Kalogirou, A orcid.org/0000-0002-4668-7747, Papageorgiou, DT and Smyrlis, Y-S (2012) Surfactant destabilization and non-linear phenomena in two-fluid shear flows at small Reynolds numbers. IMA Journal of Applied Mathematics, 77 (3). pp. 351-360. ISSN 0272-4960
Abstract
The flow of two superposed fluids in a channel in the presence of an insoluble surfactant is studied. Asymptotic analysis when one of the layers is thin yields a system of coupled weakly non-linear evolution equations for the film thickness and the local surface surfactant concentration. Film and main flow dynamics are coupled through a non-local term, and in the absence of surfactants the model is non-linearly stable with trivial large time solutions. Instability arises due to the presence of surfactants and the pseudo-differential non-linear system is solved numerically by implementing accurate linearly implicit methods. Extensive numerical experiments reveal that the dynamics are mostly organized into travelling or time-periodic travelling wave pulses, but spatiotemporal chaos is also supported when the length of the system is sufficiently large.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Keywords: | two-phase flows; surfactants; Marangoni instability |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 12 Aug 2016 15:13 |
Last Modified: | 12 Aug 2016 15:13 |
Published Version: | https://dx.doi.org/10.1093/imamat/hxs035 |
Status: | Published |
Publisher: | Oxford University Press |
Identification Number: | 10.1093/imamat/hxs035 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:88553 |