Comptes Rendus
Singularité anguleuse d'une ligne de contact en mouvement sur un substrat solide
Comptes Rendus. Physique, Volume 3 (2002) no. 1, pp. 103-110.

A suffisamment haut nombre capillaire Ca, une ligne de contact dynamique qui recule sur une surface partiellement mouillante prend une forme anguleuse. Nous montrons que l'écoulement dans le « coin » liquide correspond à une solution de similarité des équations de la lubrification gouvernant les films minces, dans laquelle l'interface peut être assimilée à un cône. La pente Ω de l'interface définie dans son plan de symétrie est liée à l'angle au sommet du coin 2φ par la relation approchée Ω3(3/2)Catan2ϕ. Nous suggérons également une origine possible de la déposition de gouttelettes à partir de la pointe, qui survient à plus haut Ca quand φ atteint π/6.

In conditions of partial wetting and at sufficiently high capillary number Ca, a dynamic contact line that recedes on a solid surface assumes a ‘saw-tooth’ shape. We show that the flow inside this liquid ‘corner’ is a similarity solution of the lubrication equations governing steady thin-film flows in which the free surface is cone shaped. The interface slope Ω defined in its symmetry plane is linked to the corner angle 2φ by the approximate relationship Ω3(3/2)Catan2ϕ. We also suggest a possible explanation of droplet emission from the corner which occurs when φ reaches π/6.

Reçu le :
Révisé le :
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DOI : 10.1016/S1631-0705(02)01288-4
Mots-clés : mouillage, démouillage, lignes de contact, écoulement en film, enduisage, singularités, théorie de la lubrification
Keywords: wetting, dewetting, contact lines, film flows, singularities, lubrication theory

Howard A. Stone 1 ; Laurent Limat 2 ; Stephen K. Wilson 3 ; J.-M. Flesselles 2 ; Thomas Podgorski 2

1 Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
2 Laboratoire de physique et de mécanique des milieux hétérogènes, UMR 7636 du CNRS, ESPCI, 10, rue Vauquelin, 75005 Paris, France
3 Department of Mathematics, University of Strathclyde, Glasgow G1 1XH, United Kingdom
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     title = {Singularit\'e anguleuse d'une ligne de contact en mouvement sur un substrat solide},
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Howard A. Stone; Laurent Limat; Stephen K. Wilson; J.-M. Flesselles; Thomas Podgorski. Singularité anguleuse d'une ligne de contact en mouvement sur un substrat solide. Comptes Rendus. Physique, Volume 3 (2002) no. 1, pp. 103-110. doi : 10.1016/S1631-0705(02)01288-4. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/S1631-0705(02)01288-4/

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