Comptes Rendus
Bending effects distorting axisymmetric capillary bridges. Generalized Young–Laplace equation and associated capillary forces
Comptes Rendus. Mécanique, Volume 351 (2023) no. S2, pp. 115-123.

This study proposes a theoretical contribution to the problem of the various distortions affecting axisymmetric capillary bridges, due to gravity or to bending effects linked to the Gaussian curvature. We deduce a clear hierarchization of effects between various reference configurations and put in a prominent position an exact first integral for the Young–Laplace equations, classical or generalized. These relationships are taken advantage of to obtain the theoretical expression of the varying inter-particle force, quantified effects of flexural strength. Finally, we establish a generalization of the classical “gorge method” to calculate accurately the capillary force of a profile subjected to distorsion due to bending when the gravity effects are negligible or not taken into account.

Cette étude propose une contribution théorique au problème des distorsions affectant les ponts capillaires axisymétriques, dues à la gravité ou aux effets de flexion liés à la courbure gaussienne. Nous en déduisons une hiérarchisation claire de ces effets pour différentes configurations de référence et nous mettons en évidence une intégrale première exacte pour les équations de Young–Laplace, classiques ou généralisées. Ces relations sont mises à profit pour obtenir une expression théorique de la force capillaire, tenant compte des effets de flexion, qui n’est plus constante. Enfin, nous établissons une généralisation de la “gorge method” classique pour calculer avec précision la force capillaire d’un doublet capillaire soumis à une distorsion due aux effets de flexion lorsque les effets de la gravité sont négligeables ou non pris en compte.

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DOI: 10.5802/crmeca.196
Classification: 49N45, 53A10, 58E12, 74F10, 74G05, 74G15
Keywords: Distortion of capillary bridges, Mean and Gaussian curvatures impact, Generalized Young–Laplace equation, Bending effects
Mot clés : Distorsion des ponts capillaires, Courbure moyenne et courbure gaussienne, Équation de Young–Laplace généralisée, Effets de flexion

Olivier Millet 1; Gérard Gagneux 1

1 LaSIE, UMR-CNRS 7356, Université de La Rochelle, avenue Michel Crépeau,17042 La Rochelle cedex 1, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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     title = {Bending effects distorting axisymmetric capillary bridges. {Generalized} {Young{\textendash}Laplace} equation and associated capillary forces},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {115--123},
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Olivier Millet; Gérard Gagneux. Bending effects distorting axisymmetric capillary bridges. Generalized Young–Laplace equation and associated capillary forces. Comptes Rendus. Mécanique, Volume 351 (2023) no. S2, pp. 115-123. doi : 10.5802/crmeca.196. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.196/

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