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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Académie des sciences
2023-09-01
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| Series: | Comptes Rendus. Mécanique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.200/ |
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| author | Millet, Olivier Gagneux , Gérard |
| author_facet | Millet, Olivier Gagneux , Gérard |
| author_sort | Millet, Olivier |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-4d7b1ecc5b25474ea8baac851ae66451 |
| institution | Kabale University |
| issn | 1873-7234 |
| language | English |
| publishDate | 2023-09-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mécanique |
| spelling | doaj-art-4d7b1ecc5b25474ea8baac851ae664512025-02-07T13:47:30ZengAcadémie des sciencesComptes Rendus. Mécanique1873-72342023-09-01351S212513710.5802/crmeca.20010.5802/crmeca.200A direct relation between bending energy and contact angles for capillary bridgesMillet, Olivier0Gagneux , Gérard1LaSIE, UMR-CNRS 7356, Université de La Rochelle, avenue Michel Crépeau, 17042 La Rochelle cedex 1, France.LaSIE, UMR-CNRS 7356, Université de La Rochelle, avenue Michel Crépeau, 17042 La Rochelle cedex 1, France.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.https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.200/Distortion of nonaxisymmetric capillary bridgesMean and Gaussian curvatures impactEuler characteristicGeneralized Young–Laplace equationBending effectsFenchel’s theorem in differential geometryGauss–Bonnet TheoremGeodesic curvatureBending stressInfluence of the contact angles |
| spellingShingle | Millet, Olivier Gagneux , Gérard A direct relation between bending energy and contact angles for capillary bridges Comptes Rendus. Mécanique 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 |
| title | A direct relation between bending energy and contact angles for capillary bridges |
| title_full | A direct relation between bending energy and contact angles for capillary bridges |
| title_fullStr | A direct relation between bending energy and contact angles for capillary bridges |
| title_full_unstemmed | A direct relation between bending energy and contact angles for capillary bridges |
| title_short | A direct relation between bending energy and contact angles for capillary bridges |
| title_sort | direct relation between bending energy and contact angles for capillary bridges |
| topic | 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 |
| url | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.200/ |
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