• français
    • English
    français
  • Login
Help
View Item 
  •   Home
  • Laboratoire Angevin de Mécanique, Procédés et InnovAtion (LAMPA)
  • View Item
  • Home
  • Laboratoire Angevin de Mécanique, Procédés et InnovAtion (LAMPA)
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Effect of the inverse Langevin approximation on the solution of the Fokker-Planck equation of non-linear dilute polymer

Article dans une revue avec comité de lecture
Author
ccAMMAR, Amine
211916 Laboratoire Angevin de Mécanique, Procédés et InnovAtion [LAMPA]

URI
http://hdl.handle.net/10985/11141
DOI
10.1016/j.jnnfm.2016.02.008
Date
2016
Journal
Journal of Non-Newtonian Fluid Mechanics

Abstract

The Langevin function is defined by L (x ) = coth (x ) −1 /x . Its inverse is useful for many applications and especially for polymer science. As the inverse exact expression has no analytic representation, many ap- proximations have been established. The most famous approximation is the one traditionally used for the finitely extensible non-linear elastic (FENE) dumbbell model in which the inverse is approximated by L −1 (y ) = 3 y/ (1 −y 2 ) . Recently Martin Kröger has published a paper entitled ‘Simple, admissible and accurate approximations of the inverse Langevin and Brillouin functions, relevant for strong polymer de- formation and flows’ (Kröger, 2015) in which he proposed approximations with very reduced error in relation to the numeric inverse of the Langevin function. The question we aim to analyze in this short communication is: when one uses the traditional approximation rather than the more accurate one pro- posed by Kröger is that really significant regarding the value of the probability distribution function (PDF) in the frame work of a kinetic theory simulation? If yes when we move to the upper scale by evaluating the value of the stress, can we observe a significant difference? By making some simple 1D simulations in homogeneous extensional flow it is demonstrated in this short communication that the PDF prediction within kinetic theory framework as well as the macroscopic stress value are both affected by the quality of the approximation.

Files in this item

Name:
LAMPA_JNNFM_2016_AMMAR.pdf
Size:
665.4Kb
Format:
PDF
Description:
Article principal
View/Open

Collections

  • Laboratoire Angevin de Mécanique, Procédés et InnovAtion (LAMPA)

Related items

Showing items related by title, author, creator and subject.

  • A reduced model to simulate the damage in composite laminates under low velocity impact 
    Article dans une revue avec comité de lecture
    METOUI, Sondes; ccPRULIERE, Etienne; ccAMMAR, Amine; ccDAU, Frédéric (Elsevier, 2018)
    This article presents an efficient numerical strategy to simulate the damage in composite laminates under low velocity impact. The proposed method is based on a separated representation of the solution in the context of ...
  • On the solution of the heat equation in very thin tapes 
    Article dans une revue avec comité de lecture
    ccPRULIERE, Etienne; ccCHINESTA SORIA, Francisco; ccAMMAR, Amine; LEYGUE, Adrien; POITOU, Arnaud (Elsevier, 2012)
    This paper addresses two issues usually encountered when simulating thermal processes in forming processes involving tape-type geometries, as is the case of tape or tow placement, surface treatments, / The first issue ...
  • Reduced modelling computation of layered soil's harmonic green functions 
    Article dans une revue avec comité de lecture
    ccOTHMAN, Ramzi; ccAMMAR, Amine; ALMITANI, Khalid H. (Elsevier BV, 2020-09)
    Ground-borne vibrations are disturbing to human beings. In order to model and reduce these vibrations, the calculation of the harmonic Green’s-functions of the soil is highly required since the most effective numerical solution ...
  • Introduction for the special Issue: statistical fluid dynamics 
    Article dans une revue avec comité de lecture
    ccAMMAR, Amine; ccVALETTE, Rudy; ccCHINESTA SORIA, Francisco (MDPI AG, 2022-06)
    Characterizing complex material consists in establishing the relationship between flow rheology during forming processes and the induced micro-structural state that affects directly the final mechanical properties of the ...
  • Parametric Analysis of Thick FGM Plates Based on 3D Thermo-Elasticity Theory: A Proper Generalized Decomposition Approach 
    Article dans une revue avec comité de lecture
    ccKAZEMZADEH-PARSI, Mohammad-Javad; ccAMMAR, Amine; ccCHINESTA SORIA, Francisco (2023)
    In the present work, the general and well-known model reduction technique, PGD (Proper Generalized Decomposition), is used for parametric analysis of thermo-elasticity of FGMs (Functionally Graded Materials). The FGMs have ...

Browse

All SAMCommunities & CollectionsAuthorsIssue DateCenter / InstitutionThis CollectionAuthorsIssue DateCenter / Institution

Newsletter

Latest newsletterPrevious newsletters

Statistics

Most Popular ItemsStatistics by CountryMost Popular Authors

ÉCOLE NATIONALE SUPERIEURE D'ARTS ET METIERS

  • Contact
  • Mentions légales

ÉCOLE NATIONALE SUPERIEURE D'ARTS ET METIERS

  • Contact
  • Mentions légales