Comptes Rendus
no. 11-12
On the incorporation of surface tension in finite-element calculations
Jean-Baptiste Leblond1  ; Hussein Amin El Sayed2 ; Jean-Michel Bergheau2
1 UPMC, Université Paris-6, UMR 7190, Institut Jean-Le-Rond-dʼAlembert, Tour 65–55, 4, place Jussieu, 75252 Paris cedex 05, France
2 Université de Lyon, ENISE, LTDS, UMR 5513 CNRS, 58, rue Jean-Parot, 42023 Saint-Étienne cedex 02, France
Comptes Rendus. Mécanique, Volume 341 (2013) no. 11-12, pp. 770-775.

The aim of this paper is to propose a new method for introduction of surface tension effects (including both the “curvature effect” and the “Marangoni effect”) into finite-element computations. Usual methods consider the loads induced by surface tension onto the fluid. We propose instead to directly model surface tension itself through the introduction into the mesh of surfacic elements having a planar hydrostatic state of stress, and representing a fictitious tight membrane stuck onto the interface. Such a method is very easy to program and very efficient. Two numerical examples are provided to illustrate this efficiency. The first pertains to a problem of small oscillations of a liquid due to combined gravity and surface tension, and illustrates the effect of the normal component of the surface tension load (curvature effect). The second pertains to a problem involving a surfacic gradient of temperature, and illustrates the effect of the tangential component of the surface tension load (Marangoni effect).

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2013.10.004
Mots clés : Surface tension, Finite-element method, Membrane elements

Jean-Baptiste Leblond 1 ; Hussein Amin El Sayed 2 ; Jean-Michel Bergheau 2

1 UPMC, Université Paris-6, UMR 7190, Institut Jean-Le-Rond-dʼAlembert, Tour 65–55, 4, place Jussieu, 75252 Paris cedex 05, France
2 Université de Lyon, ENISE, LTDS, UMR 5513 CNRS, 58, rue Jean-Parot, 42023 Saint-Étienne cedex 02, France 
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Jean-Baptiste Leblond; Hussein Amin El Sayed; Jean-Michel Bergheau. On the incorporation of surface tension in finite-element calculations. Comptes Rendus. Mécanique, Volume 341 (2013) no. 11-12, pp. 770-775. doi : 10.1016/j.crme.2013.10.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2013.10.004/

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