Comptes Rendus
no. S2
A direct relation between bending energy and contact angles for capillary bridges
[Une relation directe entre l’énergie de flexion et les angles de contact pour les ponts capillaires]
Olivier Millet1 ; Gérard Gagneux 1 
1 LaSIE, UMR-CNRS 7356, Université de La Rochelle, avenue Michel Crépeau, 17042 La Rochelle cedex 1, France.
Comptes Rendus. Mécanique, Volume 351 (2023) no. S2, pp. 125-137.

L’objet didactique de ces développements basés sur la géométrie différentielle des courbes et des surfaces est de présenter des stratégies mathématiques adaptées à l’étude des ponts capillaires. Le fil conducteur est de pouvoir calculer avec précision, dans n’importe quelle situation, la contrainte de flexion de la surface libre d’un pont capillaire, représentée mathématiquement par l’intégrale de courbure de Gauss (courbure totale) de la surface libre intervenant dans l’équation de Young–Laplace généralisée. Nous établissons en particulier un résultat très général suivant lequel la résultante de l’énergie de flexion est directement liée aux angles de mouillage au niveau de la ligne de contact.

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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DOI : 10.5802/crmeca.200
Classification : 49N45, 53A10, 58E12, 74F10, 74G05, 74G15, 53Z05
Keywords: 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
Mot clés : Distorsion des ponts capillaires non axisymétriques, impact des courbures moyennes et gaussiennes, caractéristique d’Euler, équation de Young–Laplace généralisée, effets de flexion, théorème de Fenchel en géométrie différentielle, théorème de Gauss–Bonnet, courbure géodésique, contrainte de flexion, influence des angles de contact
Olivier Millet 1 ; Gérard Gagneux  1

1 LaSIE, UMR-CNRS 7356, Université de La Rochelle, avenue Michel Crépeau, 17042 La Rochelle cedex 1, France.
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     year = {2023},
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Olivier Millet; Gérard Gagneux . A direct relation between bending energy and contact angles for capillary bridges. Comptes Rendus. Mécanique, Volume 351 (2023) no. S2, pp. 125-137. doi : 10.5802/crmeca.200. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.200/

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