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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/13698
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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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1846083080817737728 |
score |
13.22299 |