Interfacial instabilities of two-layer plane Poiseuille flows of viscoelastic fluids

Nadia Mehidi; Nawel Amatousse; Abdelmalek Bedhouche

doi:10.1016/j.crme.2015.04.004

Interfacial instabilities of two-layer plane Poiseuille flows of viscoelastic fluids

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

Comptes Rendus. Mécanique, Volume 343 (2015) no. 5-6, pp. 354-359.

Abstract
Résumé

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.

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.

Received: 2014-08-18
Accepted: 2015-04-15
Published online: 2015-04-30

DOI: 10.1016/j.crme.2015.04.004

Keywords: Long waves, Instability, Viscoelastic fluids, Weighted residual method
Mots-clés : Longues ondes, Instabilité, Fluides viscoélastiques, Méthode des résidus pondérés

Author's affiliations:

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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     author = {Nadia Mehidi and Nawel Amatousse and Abdelmalek Bedhouche},
     title = {Interfacial instabilities of two-layer plane {Poiseuille} flows of viscoelastic fluids},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {354--359},
     publisher = {Elsevier},
     volume = {343},
     number = {5-6},
     year = {2015},
     doi = {10.1016/j.crme.2015.04.004},
     language = {en},
}

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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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