Symmetry-Breaking Bifurcations of Charged Drops

Abstract. It has been observed experimentally that an electrically charged spherical drop of a conducting fluid becomes nonspherical (in fact, a spheroid) when a dimensionless number X inversely proportional to the surface tension coefficient γ is larger than some critical value (i.e., when γ<$ γ...
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Autor*in:	Fontelos, Marco A. [verfasserIn] Friedman, Avner

Format:	Artikel
Sprache:	Englisch

Erschienen:	2004

Schlagwörter:	Surface Tension Electrostatic Potential Prolate Dimensionless Number Fluid Equation

Anmerkung:	© Springer-Verlag Berlin Heidelberg 2004

Übergeordnetes Werk:	Enthalten in: Archive for rational mechanics and analysis - Springer-Verlag, 1957, 172(2004), 2 vom: 15. Jan., Seite 267-294
Übergeordnetes Werk:	volume:172 ; year:2004 ; number:2 ; day:15 ; month:01 ; pages:267-294

Links:	Volltext

DOI / URN:	10.1007/s00205-003-0298-x

Katalog-ID:	OLC2056414473

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520			\|a Abstract. It has been observed experimentally that an electrically charged spherical drop of a conducting fluid becomes nonspherical (in fact, a spheroid) when a dimensionless number X inversely proportional to the surface tension coefficient γ is larger than some critical value (i.e., when γ<$ γ_{c} $). In this paper we prove that bifurcation branches of nonspherical shapes originate from each of a sequence of surface-tension coefficients ), where $ γ_{2} $=$ γ_{c} $. We further prove that the spherical drop is stable for any γ>$ γ_{2} $, that is, the solution to the system of fluid equations coupled with the equation for the electrostatic potential created by the charged drop converges to the spherical solution as tρ∞ provided the initial drop is nearly spherical. We finally show that the part of the bifurcation branch at γ=$ γ_{2} $ which gives rise to oblate spheroids is linearly stable, whereas the part of the branch corresponding to prolate spheroids is linearly unstable.
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allfields	10.1007/s00205-003-0298-x doi (DE-627)OLC2056414473 (DE-He213)s00205-003-0298-x-p DE-627 ger DE-627 rakwb eng 530 510 VZ Fontelos, Marco A. verfasserin aut Symmetry-Breaking Bifurcations of Charged Drops 2004 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2004 Abstract. It has been observed experimentally that an electrically charged spherical drop of a conducting fluid becomes nonspherical (in fact, a spheroid) when a dimensionless number X inversely proportional to the surface tension coefficient γ is larger than some critical value (i.e., when γ<$ γ_{c} $). In this paper we prove that bifurcation branches of nonspherical shapes originate from each of a sequence of surface-tension coefficients ), where $ γ_{2} $=$ γ_{c} $. We further prove that the spherical drop is stable for any γ>$ γ_{2} $, that is, the solution to the system of fluid equations coupled with the equation for the electrostatic potential created by the charged drop converges to the spherical solution as tρ∞ provided the initial drop is nearly spherical. We finally show that the part of the bifurcation branch at γ=$ γ_{2} $ which gives rise to oblate spheroids is linearly stable, whereas the part of the branch corresponding to prolate spheroids is linearly unstable. Surface Tension Electrostatic Potential Prolate Dimensionless Number Fluid Equation Friedman, Avner aut Enthalten in Archive for rational mechanics and analysis Springer-Verlag, 1957 172(2004), 2 vom: 15. Jan., Seite 267-294 (DE-627)129519618 (DE-600)212130-X (DE-576)014933004 0003-9527 nnns volume:172 year:2004 number:2 day:15 month:01 pages:267-294 https://doi.org/10.1007/s00205-003-0298-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_62 GBV_ILN_65 GBV_ILN_70 GBV_ILN_100 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4126 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4700 AR 172 2004 2 15 01 267-294
spelling	10.1007/s00205-003-0298-x doi (DE-627)OLC2056414473 (DE-He213)s00205-003-0298-x-p DE-627 ger DE-627 rakwb eng 530 510 VZ Fontelos, Marco A. verfasserin aut Symmetry-Breaking Bifurcations of Charged Drops 2004 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2004 Abstract. It has been observed experimentally that an electrically charged spherical drop of a conducting fluid becomes nonspherical (in fact, a spheroid) when a dimensionless number X inversely proportional to the surface tension coefficient γ is larger than some critical value (i.e., when γ<$ γ_{c} $). In this paper we prove that bifurcation branches of nonspherical shapes originate from each of a sequence of surface-tension coefficients ), where $ γ_{2} $=$ γ_{c} $. We further prove that the spherical drop is stable for any γ>$ γ_{2} $, that is, the solution to the system of fluid equations coupled with the equation for the electrostatic potential created by the charged drop converges to the spherical solution as tρ∞ provided the initial drop is nearly spherical. We finally show that the part of the bifurcation branch at γ=$ γ_{2} $ which gives rise to oblate spheroids is linearly stable, whereas the part of the branch corresponding to prolate spheroids is linearly unstable. Surface Tension Electrostatic Potential Prolate Dimensionless Number Fluid Equation Friedman, Avner aut Enthalten in Archive for rational mechanics and analysis Springer-Verlag, 1957 172(2004), 2 vom: 15. Jan., Seite 267-294 (DE-627)129519618 (DE-600)212130-X (DE-576)014933004 0003-9527 nnns volume:172 year:2004 number:2 day:15 month:01 pages:267-294 https://doi.org/10.1007/s00205-003-0298-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_62 GBV_ILN_65 GBV_ILN_70 GBV_ILN_100 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4126 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4700 AR 172 2004 2 15 01 267-294
allfields_unstemmed	10.1007/s00205-003-0298-x doi (DE-627)OLC2056414473 (DE-He213)s00205-003-0298-x-p DE-627 ger DE-627 rakwb eng 530 510 VZ Fontelos, Marco A. verfasserin aut Symmetry-Breaking Bifurcations of Charged Drops 2004 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2004 Abstract. It has been observed experimentally that an electrically charged spherical drop of a conducting fluid becomes nonspherical (in fact, a spheroid) when a dimensionless number X inversely proportional to the surface tension coefficient γ is larger than some critical value (i.e., when γ<$ γ_{c} $). In this paper we prove that bifurcation branches of nonspherical shapes originate from each of a sequence of surface-tension coefficients ), where $ γ_{2} $=$ γ_{c} $. We further prove that the spherical drop is stable for any γ>$ γ_{2} $, that is, the solution to the system of fluid equations coupled with the equation for the electrostatic potential created by the charged drop converges to the spherical solution as tρ∞ provided the initial drop is nearly spherical. We finally show that the part of the bifurcation branch at γ=$ γ_{2} $ which gives rise to oblate spheroids is linearly stable, whereas the part of the branch corresponding to prolate spheroids is linearly unstable. Surface Tension Electrostatic Potential Prolate Dimensionless Number Fluid Equation Friedman, Avner aut Enthalten in Archive for rational mechanics and analysis Springer-Verlag, 1957 172(2004), 2 vom: 15. Jan., Seite 267-294 (DE-627)129519618 (DE-600)212130-X (DE-576)014933004 0003-9527 nnns volume:172 year:2004 number:2 day:15 month:01 pages:267-294 https://doi.org/10.1007/s00205-003-0298-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_62 GBV_ILN_65 GBV_ILN_70 GBV_ILN_100 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4126 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4700 AR 172 2004 2 15 01 267-294
allfieldsGer	10.1007/s00205-003-0298-x doi (DE-627)OLC2056414473 (DE-He213)s00205-003-0298-x-p DE-627 ger DE-627 rakwb eng 530 510 VZ Fontelos, Marco A. verfasserin aut Symmetry-Breaking Bifurcations of Charged Drops 2004 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2004 Abstract. It has been observed experimentally that an electrically charged spherical drop of a conducting fluid becomes nonspherical (in fact, a spheroid) when a dimensionless number X inversely proportional to the surface tension coefficient γ is larger than some critical value (i.e., when γ<$ γ_{c} $). In this paper we prove that bifurcation branches of nonspherical shapes originate from each of a sequence of surface-tension coefficients ), where $ γ_{2} $=$ γ_{c} $. We further prove that the spherical drop is stable for any γ>$ γ_{2} $, that is, the solution to the system of fluid equations coupled with the equation for the electrostatic potential created by the charged drop converges to the spherical solution as tρ∞ provided the initial drop is nearly spherical. We finally show that the part of the bifurcation branch at γ=$ γ_{2} $ which gives rise to oblate spheroids is linearly stable, whereas the part of the branch corresponding to prolate spheroids is linearly unstable. Surface Tension Electrostatic Potential Prolate Dimensionless Number Fluid Equation Friedman, Avner aut Enthalten in Archive for rational mechanics and analysis Springer-Verlag, 1957 172(2004), 2 vom: 15. Jan., Seite 267-294 (DE-627)129519618 (DE-600)212130-X (DE-576)014933004 0003-9527 nnns volume:172 year:2004 number:2 day:15 month:01 pages:267-294 https://doi.org/10.1007/s00205-003-0298-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_62 GBV_ILN_65 GBV_ILN_70 GBV_ILN_100 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4126 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4700 AR 172 2004 2 15 01 267-294
allfieldsSound	10.1007/s00205-003-0298-x doi (DE-627)OLC2056414473 (DE-He213)s00205-003-0298-x-p DE-627 ger DE-627 rakwb eng 530 510 VZ Fontelos, Marco A. verfasserin aut Symmetry-Breaking Bifurcations of Charged Drops 2004 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2004 Abstract. It has been observed experimentally that an electrically charged spherical drop of a conducting fluid becomes nonspherical (in fact, a spheroid) when a dimensionless number X inversely proportional to the surface tension coefficient γ is larger than some critical value (i.e., when γ<$ γ_{c} $). In this paper we prove that bifurcation branches of nonspherical shapes originate from each of a sequence of surface-tension coefficients ), where $ γ_{2} $=$ γ_{c} $. We further prove that the spherical drop is stable for any γ>$ γ_{2} $, that is, the solution to the system of fluid equations coupled with the equation for the electrostatic potential created by the charged drop converges to the spherical solution as tρ∞ provided the initial drop is nearly spherical. We finally show that the part of the bifurcation branch at γ=$ γ_{2} $ which gives rise to oblate spheroids is linearly stable, whereas the part of the branch corresponding to prolate spheroids is linearly unstable. Surface Tension Electrostatic Potential Prolate Dimensionless Number Fluid Equation Friedman, Avner aut Enthalten in Archive for rational mechanics and analysis Springer-Verlag, 1957 172(2004), 2 vom: 15. Jan., Seite 267-294 (DE-627)129519618 (DE-600)212130-X (DE-576)014933004 0003-9527 nnns volume:172 year:2004 number:2 day:15 month:01 pages:267-294 https://doi.org/10.1007/s00205-003-0298-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_62 GBV_ILN_65 GBV_ILN_70 GBV_ILN_100 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4126 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4700 AR 172 2004 2 15 01 267-294
language	English
source	Enthalten in Archive for rational mechanics and analysis 172(2004), 2 vom: 15. Jan., Seite 267-294 volume:172 year:2004 number:2 day:15 month:01 pages:267-294
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author	Fontelos, Marco A.
spellingShingle	Fontelos, Marco A. ddc 530 misc Surface Tension misc Electrostatic Potential misc Prolate misc Dimensionless Number misc Fluid Equation Symmetry-Breaking Bifurcations of Charged Drops
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topic_title	530 510 VZ Symmetry-Breaking Bifurcations of Charged Drops Surface Tension Electrostatic Potential Prolate Dimensionless Number Fluid Equation
topic	ddc 530 misc Surface Tension misc Electrostatic Potential misc Prolate misc Dimensionless Number misc Fluid Equation
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title	Symmetry-Breaking Bifurcations of Charged Drops
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title_full	Symmetry-Breaking Bifurcations of Charged Drops
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title_sort	symmetry-breaking bifurcations of charged drops
title_auth	Symmetry-Breaking Bifurcations of Charged Drops
abstract	Abstract. It has been observed experimentally that an electrically charged spherical drop of a conducting fluid becomes nonspherical (in fact, a spheroid) when a dimensionless number X inversely proportional to the surface tension coefficient γ is larger than some critical value (i.e., when γ<$ γ_{c} $). In this paper we prove that bifurcation branches of nonspherical shapes originate from each of a sequence of surface-tension coefficients ), where $ γ_{2} $=$ γ_{c} $. We further prove that the spherical drop is stable for any γ>$ γ_{2} $, that is, the solution to the system of fluid equations coupled with the equation for the electrostatic potential created by the charged drop converges to the spherical solution as tρ∞ provided the initial drop is nearly spherical. We finally show that the part of the bifurcation branch at γ=$ γ_{2} $ which gives rise to oblate spheroids is linearly stable, whereas the part of the branch corresponding to prolate spheroids is linearly unstable. © Springer-Verlag Berlin Heidelberg 2004
abstractGer	Abstract. It has been observed experimentally that an electrically charged spherical drop of a conducting fluid becomes nonspherical (in fact, a spheroid) when a dimensionless number X inversely proportional to the surface tension coefficient γ is larger than some critical value (i.e., when γ<$ γ_{c} $). In this paper we prove that bifurcation branches of nonspherical shapes originate from each of a sequence of surface-tension coefficients ), where $ γ_{2} $=$ γ_{c} $. We further prove that the spherical drop is stable for any γ>$ γ_{2} $, that is, the solution to the system of fluid equations coupled with the equation for the electrostatic potential created by the charged drop converges to the spherical solution as tρ∞ provided the initial drop is nearly spherical. We finally show that the part of the bifurcation branch at γ=$ γ_{2} $ which gives rise to oblate spheroids is linearly stable, whereas the part of the branch corresponding to prolate spheroids is linearly unstable. © Springer-Verlag Berlin Heidelberg 2004
abstract_unstemmed	Abstract. It has been observed experimentally that an electrically charged spherical drop of a conducting fluid becomes nonspherical (in fact, a spheroid) when a dimensionless number X inversely proportional to the surface tension coefficient γ is larger than some critical value (i.e., when γ<$ γ_{c} $). In this paper we prove that bifurcation branches of nonspherical shapes originate from each of a sequence of surface-tension coefficients ), where $ γ_{2} $=$ γ_{c} $. We further prove that the spherical drop is stable for any γ>$ γ_{2} $, that is, the solution to the system of fluid equations coupled with the equation for the electrostatic potential created by the charged drop converges to the spherical solution as tρ∞ provided the initial drop is nearly spherical. We finally show that the part of the bifurcation branch at γ=$ γ_{2} $ which gives rise to oblate spheroids is linearly stable, whereas the part of the branch corresponding to prolate spheroids is linearly unstable. © Springer-Verlag Berlin Heidelberg 2004
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title_short	Symmetry-Breaking Bifurcations of Charged Drops
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up_date	2024-07-04T04:20:05.705Z
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