From the phan–thien–tanner/oldroyd-B non-newtonian model to the double shear thining rabinowisch thin film model / Guy Bayada in Transactions of the ASME . Journal of tribology, Vol. 133 N° 3 (Juillet 2011)  

Public ISBD [article]  inTransactions of the ASME . Journal of tribology > Vol. 133 N° 3 (Juillet 2011) . - 13 p. Titre : From the phan–thien–tanner/oldroyd-B non-newtonian model to the double shear thining rabinowisch thin film model Type de document : texte imprimé Auteurs : Guy Bayada, Auteur ; Laurent Chupin, Auteur ; Sébastien Martin, Auteur Année de publication : 2012 Article en page(s) : 13 p. Note générale : Tribology Langues : Anglais (eng) Mots-clés : Convection Elongation Film flow Liquid films Non-Newtonian Shear Slip Viscosity Index. décimale : 621.5 Energie pneumatique. Machinerie et outils. Réfrigération Résumé : In this paper, an asymptotic expansion is used to derive a description of Phan–Tien– Tanner (PTT)/Oldroyd-B flows in the thin film situation without the classical “upper convective maxwell”(UCM) assumption. We begin with a short presentation of the Phan–Thien–Tanner/Oldroyd-B models, which introduce viscoelastic effects in a solute–solvent mixture. The three-dimensional flow is described using five parameters, namely the Deborah number (De) (or the relaxation parameter lambda), the viscosity ratio r, the bulk fluid viscosity eta, the material slip parameter a related to the “convected derivative” and an elongation number kappa. 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 kappa 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. DEWEY : 621.5 ISSN : 0742-4787 En ligne : http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JOTRE900013 [...] [article] From the phan–thien–tanner/oldroyd-B non-newtonian model to the double shear thining rabinowisch thin film model [texte imprimé] / Guy Bayada, Auteur ; Laurent Chupin, Auteur ; Sébastien Martin, Auteur . - 2012 . - 13 p. Tribology Langues : Anglais (eng) in Transactions of the ASME . Journal of tribology > Vol. 133 N° 3 (Juillet 2011) . - 13 p. Mots-clés : Convection Elongation Film flow Liquid films Non-Newtonian Shear Slip Viscosity Index. décimale : 621.5 Energie pneumatique. Machinerie et outils. Réfrigération Résumé : In this paper, an asymptotic expansion is used to derive a description of Phan–Tien– Tanner (PTT)/Oldroyd-B flows in the thin film situation without the classical “upper convective maxwell”(UCM) assumption. We begin with a short presentation of the Phan–Thien–Tanner/Oldroyd-B models, which introduce viscoelastic effects in a solute–solvent mixture. The three-dimensional flow is described using five parameters, namely the Deborah number (De) (or the relaxation parameter lambda), the viscosity ratio r, the bulk fluid viscosity eta, the material slip parameter a related to the “convected derivative” and an elongation number kappa. 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 kappa 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. DEWEY : 621.5 ISSN : 0742-4787 En ligne : http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JOTRE900013 [...]

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