Valette, Rudy (2001) Stability study of the Poiseuille flow of viscoelastic fluids. Application to the coextrusion process. PhD thesis Sciences et Génie des Matériaux, ENSMP - CEMEF Centre de Mise en Forme des Matériaux, ENSMP.

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Abstract

The flow motion in the coextrusion process looks like the multilayer Poiseuille flow of viscoelastic fluids. We have experimentally analyzed the influence of operating conditions on the stability of two-layer polyethylene/polystyrene flow. We have developped a longwave stability analysis of the flow for White-Metzner fluids. This study gave a partial agreement with experimental results. We have then showed that the instability is convective by using two experimental devices: a coextrusion die that can be dismantled and a transparent die. We have then developped two numerical tools in order to describe the convective nature of the instability: a direct numerical simulation for Maxwell fluids and a linear spatial stability analysis for White-Metzner fluids. Such a tool gave good agreement with experimental results.

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Table of content

1 Introduction
1.1 Le procédé de coextrusion et ses limites
1.2 Etude des instabilités interfaciales
2 Vers une approche "produit": la transition stable/instable dans le procédé
2.1 Le procédé de coextrusion: étude bibliographique
2.2 Caractérisation rhéologique en cisaillement des produits
2.2.1 Méthodes de mesure
2.2.2 Le polyéthylène 1003 FE 23
2.2.3 Le polystyrène 1240
2.2.4 Propriétés rhéologiques relatives des produits
2.3 Les dispositifs expérimentaux
2.3.1 La filière multicanaux
2.3.2 La filière à bloc de répartition
2.4 Caractérisation des défauts
2.4.1 Le film recueilli en filière multicanaux
2.4.2 Analyse du film en filière porte-manteau
2.5 Résumé des résultats expérimentaux
2.5.1 Approche deux couches en filière multicanaux
2.5.2 Approche deux couches en filière porte-manteau
2.6 Conclusions
3 Une première modélisation de l'instabilité: l'étude asymptotique.
3.1 Modélisation du problème
3.1.1 Les équations
3.1.2 La solution de base
3.1.3 La stabilité linéaire
3.2 L'étude asymptotique
3.2.1 Fluides de Carreau-Yasuda
3.2.2 Fluides de White-Metzner
3.2.3 Loi de comportement multi-Maxwell
3.2.4 Choix d'une loi de comportement pour le couple de produits utilisé
3.3 Comparaison à l'étude expérimentale
3.3.1 Approche deux couches en filière multicanaux
3.3.2 Approche deux couches en filière à bloc de répartition
3.4 Conclusion
4 Vers une approche plus analytique: mise en évidence du développement de l'instabilité dans la filière
4.1 Mise en évidence de l'instabilité dans la filière par figeage de l'écoulement
4.1.1 Présentation de l'expérience
4.1.2 Le déroulement des essais
4.1.3 Les résultats expérimentaux
4.1.4 Conclusion
4.2 Etude d'une perturbation en filière transparente
4.2.1 Etude bibliographique
4.2.2 Le dispositif expérimental
4.2.3 Les essais
4.2.4 Le dépouillement des essais
4.2.5 Observation d'une configuration fortement instable
4.2.6 Perturbation d'une configuration "stable"
4.2.7 Perturbation d'une configuration faiblement instable
4.2.8 Conclusion
4.3 Conclusions
4.3.1 Influence de la longueur de la filière
4.3.2 Sélection d'un nombre d'onde
4.3.3 Reculer les limites du procédé
5 Simulation directe de l'écoulement bicouche de fluides de Maxwell
5.1 Objectif
5.2 Formulation du problème
5.2.1 Equations de conservation
5.2.2 Traitement des conditions aux limites
5.3 Stratégie numérique
5.4 Génération de paquets d'ondes
5.5 Effets de la viscoélasticité
5.5.1 Effet déstabilisant de la viscoélasticité
5.5.2 Effet de la stratification d'élasticité
5.5.3 Effet stabilisant de la viscoélasticité
5.6 Conclusion
6 Modélisation de l'instabilité convective
6.1 L'étude de la stabilité spatiale
6.1.1 Principe de l'étude
6.1.2 La relation de Gaster
6.1.3 Bibliographie
6.1.4 Le calcul de la stabilité temporelle à nombre d'onde fixé
6.1.5 Exemple d'utilisation de la transformation de Gaster
6.1.6 Validation de l'approche de Gaster: confrontation aux résultats expérimentaux
6.1.7 Confrontation aux résultats de simulation directe
6.1.8 Conclusion
6.2 Relecture des expériences bicouche
6.2.1 Méthodologie
6.2.2 Campagne d'essais en filière multicanaux
6.2.3 Campagne d'essais en filière porte-manteau
6.2.4 Conclusion
7 Conclusion
8 Annexes
8.1 Caractérisation rhéologique en cisaillement des produits
8.1.1 Objectifs
8.1.2 Lois de comportement
8.1.3 Méthodes de mesure
8.1.4 Le polyéthylène 1003 FE 23
8.1.5 Le polystyrène 1240
8.1.6 Conclusions
8.2 Equations du problème bicouche
8.2.1 Ecoulement bicouche de fluides de White-Metzner
8.2.2 L'étude de la stabilité
8.3 Etude expérimentale en configuration tricouche
8.3.1 Déroulement des essais
8.3.2 Analyse du film
8.3.3 Résumé des résultats expérimentaux
8.4 Résultats de stabilité asymptotique en configuration tricouche
8.4.1 L'étude de stabilité asymptotique
8.4.2 Comparaison à l'expérience
8.5 Méthode de la puissance inverse
Bibliographie

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