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Pulse dynamics in a power-law falling film

Pradas, M.; Tseluiko, D.; Ruyer-Quil, C. and Kalliadasis, S. (2014). Pulse dynamics in a power-law falling film. Journal of Fluid Mechanics, 747 pp. 460–480.

URL: http://journals.cambridge.org/article_S00221120140...
DOI (Digital Object Identifier) Link: https://doi.org/10.1017/jfm.2014.176
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Abstract

We examine the stability, dynamics and interactions of solitary waves in a two-dimensional vertically falling thin liquid film that exhibits shear-thinning effects. We use a low-dimensional two-field model that describes the evolution of both the local flow rate and the film thickness and is consistent up to second-order terms in the long-wave expansion. The shear-thinning behaviour is modelled via a power-law formulation with a Newtonian plateau in the limit of small strain rates. our results show the emergence of a hysteresis behaviour as the control parameter (the Reynolds number) is increased which is directly related to the shear-thinning character of the liquid an can be quantified with both linear analysis arguments and a physical interpretation. We also study pulse interactions, observing that two pulses may attract or repel each other either monotonically or in an oscillatory manner. In large domains we find that for a given Reynolds number the final state depends on the initial condition, a consequence of the presence of multiple solutions.

Item Type: Journal Item
Copyright Holders: 2014 Cambridge University Press
ISSN: 1469-7645
Keywords: non-Newtonian flows; pattern formation; thin films
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 41221
Depositing User: Marc Pradas
Date Deposited: 03 Nov 2014 09:54
Last Modified: 07 Dec 2018 10:26
URI: http://oro.open.ac.uk/id/eprint/41221
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