[Distorsion des ponts capillaires axisymétriques due aux effets de flexion. Équation de Young-Laplace généralisée et forces capillaires associée]
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.
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.
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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
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@article{CRMECA_2023__351_S2_115_0,
author = {Olivier Millet and G\'erard Gagneux},
title = {Bending effects distorting axisymmetric capillary bridges. {Generalized} {Young{\textendash}Laplace} equation and associated capillary forces},
journal = {Comptes Rendus. M\'ecanique},
pages = {115--123},
publisher = {Acad\'emie des sciences, Paris},
volume = {351},
number = {S2},
year = {2023},
doi = {10.5802/crmeca.196},
language = {en},
}
TY - JOUR AU - Olivier Millet AU - Gérard Gagneux TI - Bending effects distorting axisymmetric capillary bridges. Generalized Young–Laplace equation and associated capillary forces JO - Comptes Rendus. Mécanique PY - 2023 SP - 115 EP - 123 VL - 351 IS - S2 PB - Académie des sciences, Paris DO - 10.5802/crmeca.196 LA - en ID - CRMECA_2023__351_S2_115_0 ER -
%0 Journal Article %A Olivier Millet %A Gérard Gagneux %T Bending effects distorting axisymmetric capillary bridges. Generalized Young–Laplace equation and associated capillary forces %J Comptes Rendus. Mécanique %D 2023 %P 115-123 %V 351 %N S2 %I Académie des sciences, Paris %R 10.5802/crmeca.196 %G en %F CRMECA_2023__351_S2_115_0
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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