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Analytical solutions to the gravity-driven rain-fed free-surface Stokes equations
[Solutions analytiques aux équations de Stokes à surface libre alimentées par la pluie et sous l’effet de la gravité]
Simeon Djambov1, 2 orcid  ; François Gallaire1 orcid
1Laboratory of Fluid Mechanics and Instabilities, EPFL, Lausanne CH-1015, Switzerland
2LadHyX, CNRS, École Polytechnique, Institut Polytechnique de Paris, 91128 Palaiseau cedex, France
Comptes Rendus. Mécanique, Volume 354 (2026), pp. 451-459

The present paper concerns the continuously-fed, gravity-driven film flows of rainwater over hemispheres and semicircular cylinders. We extend previous lubrication results to arbitrarily thick films, while remaining in the creeping flow limit. We show that the predictions of uniform thickness profiles, amusingly, remain qualitatively accurate under these relaxed assumptions.

Le présent article traite des écoulements en film engendrés par la gravité et alimentés par la pluie sur des hémisphères et des cylindres semi-circulaires. Nous étendons des résultats précédents, obtenus dans le cadre de la théorie de lubrification, à des films d’épaisseur arbitraire, tout en restant dans la limite des écoulements lents. Nous montrons que les prédictions de profils d’épaisseur uniformes restent qualitativement exactes dans le cadre de ces hypothèses relaxées.

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Révisé le :
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DOI : 10.5802/crmeca.365
Keywords: Thin film, free surface, rain
Mots-clés : Film mince, surface libre, pluie

Simeon Djambov  1 , 2   ; François Gallaire  1

1 Laboratory of Fluid Mechanics and Instabilities, EPFL, Lausanne CH-1015, Switzerland
2 LadHyX, CNRS, École Polytechnique, Institut Polytechnique de Paris, 91128 Palaiseau cedex, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
Simeon Djambov; François Gallaire. Analytical solutions to the gravity-driven rain-fed free-surface Stokes equations. Comptes Rendus. Mécanique, Volume 354 (2026), pp. 451-459. doi: 10.5802/crmeca.365
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     title = {Analytical solutions to the gravity-driven rain-fed free-surface {Stokes} equations},
     journal = {Comptes Rendus. M\'ecanique},
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     year = {2026},
     publisher = {Acad\'emie des sciences, Paris},
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     doi = {10.5802/crmeca.365},
     language = {en},
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