Electroconvection in a dielectric liquid between two concentric half-cylinders with rigid walls: Linear and nonlinear analysis

We study the linear stability and nonlinear behavior of the electroconvection between two concentric halfcylinders with no-slip conditions on all boundaries. The no-slip condition makes impossible to apply the standard modal approach. Hence, we apply a finite element technique similar to the one we...

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Autores: Vázquez González, Pedro Ángel, Pérez Izquierdo, Alberto Tomás, Traoré, Philippe, Wu, Jiam
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2018
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/77723
Acceso en línea:https://hdl.handle.net/11441/77723
https://doi.org/10.1103/PhysRevE.97.023106
Access Level:acceso abierto
Palabra clave:Electroconvection
Dielectric liquid
Linear and nonlinear analysis
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spelling Electroconvection in a dielectric liquid between two concentric half-cylinders with rigid walls: Linear and nonlinear analysisVázquez González, Pedro ÁngelPérez Izquierdo, Alberto TomásTraoré, PhilippeWu, JiamElectroconvectionDielectric liquidLinear and nonlinear analysisWe study the linear stability and nonlinear behavior of the electroconvection between two concentric halfcylinders with no-slip conditions on all boundaries. The no-slip condition makes impossible to apply the standard modal approach. Hence, we apply a finite element technique similar to the one we have used in a previous paper about the electroconvection in a rectangular enclosed domain. When compared to the classical problem of electroconvection between two full concentric cylinders, the linear criterion is higher, due to the viscous shear introduced by the lateral walls. As a consequence, the structure of the eigenmodes is very different. There is a repulsion between modeswith the same symmetry, forcing pairs of modes to cross each other repeatedly. For inner injection and small value of the ratio between the inner and outer radii the no-slip condition changes the nature of the bifurcation from subcritical to supercritical, while it is always subcritical for outer injection. To understand this behavior, we perform a modal analysis using the eigenfunctions obtained from the linear stability analysis as modal basis. We show that the supercritical branch is originated by the nonorthogonality of the modes when no-slip boundary conditions are imposed. These mechanism explains the previously unexplained appearance of the supercritical branch in the enclosed rectangular configuration.Ministerio de Economía y Competitividad FIS2014-54539-PAmerican Physical SocietyFísica Aplicada IIIElectrónica y ElectromagnetismoMinisterio de Economía y Competitividad (MINECO). España2018info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/77723https://doi.org/10.1103/PhysRevE.97.023106reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésPhysical Review E, 97, 023106-1-023106-15.FIS2014-54539-Phttps://www.ncbi.nlm.nih.gov/pubmed/29548177info:eu-repo/semantics/openAccessoai:idus.us.es:11441/777232026-06-17T12:51:07Z
dc.title.none.fl_str_mv Electroconvection in a dielectric liquid between two concentric half-cylinders with rigid walls: Linear and nonlinear analysis
title Electroconvection in a dielectric liquid between two concentric half-cylinders with rigid walls: Linear and nonlinear analysis
spellingShingle Electroconvection in a dielectric liquid between two concentric half-cylinders with rigid walls: Linear and nonlinear analysis
Vázquez González, Pedro Ángel
Electroconvection
Dielectric liquid
Linear and nonlinear analysis
title_short Electroconvection in a dielectric liquid between two concentric half-cylinders with rigid walls: Linear and nonlinear analysis
title_full Electroconvection in a dielectric liquid between two concentric half-cylinders with rigid walls: Linear and nonlinear analysis
title_fullStr Electroconvection in a dielectric liquid between two concentric half-cylinders with rigid walls: Linear and nonlinear analysis
title_full_unstemmed Electroconvection in a dielectric liquid between two concentric half-cylinders with rigid walls: Linear and nonlinear analysis
title_sort Electroconvection in a dielectric liquid between two concentric half-cylinders with rigid walls: Linear and nonlinear analysis
dc.creator.none.fl_str_mv Vázquez González, Pedro Ángel
Pérez Izquierdo, Alberto Tomás
Traoré, Philippe
Wu, Jiam
author Vázquez González, Pedro Ángel
author_facet Vázquez González, Pedro Ángel
Pérez Izquierdo, Alberto Tomás
Traoré, Philippe
Wu, Jiam
author_role author
author2 Pérez Izquierdo, Alberto Tomás
Traoré, Philippe
Wu, Jiam
author2_role author
author
author
dc.contributor.none.fl_str_mv Física Aplicada III
Electrónica y Electromagnetismo
Ministerio de Economía y Competitividad (MINECO). España
dc.subject.none.fl_str_mv Electroconvection
Dielectric liquid
Linear and nonlinear analysis
topic Electroconvection
Dielectric liquid
Linear and nonlinear analysis
description We study the linear stability and nonlinear behavior of the electroconvection between two concentric halfcylinders with no-slip conditions on all boundaries. The no-slip condition makes impossible to apply the standard modal approach. Hence, we apply a finite element technique similar to the one we have used in a previous paper about the electroconvection in a rectangular enclosed domain. When compared to the classical problem of electroconvection between two full concentric cylinders, the linear criterion is higher, due to the viscous shear introduced by the lateral walls. As a consequence, the structure of the eigenmodes is very different. There is a repulsion between modeswith the same symmetry, forcing pairs of modes to cross each other repeatedly. For inner injection and small value of the ratio between the inner and outer radii the no-slip condition changes the nature of the bifurcation from subcritical to supercritical, while it is always subcritical for outer injection. To understand this behavior, we perform a modal analysis using the eigenfunctions obtained from the linear stability analysis as modal basis. We show that the supercritical branch is originated by the nonorthogonality of the modes when no-slip boundary conditions are imposed. These mechanism explains the previously unexplained appearance of the supercritical branch in the enclosed rectangular configuration.
publishDate 2018
dc.date.none.fl_str_mv 2018
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/77723
https://doi.org/10.1103/PhysRevE.97.023106
url https://hdl.handle.net/11441/77723
https://doi.org/10.1103/PhysRevE.97.023106
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Physical Review E, 97, 023106-1-023106-15.
FIS2014-54539-P
https://www.ncbi.nlm.nih.gov/pubmed/29548177
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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