Effects of small surface tension in Hele-Shaw multifinger dynamics: an analytical and numerical study

We study the singular effects of vanishingly small surface tension on the dynamics of finger competition in the Saffman-Taylor problem, using the asymptotic techniques described by Tanveer [Philos. Trans. R. Soc. London, Ser. A 343, 155 (1993)] and Siegel and Tanveer [Phys. Rev. Lett. 76, 419 (1996)...

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Authors: Pauné i Xuriguera, Eduard, Siegel, Michael, Casademunt i Viader, Jaume
Format: article
Status:Published version
Publication Date:2002
Country:España
Institution:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repository:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2445/18692
Online Access:https://hdl.handle.net/2445/18692
Access Level:Open access
Keyword:Dinàmica de fluids
Fluid dynamics
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spelling Effects of small surface tension in Hele-Shaw multifinger dynamics: an analytical and numerical studyPauné i Xuriguera, EduardSiegel, MichaelCasademunt i Viader, JaumeDinàmica de fluidsFluid dynamicsWe study the singular effects of vanishingly small surface tension on the dynamics of finger competition in the Saffman-Taylor problem, using the asymptotic techniques described by Tanveer [Philos. Trans. R. Soc. London, Ser. A 343, 155 (1993)] and Siegel and Tanveer [Phys. Rev. Lett. 76, 419 (1996)], as well as direct numerical computation, following the numerical scheme of Hou, Lowengrub, and Shelley [J. Comput. Phys. 114, 312 (1994)]. We demonstrate the dramatic effects of small surface tension on the late time evolution of two-finger configurations with respect to exact (nonsingular) zero-surface-tension solutions. The effect is present even when the relevant zero-surface-tension solution has asymptotic behavior consistent with selection theory. Such singular effects, therefore, cannot be traced back to steady state selection theory, and imply a drastic global change in the structure of phase-space flow. They can be interpreted in the framework of a recently introduced dynamical solvability scenario according to which surface tension unfolds the structurally unstable flow, restoring the hyperbolicity of multifinger fixed points.The American Physical Society201120112002info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersion13 p.application/pdfhttps://hdl.handle.net/2445/18692Articles publicats en revistes (Física Quàntica i Astrofísica)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésReproducció del document publicat a: http://dx.doi.org/10.1103/PhysRevE.66.046205Physical Review E, 2002, vol. 66, núm. 4, p. 046205http://dx.doi.org/10.1103/PhysRevE.66.046205(c) The American Physical Society, 2002info:eu-repo/semantics/openAccessoai:recercat.cat:2445/186922026-05-29T05:05:01Z
dc.title.none.fl_str_mv Effects of small surface tension in Hele-Shaw multifinger dynamics: an analytical and numerical study
title Effects of small surface tension in Hele-Shaw multifinger dynamics: an analytical and numerical study
spellingShingle Effects of small surface tension in Hele-Shaw multifinger dynamics: an analytical and numerical study
Pauné i Xuriguera, Eduard
Dinàmica de fluids
Fluid dynamics
title_short Effects of small surface tension in Hele-Shaw multifinger dynamics: an analytical and numerical study
title_full Effects of small surface tension in Hele-Shaw multifinger dynamics: an analytical and numerical study
title_fullStr Effects of small surface tension in Hele-Shaw multifinger dynamics: an analytical and numerical study
title_full_unstemmed Effects of small surface tension in Hele-Shaw multifinger dynamics: an analytical and numerical study
title_sort Effects of small surface tension in Hele-Shaw multifinger dynamics: an analytical and numerical study
dc.creator.none.fl_str_mv Pauné i Xuriguera, Eduard
Siegel, Michael
Casademunt i Viader, Jaume
author Pauné i Xuriguera, Eduard
author_facet Pauné i Xuriguera, Eduard
Siegel, Michael
Casademunt i Viader, Jaume
author_role author
author2 Siegel, Michael
Casademunt i Viader, Jaume
author2_role author
author
dc.subject.none.fl_str_mv Dinàmica de fluids
Fluid dynamics
topic Dinàmica de fluids
Fluid dynamics
description We study the singular effects of vanishingly small surface tension on the dynamics of finger competition in the Saffman-Taylor problem, using the asymptotic techniques described by Tanveer [Philos. Trans. R. Soc. London, Ser. A 343, 155 (1993)] and Siegel and Tanveer [Phys. Rev. Lett. 76, 419 (1996)], as well as direct numerical computation, following the numerical scheme of Hou, Lowengrub, and Shelley [J. Comput. Phys. 114, 312 (1994)]. We demonstrate the dramatic effects of small surface tension on the late time evolution of two-finger configurations with respect to exact (nonsingular) zero-surface-tension solutions. The effect is present even when the relevant zero-surface-tension solution has asymptotic behavior consistent with selection theory. Such singular effects, therefore, cannot be traced back to steady state selection theory, and imply a drastic global change in the structure of phase-space flow. They can be interpreted in the framework of a recently introduced dynamical solvability scenario according to which surface tension unfolds the structurally unstable flow, restoring the hyperbolicity of multifinger fixed points.
publishDate 2002
dc.date.none.fl_str_mv 2002
2011
2011
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/2445/18692
url https://hdl.handle.net/2445/18692
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Reproducció del document publicat a: http://dx.doi.org/10.1103/PhysRevE.66.046205
Physical Review E, 2002, vol. 66, núm. 4, p. 046205
http://dx.doi.org/10.1103/PhysRevE.66.046205
dc.rights.none.fl_str_mv (c) The American Physical Society, 2002
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) The American Physical Society, 2002
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 13 p.
application/pdf
dc.publisher.none.fl_str_mv The American Physical Society
publisher.none.fl_str_mv The American Physical Society
dc.source.none.fl_str_mv Articles publicats en revistes (Física Quàntica i Astrofísica)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.811543

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