Comptes Rendus
Interfacial instabilities of two-layer plane Poiseuille flows of viscoelastic fluids
Comptes Rendus. Mécanique, Volume 343 (2015) no. 5-6, pp. 354-359.

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:
Accepted:
Published online:
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
@article{CRMECA_2015__343_5-6_354_0,
     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},
}
TY  - JOUR
AU  - Nadia Mehidi
AU  - Nawel Amatousse
AU  - Abdelmalek Bedhouche
TI  - Interfacial instabilities of two-layer plane Poiseuille flows of viscoelastic fluids
JO  - Comptes Rendus. Mécanique
PY  - 2015
SP  - 354
EP  - 359
VL  - 343
IS  - 5-6
PB  - Elsevier
DO  - 10.1016/j.crme.2015.04.004
LA  - en
ID  - CRMECA_2015__343_5-6_354_0
ER  - 
%0 Journal Article
%A Nadia Mehidi
%A Nawel Amatousse
%A Abdelmalek Bedhouche
%T Interfacial instabilities of two-layer plane Poiseuille flows of viscoelastic fluids
%J Comptes Rendus. Mécanique
%D 2015
%P 354-359
%V 343
%N 5-6
%I Elsevier
%R 10.1016/j.crme.2015.04.004
%G en
%F CRMECA_2015__343_5-6_354_0
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/

[1] G.M. Wilson; B. Khomami An experimental investigation of interfacial instabilities in multilayer flow of viscoelastic fluids. Part I. Incompatible polymer systems, J. Non-Newton. Fluid Mech., Volume 45 (1992), pp. 355-384

[2] B. Khomami; K.C. Su An experimental/theoretical investigation of interfacial instabilities in superposed pressure-driven channel flow of Newtonian and well characterized viscoelastic fluids. Part I: linear stability and encapsulation effects, J. Non-Newton. Fluid Mech., Volume 91 (2000), pp. 59-84

[3] C.-H. Li Stability of two superposed elasticoviscous liquids in plane Couette flow, Phys. Fluids, Volume 12 (1969), pp. 531-538

[4] C. Ruyer-Quil; P. Manneville Improved modeling of flows inclined planes, Eur. Phys. J. B, Volume 15 (2002), pp. 357-369

[5] M. Amaouche; N. Mehidi; N. Amatousse Linear stability of two-layer film flow an inclined channel: a second-order weighted residual approach, Phys. Fluids, Volume 19 (2007) no. 8, p. 0841106

[6] V.Ya. Shkadov Linear theory of wave flow of thin layer of viscous liquid, Izv. Akad. Nauk SSSR, Meh. Židk. Gaza, Volume 2 (1968), p. 20

[7] N. Amatousse; H. Ait Abderrahmane; N. Mehidi Traveling waves on a falling weakly viscoelastic fluid film, Int. J. Embed. Syst., Volume 54 (2012), pp. 27-41

[8] S.G. Yiantsios; B.G. Higgins Linear stability of plane Poiseuille flow of two superposed fluids, Phys. Fluids, Volume 31 (1988), p. 3225

[9] T.G. Theofanous; R.R. Nourgaliev; B. Khomami Short communication “An experimental/theoretical investigation of interfacial instabilities in superposed pressure-driven channel flow of Newtonian and well characterized viscoelastic fluids, by Bamin Khomami and Kuan C. Su”, J. Non-Newton. Fluid Mech., Volume 143 (2007), pp. 131-132

[10] K. Alba; P. Laure; R.E. Khayat Transient two-layer thin-film flow inside a channel, Phys. Rev. E, Volume 84 (2011), p. 026320

Cited by Sources:

Comments - Policy