From the Phan-Thien Tanner / Oldroyd-B non-Newtonian model to the double shear thining Rabinowisch thin film model

Guy Bayada; Laurent Chupin; Sébastien Martin

hal-00552059, version 1

From the Phan-Thien Tanner / Oldroyd-B non-Newtonian model to the double shear thining Rabinowisch thin film model

Guy Bayada ^1, 2, Laurent Chupin () ³, Sébastien Martin () ⁴

1 : Institut Camille Jordan (ICJ)
CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon Bât. Jean Braconnier n° 101 43 Bd du 11 novembre 1918 69622 VILLEURBANNE CEDEX France
2 : Laboratoire de Mécanique des Contacts et des Structures (LaMCoS)
http://lamcos.insa-lyon.fr/
CNRS : UMR5259 – Institut National des Sciences Appliquées (INSA) - Lyon Bâtiment Jean d'Alembert 18-20, rue des Sciences F69621 VILLEURBANNE CEDEX France
3 : Laboratoire de Mathématiques
http://math.univ-bpclermont.fr/index.html
CNRS : UMR6620 – Université Blaise Pascal - Clermont-Ferrand II 24 avenue des Landais 63177 AUBIERE CEDEX France
4 : Laboratoire de Mathématiques d'Orsay (LM-Orsay)
http://www.math.u-psud.fr
CNRS : UMR8628 – Université Paris XI - Paris Sud France

Références bibliographiques

Liste des fichiers attachés à ce document :

PDF

asme-bcm-final.pdf

(2.3 MB)

hal-00552059, version 1
http://hal.archives-ouvertes.fr/hal-00552059
oai:hal.archives-ouvertes.fr:hal-00552059
Contributeur : Sébastien Martin <>
Soumis le : Mercredi 5 Janvier 2011, 12:43:22
Dernière modification le : Mercredi 5 Janvier 2011, 13:20:37

Voir la fiche concise

Documents associés

PDF :

Exporter

Bibtex EndNote TEI RefWorks

%% hal-00552059, version 1
%% http://hal.archives-ouvertes.fr/hal-00552059
@unpublished{bayada:hal-00552059,
    hal_id = {hal-00552059},
    url = {http://hal.archives-ouvertes.fr/hal-00552059},
    title = {{From the Phan-Thien Tanner / Oldroyd-B non-Newtonian model to the double shear thining Rabinowisch thin film model}},
    author = {Bayada, Guy and Chupin, Laurent and Martin, S{\'e}bastien},
    abstract = {{In this paper, an asymptotic expansion is used to derive a description of Phan-Tien Tanner\~/ Oldroyd-B flows in the thin film situation without the classical "Upper Convective Maxwell'' assumption. We begin with a short presentation of the Phan-Thien Tanner\~/ Oldroyd-B models which introduce viscoelastic effects in a solute-solvant mixture. The three dimensional flow is described using five parameters, namely the Deborah number (or the relaxation parameter), the viscosity ratio, the bulk fluid viscosity, the material slip parameter related to the "convected derivative'' and an elongation number. Then we focus on the thin film assumption and the related asymptotic analysis that allows us to derive a reduced model. A perturbation procedure for "not too small'' values of the elongation number allows us to obtain further results such as an asymptotic "effective viscosity / shear rate'' law which appears to be a perturbation of the double Rabinowisch model whose parameters are completely defined by those of the original three dimensional model. And last a numerical procedure is proposed based on a penalized Uzawa method, to compute the corresponding solution. This algorithm can also be used for any generalized double Newtonian shear thinning Carreau law.}},
    language = {Anglais},
    affiliation = {Institut Camille Jordan - ICJ , Laboratoire de M{\'e}canique des Contacts et des Structures - LaMCoS , Laboratoire de Math{\'e}matiques , Laboratoire de Math{\'e}matiques d'Orsay - LM-Orsay},
    pdf = {http://hal.archives-ouvertes.fr/hal-00552059/PDF/asme-bcm-final.pdf},
}

<?xml version="1.0" encoding="UTF-8"?>
<listBibl xmlns="http://www.tei-c.org/ns/1.0" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML">
<listBibl type="article"><head>Documents sans référence de publication (Preprint)</head>
<biblStruct type="article" xml:id="hal-00552059"><analytic>
<author><persName><forename>Guy</forename><surname>Bayada</surname></persName>
<affiliation>
<orgName type="laboratory">ICJ</orgName>
<orgName type="team">Institut Camille Jordan</orgName>
<country>FR</country>
<orgName type="institution">CNRS : UMR5208</orgName>
<orgName type="institution">Université Claude Bernard - Lyon I</orgName>
<orgName type="institution">Ecole Centrale de Lyon</orgName>
<orgName type="institution">Institut National des Sciences Appliquées (INSA) - Lyon</orgName>
</affiliation>
<affiliation>
<orgName type="laboratory">LaMCoS</orgName>
<orgName type="team">Laboratoire de Mécanique des Contacts et des Structures</orgName>
<country>FR</country>
<orgName type="institution">CNRS : UMR5259</orgName>
<orgName type="institution">Institut National des Sciences Appliquées (INSA) - Lyon</orgName>
</affiliation>
</author>
<author><persName><forename>Laurent</forename><surname>Chupin</surname></persName>
<affiliation>
<orgName type="team">Laboratoire de Mathématiques</orgName>
<country>FR</country>
<orgName type="institution">CNRS : UMR6620</orgName>
<orgName type="institution">Université Blaise Pascal - Clermont-Ferrand II</orgName>
</affiliation>
</author>
<author><persName><forename>Sébastien</forename><surname>Martin</surname></persName>
<affiliation>
<orgName type="laboratory">LM-Orsay</orgName>
<orgName type="team">Laboratoire de Mathématiques d'Orsay</orgName>
<country>FR</country>
<orgName type="institution">CNRS : UMR8628</orgName>
<orgName type="institution">Université Paris XI - Paris Sud</orgName>
</affiliation>
</author>
<title type="main" level="a">From the Phan-Thien Tanner / Oldroyd-B non-Newtonian model to the double shear thining Rabinowisch thin film model</title></analytic><monogr><imprint/></monogr><idno type="HALid">http://hal.archives-ouvertes.fr/hal-00552059</idno><idno type="HALFile">http://hal.archives-ouvertes.fr/hal-00552059/PDF/asme-bcm-final.pdf</idno></biblStruct>
</listBibl>
</listBibl>