Pulse dynamics in a power-law falling film
File(s)
Accepted version
Author(s)
Pradas, M
Tseluiko, D
Ruyer-Quil, C
Kalliadasis, S
Type
Journal Article
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.
Date Issued
2014-05-25
Date Acceptance
2014-03-31
Citation
Journal of Fluid Mechanics, 2014, 747, pp.460-480
ISSN
0022-1120
Publisher
Cambridge University Press
Start Page
460
End Page
480
Journal / Book Title
Journal of Fluid Mechanics
Volume
747
Copyright Statement
© 2014 Cambridge University Press.
Identifier
https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000336805500020&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=a2bf6146997ec60c407a63945d4e92bb
Subjects
FLOW
INSTABILITIES
Mechanics
non-Newtonian flows
pattern formation
Physical Sciences
Physics
Physics, Fluids & Plasmas
Science & Technology
SOLITARY PULSES
STABILITY
Technology
thin films
WAVES
Publication Status
Published
Date Publish Online
2014-04-17