Geodesic
A conservative saint-venant type model to describe the dynamics of thin partially wetting films with regularized forces at the contact line
Pierre Trontin1 ; Julien Lallement1 ; Philippe Villedieu1
1 ONERA/DMPE, Université de Toulouse, F-31055 Toulouse, France
ESAIM. Proceedings, Tome 69 (2020), pp. 79-103.

Voir la notice de l'article provenant de la source EDP Sciences

This paper deals with the numerical simulation of thin liquid films flowing on partially wetting solid substrates. A 2D Saint-Venant like model is proposed. Its originality lies in the conservative formulation of the capillary forces and in the model used for the disjoining pressure that accounts for the contact line capillary forces. A finite volume scheme is proposed for the resolution of the system and various numerical examples are presented and discussed. In particular, when the mesh resolution is fine enough, the model is proved to be able to predict correctly the spreading of a film with the exact contact angle in the vicinity of the contact line. When the mesh size is larger than the film thickness (which could be the case for many industrial applications), it is of course no longer possible to recover the contact angle. However, the model is proved to correctly predict the spreading of the film. This important feature is related to the thermodynamic consistency of the model in the sense that the latter ensures by construction the decrease of the film total free energy in the absence of external driving forces.
DOI : 10.1051/proc/202069079

Pierre Trontin 1 ; Julien Lallement 1 ; Philippe Villedieu 1

1 ONERA/DMPE, Université de Toulouse, F-31055 Toulouse, France 
@article{EP_2020_69_a6,
     author = {Pierre Trontin and Julien Lallement and Philippe Villedieu},
     title = {A conservative saint-venant type model to describe the dynamics of thin partially wetting films with regularized forces at the contact line},
     journal = {ESAIM. Proceedings},
     pages = {79--103},
     publisher = {mathdoc},
     volume = {69},
     year = {2020},
     doi = {10.1051/proc/202069079},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/202069079/}
}
TY  - JOUR
AU  - Pierre Trontin
AU  - Julien Lallement
AU  - Philippe Villedieu
TI  - A conservative saint-venant type model to describe the dynamics of thin partially wetting films with regularized forces at the contact line
JO  - ESAIM. Proceedings
PY  - 2020
SP  - 79
EP  - 103
VL  - 69
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1051/proc/202069079/
DO  - 10.1051/proc/202069079
LA  - en
ID  - EP_2020_69_a6
ER  - 
%0 Journal Article
%A Pierre Trontin
%A Julien Lallement
%A Philippe Villedieu
%T A conservative saint-venant type model to describe the dynamics of thin partially wetting films with regularized forces at the contact line
%J ESAIM. Proceedings
%D 2020
%P 79-103
%V 69
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1051/proc/202069079/
%R 10.1051/proc/202069079
%G en
%F EP_2020_69_a6
Pierre Trontin; Julien Lallement; Philippe Villedieu. A conservative saint-venant type model to describe the dynamics of thin partially wetting films with regularized forces at the contact line. ESAIM. Proceedings, Tome 69 (2020), pp. 79-103. doi : 10.1051/proc/202069079. http://geodesic.mathdoc.fr/articles/10.1051/proc/202069079/

Cité par Sources :