Open Access
June 2009 The FENE Model for Viscoelastic Thin Film Flows
Laurent Chupin
Methods Appl. Anal. 16(2): 217-262 (June 2009).


In this article, we are interested in the behavior of the FENE (Finitely Extensible Non-Linear Elastic), a constitutive relation within an almost shear flow. As this relation results from a microscopic analysis of the polymer chains, the study presented here is based on new results from the Fokker-Planck equation. Thin flows are generally considered like almost one-dimensional flows and almost shear flows. The study of the FENE model makes it possible to understand which could be the dominant terms in the equations coupling this rheology (the FENE model) and the hydrodynamic (via the conservation equations). Some possible examples of applications are given at the end of this article, for example, in the field of lubrication, the phenomena of boundary layers, the industry of the nanotechnology, biology or Shallow-Water equations.


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Laurent Chupin. "The FENE Model for Viscoelastic Thin Film Flows." Methods Appl. Anal. 16 (2) 217 - 262, June 2009.


Published: June 2009
First available in Project Euclid: 2 November 2009

zbMATH: 1185.35185
MathSciNet: MR2563748

Primary: 35J70 , 35K10 , 35K55 , 35Q35 , 74D10 , 74H40 , 76A05 , 76A10 , 76A20 , 76D08 , 76N20 , 78M35

Keywords: boundary layer , Degenerate elliptic equation , FENE model , Fokker-Planck equation , long time behavior , lubrication , microfluidic , non-coercive elliptic equation , thin films , viscoelastic fluid

Rights: Copyright © 2009 International Press of Boston

Vol.16 • No. 2 • June 2009
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