Comptes Rendus
no. 1
A modified Shkadov's model for thin film flow of a power law fluid over an inclined surface
[Modèle de Shkadov modifié pour l'écoulement de film mince de fluide en loi de puissance sur une plaque inclinée]

Présenté par : Patrick Huerre

Mustapha Amaouche1 ; Amar Djema1  ; L. Bourdache1
1 UAMB, Université de Bejaia, route de Targa Ouzemmour, 06000 Bejaia, Algeria
Comptes Rendus. Mécanique, Volume 337 (2009) no. 1, pp. 48-52.

Un modèle non linéaire, cohérent à l'ordre un et combinant les avantages de l'approche asymptotique de Benney et de la méthode intégrale de Shkadov est proposée pour décrire le comportement d'un film mince de fluide en loi de puissance pour des nombres de Reynolds petits et modérés. La procédure utilisée est inspirée de la méthode des résidus pondérés développée par Ruyer-Quil et Manneville (2000) dans le cadre des fluides Newtoniens.

A new evolution equation coherent up to order one in the long wave parameter is derived to describe the non-linear behavior of a thin film flow down an inclined plane of a power law fluid for small to moderate Reynolds numbers. The method we have used combines the lubrication theory and the weighted residual approach, with a suitable weighting function. That approach was first developed by Ruyer-Quil and Manneville (2000) for Newtonian fluids. The model has the advantages of both the Shkadov type approach far from criticality and that of Benney close to criticality.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2009.01.002
Keywords: Fluid mechanics, Shkadov's model, Thin film flow
Mot clés : Mécanique des fluids, Modèle de Shkadov, Écoulement de film mince de fluide
Mustapha Amaouche 1 ; Amar Djema 1 ; L. Bourdache 1

1 UAMB, Université de Bejaia, route de Targa Ouzemmour, 06000 Bejaia, Algeria 
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Mustapha Amaouche; Amar Djema; L. Bourdache. A modified Shkadov's model for thin film flow of a power law fluid over an inclined surface. Comptes Rendus. Mécanique, Volume 337 (2009) no. 1, pp. 48-52. doi : 10.1016/j.crme.2009.01.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2009.01.002/

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[7] J.S. Lin; C.C. Hwang Finite amplitude long-wave instability of power-law liquid films, Int. J. Non-Lin. Mech., Volume 35 (2000), pp. 769-777

[8] S. Miladinova; G. Lebon; E. Toshev Thin-film flow of a power-law liquid falling down an inclined plate, J. Non-Newtonian Fluid Mech., Volume 122 (2004), pp. 69-78

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