Comptes Rendus
no. 5-6
Interfacial instabilities of two-layer plane Poiseuille flows of viscoelastic fluids
[Instabilités interfaciales de l'écoulement de Poiseuille plan de deux couches de fluides viscoélastiques]
Nadia Mehidi1  ; Nawel Amatousse1  ; Abdelmalek Bedhouche1
1 Laboratoire de physique théorique, Faculté des sciences exactes, Université de Bejaia, route de Targa Ouzemmour, 06000 Bejaia, Algeria
Comptes Rendus. Mécanique, Volume 343 (2015) no. 5-6, pp. 354-359.

Nous présentons une étude de stabilité linéaire de deux couches de fluides viscoélastiques s'écoulant par gravité dans un canal incliné. Un modèle simplifié basé sur une méthode aux résidus pondérés et une approximation polynomiale du champ des vitesses est développé. Il s'agit d'un système de deux équations couplées, décrivant l'évolution de l'interface h(x,t) et du débit local q(x,t). Le modèle permet de prédire le seuil de l'instabilité de façon précise. L'effet de la différence d'élasticité sur la stabilité de l'interface est examiné dans le cadre de l'approximation des grandes longueurs d'onde.

The linear stability of a two-layer flow of viscoelastic fluids on an inclined channel is examined. A simplified model is derived by using a weighted residual method combined with a long-wavelength expansion. A set of two coupled evolution equations for two fields, the film thickness h(x,t) and the flow rate q(x,t), is obtained. Then, the correct threshold of instability of the interface is characterized analytically. The effect of the elasticity stratification on the stability of the interface is considered within the long-wavelength assumption.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2015.04.004
Keywords: Long waves, Instability, Viscoelastic fluids, Weighted residual method
Mot clés : Longues ondes, Instabilité, Fluides viscoélastiques, Méthode des résidus pondérés
Nadia Mehidi 1 ; Nawel Amatousse 1 ; Abdelmalek Bedhouche 1

1 Laboratoire de physique théorique, Faculté des sciences exactes, Université de Bejaia, route de Targa Ouzemmour, 06000 Bejaia, Algeria 
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Nadia Mehidi; Nawel Amatousse; Abdelmalek Bedhouche. Interfacial instabilities of two-layer plane Poiseuille flows of viscoelastic fluids. Comptes Rendus. Mécanique, Volume 343 (2015) no. 5-6, pp. 354-359. doi : 10.1016/j.crme.2015.04.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2015.04.004/

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