborated by contour plots of component concentrations throughout the drop at selected times, this supports a picture whereby mass fractions become roughly uniform along individual streamlines, but mass is transferred diffusively from streamline to streamline.
Fil: Ubal, Sebastian. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química (i); Argentina
Fil: Harrison, C. H.. University Of Manchester; Reino Unido
Fil: Grassia, P.. University Of Manchester; Reino Unido
Fil: Korchinsky, W. J.. University Of Manchester; Reino Unido
description Numerical simulations of mass transfer are performed for a circulating liquid drop with applications in liquid–liquid extraction. Simulation parameters are chosen for a multi-component ternary system acetone–methanol–benzene. The drop circulation pattern is estimated via a truncated Galerkin representation of the drop streamfunction. Fickian diffusivities for multi-component mass transfer are obtained via Maxwell–Stefan theory with thermodynamic corrections. The advection–diffusion equations governing mass transfer are solved via two distinct numerical methods: a finite difference scheme (using the alternating direction implicit method) and a finite element scheme. Good agreement was obtained between both schemes. Simulation results are presented for a Reynolds number (Re=30) and for a selection of Peclet numbers (Pe=100, 1000 and 10 000, thereby giving insight into the effects of increasing Peclet number). The numerical simulations of the full advection–diffusion equations are compared against predictions of a rigid drop model (i.e. without circulation) and also against predictions of a semi-analytical boundary layer model developed by Uribe-Ramirez and Korchinsky. Results for bulk mass fractions reveal that the rigid drop model predictions evolve too slowly, while the boundary layer model predictions evolve much more quickly than the numerical simulations. Advection–diffusion simulation results for the evolution of mass fractions at selected individual locations in the drop show that points on streamlines nearest to the drop surface and/or drop axis evolve fastest, while those closest to the drop internal stagnation point evolve slowest. Corroborated by contour plots of component concentrations throughout the drop at selected times, this supports a picture whereby mass fractions become roughly uniform along individual streamlines, but mass is transferred diffusively from streamline to streamline.
publishDate 2010
dc.date.none.fl_str_mv 2010-05
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/13698
Ubal, Sebastian; Harrison, C. H.; Grassia, P.; Korchinsky, W. J.; Numerical simulation of mass transfer in circulating drops; Elsevier; Chemical Engineering Science; 65; 10; 5-2010; 2934-2956
0009-2509
url http://hdl.handle.net/11336/13698
identifier_str_mv Ubal, Sebastian; Harrison, C. H.; Grassia, P.; Korchinsky, W. J.; Numerical simulation of mass transfer in circulating drops; Elsevier; Chemical Engineering Science; 65; 10; 5-2010; 2934-2956
0009-2509
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0009250910000382
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.ces.2010.01.021
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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