| Titre : | From the phan–thien–tanner/oldroyd-B non-newtonian model to the double shear thining rabinowisch thin film model (2012) |
| Auteurs : | Guy Bayada, Auteur ; Laurent Chupin, Auteur ; Sébastien Martin, Auteur |
| Type de document : | Article : texte imprimé |
| Dans : | Transactions of the ASME . Journal of tribology (Vol. 133 N° 3, Juillet 2011) |
| Article en page(s) : | 13 p. |
| Note générale : | Tribology |
| Langues : | Anglais |
| Index. décimale : | 621.5 (Energie pneumatique. Machinerie et outils. Réfrigération) |
| Tags : | Convection Elongation Film flow Liquid films Non-Newtonian Shear Slip Viscosity |
| 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=JOTRE9000133000003031802000001&idtype=cvips&gifs=Yes&ref=no |
