Comptes Rendus
Partial Differential Equations
The FENE viscoelastic model and thin film flows
Comptes Rendus. Mathématique, Volume 347 (2009) no. 17-18, pp. 1041-1046.

This Note has as objective to determine, in a rigorous way, a simplified expression of the constitutive law for a visco-elastic fluid of FENE type in thin domains. The proof uses the FENE model behavior for long times and the existence of a stationary solution for this behavioral law. Some possible applications of this study are then briefly described in the domains of lubrication, blood flow, microfluidic, boundary layers, ….

L'objet de cette Note est de déterminer, de manière rigoureuse, une expression simplifiée de la loi comportementale d'un fluide visco-élastique de type FENE dans un écoulement en domaine mince. Le principe de la preuve utilise à la fois le comportement en temps long d'un écoulement FENE et l'existence d'une solution stationnaire à ce type de loi. On décrit brièvement quelques applications possibles de cette étude : dans les domaines de la lubrification, des écoulements sanguins, de la microfluidique, des couches limites, ….

Published online:
DOI: 10.1016/j.crma.2009.06.014

Laurent Chupin 1

1 Institut Camille Jordan (CNRS UMR 5208), 43, boulevard du 11 novembre 1918, 69622 Villeurbanne cedex, France
     author = {Laurent Chupin},
     title = {The {FENE} viscoelastic model and thin film flows},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1041--1046},
     publisher = {Elsevier},
     volume = {347},
     number = {17-18},
     year = {2009},
     doi = {10.1016/j.crma.2009.06.014},
     language = {en},
AU  - Laurent Chupin
TI  - The FENE viscoelastic model and thin film flows
JO  - Comptes Rendus. Mathématique
PY  - 2009
SP  - 1041
EP  - 1046
VL  - 347
IS  - 17-18
PB  - Elsevier
DO  - 10.1016/j.crma.2009.06.014
LA  - en
ID  - CRMATH_2009__347_17-18_1041_0
ER  - 
%0 Journal Article
%A Laurent Chupin
%T The FENE viscoelastic model and thin film flows
%J Comptes Rendus. Mathématique
%D 2009
%P 1041-1046
%V 347
%N 17-18
%I Elsevier
%R 10.1016/j.crma.2009.06.014
%G en
%F CRMATH_2009__347_17-18_1041_0
Laurent Chupin. The FENE viscoelastic model and thin film flows. Comptes Rendus. Mathématique, Volume 347 (2009) no. 17-18, pp. 1041-1046. doi : 10.1016/j.crma.2009.06.014.

[1] J.-W. Barrett; C. Schwab; E. Süli Existence of global weak solutions for some polymeric flow models, Math. Models Methods Appl. Sci., Volume 15 (2005) no. 6, pp. 939-983

[2] G. Bayada; M. Chambat The transition between the Stokes equations and the Reynolds equation: A mathematical proof, Appl. Math. Optim., Volume 14 (1986), pp. 73-93

[3] R.-B. Bird; O. Hassager; R.C. Armstrong; C.F. Curtiss Dynamics of Polymeric Fluids, vol. 2, Kinetic Theory, John Wiley and Sons, New York, 1977

[4] L. Chupin, Some results about the FENE viscoelastic model, Methods and Applications of Analysis (2009), in press

[5] J. Droniou Non-coercive linear elliptic problems, Potential Anal., Volume 17 (2002) no. 2, pp. 181-203

[6] B. Jourdain, T. Lelièvre, Mathematical analysis of a stochastic differential equation arising in the micro–macro modelling of polymeric fluids, in: Probabilistic Methods in Fluids, Proceedings of the Swansea 2002 Workshop, 2003, pp. 205–223

[7] B. Jourdain; C. Le Bris; T. Lelièvre; F. Otto Long-time asymptotics of a multiscale model for polymeric fluid flows, Arch. Rational Mech. Anal., Volume 181 (2006) no. 1, pp. 97-148

[8] P.-L. Lions; N. Masmoudi Global existence of weak solutions to micro–macro models, C. R. Math. Acad. Sci. Paris, Volume 345 (2007) no. 1, pp. 15-20

[9] H.C. Öttinger Stochastic Processes in Polymeric Fluids, Springer-Verlag, Berlin, 1996

[10] H. Schlichting Boundary-Layer Theory, McGraw–Hill Series in Mechanical Engineering, McGraw–Hill Book Co., Inc./Verlag G. Braun, New York, Toronto, London/Karlsruhe, 1960 (xx+647 pp)

[11] H. Zhang; P. Zhang Local existence for the FENE-Dumbbell model of polymeric fluids, Arch. Rational Mech. Anal., Volume 181 (2006), pp. 373-400

Cited by Sources:

Comments - Policy