A direct relation between bending energy and contact angles for capillary bridges

The didactic object of these developments on differential geometry of curves and surfaces is to present fine and convenient mathematical strategies, adapted to the study of capillary bridges. The common thread is to be able to calculate accurately in any situation the bending stress over the free su...
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Autor*in:	Millet, Olivier [verfasserIn] Gagneux , Gérard [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch ; Französisch

Erschienen:	2023

Schlagwörter:	Distortion of nonaxisymmetric capillary bridges Mean and Gaussian curvatures impact Euler characteristic Generalized Young–Laplace equation Bending effects Fenchel’s theorem in differential geometry Gauss–Bonnet Theorem Geodesic curvature Bending stress Influence of the contact angles

Übergeordnetes Werk:	In: Comptes Rendus. Mécanique - Académie des sciences, 2022, 351(2023), S2, Seite 125-137
Übergeordnetes Werk:	volume:351 ; year:2023 ; number:S2 ; pages:125-137

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.5802/crmeca.200

Katalog-ID:	DOAJ092554946

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650		4	\|a Distortion of nonaxisymmetric capillary bridges
650		4	\|a Mean and Gaussian curvatures impact
650		4	\|a Euler characteristic
650		4	\|a Generalized Young–Laplace equation
650		4	\|a Bending effects
650		4	\|a Fenchel’s theorem in differential geometry
650		4	\|a Gauss–Bonnet Theorem
650		4	\|a Geodesic curvature
650		4	\|a Bending stress
650		4	\|a Influence of the contact angles
653		0	\|a Materials of engineering and construction. Mechanics of materials
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spelling	10.5802/crmeca.200 doi (DE-627)DOAJ092554946 (DE-599)DOAJ4d7b1ecc5b25474ea8baac851ae66451 DE-627 ger DE-627 rakwb eng fre TA401-492 Millet, Olivier verfasserin aut A direct relation between bending energy and contact angles for capillary bridges 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The didactic object of these developments on differential geometry of curves and surfaces is to present fine and convenient mathematical strategies, adapted to the study of capillary bridges. The common thread is to be able to calculate accurately in any situation the bending stress over the free surface, represented mathematically by the integral of the Gaussian curvature over the surface (called the total curvature) involved in the generalized Young–Laplace equation. We prove in particular that the resultant of the bending energy is directly linked to the wetting angles at the contact line. Distortion of nonaxisymmetric capillary bridges Mean and Gaussian curvatures impact Euler characteristic Generalized Young–Laplace equation Bending effects Fenchel’s theorem in differential geometry Gauss–Bonnet Theorem Geodesic curvature Bending stress Influence of the contact angles Materials of engineering and construction. Mechanics of materials Gagneux , Gérard verfasserin aut In Comptes Rendus. Mécanique Académie des sciences, 2022 351(2023), S2, Seite 125-137 (DE-627)348585381 (DE-600)2079504-X 18737234 nnns volume:351 year:2023 number:S2 pages:125-137 https://doi.org/10.5802/crmeca.200 kostenfrei https://doaj.org/article/4d7b1ecc5b25474ea8baac851ae66451 kostenfrei https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.200/ kostenfrei https://doaj.org/toc/1873-7234 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_165 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2004 GBV_ILN_2014 GBV_ILN_2336 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 351 2023 S2 125-137
allfields_unstemmed	10.5802/crmeca.200 doi (DE-627)DOAJ092554946 (DE-599)DOAJ4d7b1ecc5b25474ea8baac851ae66451 DE-627 ger DE-627 rakwb eng fre TA401-492 Millet, Olivier verfasserin aut A direct relation between bending energy and contact angles for capillary bridges 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The didactic object of these developments on differential geometry of curves and surfaces is to present fine and convenient mathematical strategies, adapted to the study of capillary bridges. The common thread is to be able to calculate accurately in any situation the bending stress over the free surface, represented mathematically by the integral of the Gaussian curvature over the surface (called the total curvature) involved in the generalized Young–Laplace equation. We prove in particular that the resultant of the bending energy is directly linked to the wetting angles at the contact line. Distortion of nonaxisymmetric capillary bridges Mean and Gaussian curvatures impact Euler characteristic Generalized Young–Laplace equation Bending effects Fenchel’s theorem in differential geometry Gauss–Bonnet Theorem Geodesic curvature Bending stress Influence of the contact angles Materials of engineering and construction. Mechanics of materials Gagneux , Gérard verfasserin aut In Comptes Rendus. Mécanique Académie des sciences, 2022 351(2023), S2, Seite 125-137 (DE-627)348585381 (DE-600)2079504-X 18737234 nnns volume:351 year:2023 number:S2 pages:125-137 https://doi.org/10.5802/crmeca.200 kostenfrei https://doaj.org/article/4d7b1ecc5b25474ea8baac851ae66451 kostenfrei https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.200/ kostenfrei https://doaj.org/toc/1873-7234 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_165 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2004 GBV_ILN_2014 GBV_ILN_2336 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 351 2023 S2 125-137
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allfieldsSound	10.5802/crmeca.200 doi (DE-627)DOAJ092554946 (DE-599)DOAJ4d7b1ecc5b25474ea8baac851ae66451 DE-627 ger DE-627 rakwb eng fre TA401-492 Millet, Olivier verfasserin aut A direct relation between bending energy and contact angles for capillary bridges 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The didactic object of these developments on differential geometry of curves and surfaces is to present fine and convenient mathematical strategies, adapted to the study of capillary bridges. The common thread is to be able to calculate accurately in any situation the bending stress over the free surface, represented mathematically by the integral of the Gaussian curvature over the surface (called the total curvature) involved in the generalized Young–Laplace equation. We prove in particular that the resultant of the bending energy is directly linked to the wetting angles at the contact line. Distortion of nonaxisymmetric capillary bridges Mean and Gaussian curvatures impact Euler characteristic Generalized Young–Laplace equation Bending effects Fenchel’s theorem in differential geometry Gauss–Bonnet Theorem Geodesic curvature Bending stress Influence of the contact angles Materials of engineering and construction. Mechanics of materials Gagneux , Gérard verfasserin aut In Comptes Rendus. Mécanique Académie des sciences, 2022 351(2023), S2, Seite 125-137 (DE-627)348585381 (DE-600)2079504-X 18737234 nnns volume:351 year:2023 number:S2 pages:125-137 https://doi.org/10.5802/crmeca.200 kostenfrei https://doaj.org/article/4d7b1ecc5b25474ea8baac851ae66451 kostenfrei https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.200/ kostenfrei https://doaj.org/toc/1873-7234 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_165 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2004 GBV_ILN_2014 GBV_ILN_2336 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 351 2023 S2 125-137
language	English French
source	In Comptes Rendus. Mécanique 351(2023), S2, Seite 125-137 volume:351 year:2023 number:S2 pages:125-137
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topic_facet	Distortion of nonaxisymmetric capillary bridges Mean and Gaussian curvatures impact Euler characteristic Generalized Young–Laplace equation Bending effects Fenchel’s theorem in differential geometry Gauss–Bonnet Theorem Geodesic curvature Bending stress Influence of the contact angles Materials of engineering and construction. Mechanics of materials
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callnumber-first	T - Technology
author	Millet, Olivier
spellingShingle	Millet, Olivier misc TA401-492 misc Distortion of nonaxisymmetric capillary bridges misc Mean and Gaussian curvatures impact misc Euler characteristic misc Generalized Young–Laplace equation misc Bending effects misc Fenchel’s theorem in differential geometry misc Gauss–Bonnet Theorem misc Geodesic curvature misc Bending stress misc Influence of the contact angles misc Materials of engineering and construction. Mechanics of materials A direct relation between bending energy and contact angles for capillary bridges
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topic_title	TA401-492 A direct relation between bending energy and contact angles for capillary bridges Distortion of nonaxisymmetric capillary bridges Mean and Gaussian curvatures impact Euler characteristic Generalized Young–Laplace equation Bending effects Fenchel’s theorem in differential geometry Gauss–Bonnet Theorem Geodesic curvature Bending stress Influence of the contact angles
topic	misc TA401-492 misc Distortion of nonaxisymmetric capillary bridges misc Mean and Gaussian curvatures impact misc Euler characteristic misc Generalized Young–Laplace equation misc Bending effects misc Fenchel’s theorem in differential geometry misc Gauss–Bonnet Theorem misc Geodesic curvature misc Bending stress misc Influence of the contact angles misc Materials of engineering and construction. Mechanics of materials
topic_unstemmed	misc TA401-492 misc Distortion of nonaxisymmetric capillary bridges misc Mean and Gaussian curvatures impact misc Euler characteristic misc Generalized Young–Laplace equation misc Bending effects misc Fenchel’s theorem in differential geometry misc Gauss–Bonnet Theorem misc Geodesic curvature misc Bending stress misc Influence of the contact angles misc Materials of engineering and construction. Mechanics of materials
topic_browse	misc TA401-492 misc Distortion of nonaxisymmetric capillary bridges misc Mean and Gaussian curvatures impact misc Euler characteristic misc Generalized Young–Laplace equation misc Bending effects misc Fenchel’s theorem in differential geometry misc Gauss–Bonnet Theorem misc Geodesic curvature misc Bending stress misc Influence of the contact angles misc Materials of engineering and construction. Mechanics of materials
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title	A direct relation between bending energy and contact angles for capillary bridges
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title_full	A direct relation between bending energy and contact angles for capillary bridges
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title_sort	direct relation between bending energy and contact angles for capillary bridges
callnumber	TA401-492
title_auth	A direct relation between bending energy and contact angles for capillary bridges
abstract	The didactic object of these developments on differential geometry of curves and surfaces is to present fine and convenient mathematical strategies, adapted to the study of capillary bridges. The common thread is to be able to calculate accurately in any situation the bending stress over the free surface, represented mathematically by the integral of the Gaussian curvature over the surface (called the total curvature) involved in the generalized Young–Laplace equation. We prove in particular that the resultant of the bending energy is directly linked to the wetting angles at the contact line.
abstractGer	The didactic object of these developments on differential geometry of curves and surfaces is to present fine and convenient mathematical strategies, adapted to the study of capillary bridges. The common thread is to be able to calculate accurately in any situation the bending stress over the free surface, represented mathematically by the integral of the Gaussian curvature over the surface (called the total curvature) involved in the generalized Young–Laplace equation. We prove in particular that the resultant of the bending energy is directly linked to the wetting angles at the contact line.
abstract_unstemmed	The didactic object of these developments on differential geometry of curves and surfaces is to present fine and convenient mathematical strategies, adapted to the study of capillary bridges. The common thread is to be able to calculate accurately in any situation the bending stress over the free surface, represented mathematically by the integral of the Gaussian curvature over the surface (called the total curvature) involved in the generalized Young–Laplace equation. We prove in particular that the resultant of the bending energy is directly linked to the wetting angles at the contact line.
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title_short	A direct relation between bending energy and contact angles for capillary bridges
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A direct relation between bending energy and contact angles for capillary bridges

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