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Pulse dynamics in a power-law falling film

Published online by Cambridge University Press:  17 April 2014

M. Pradas ,
D. Tseluiko ,
C. Ruyer-Quil  and
S. Kalliadasis
M. Pradas
Affiliation:
Department of Chemical Engineering, Imperial College London, London SW7 2AZ, UK
D. Tseluiko
Affiliation:
School of Mathematical Sciences, Loughborough University, Leicestershire LE11 3TU, UK
C. Ruyer-Quil
Affiliation:
Université de Savoie, CNRS – Laboratoire LOCIE, 73376 Le Bourget du Lac, France Institut Universitaire de France
S. Kalliadasis*
Affiliation:
Department of Chemical Engineering, Imperial College London, London SW7 2AZ, UK
*
†Email address for correspondence: [email protected]
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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 and 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.

JFM classification

Non-Newtonian Flows: Non-Newtonian Flows Nonlinear Dynamical Systems: Pattern formation Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 747 , 25 May 2014 , pp. 460 - 480
Copyright
© 2014 Cambridge University Press 

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