Surfactant destabilization and non-linear phenomena in two-fluid shear flows at small Reynolds numbers

Kalogirou, A.; Papageorgiou, Demetrios T.; Smyrlis, Yiorgos- Sokratis

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 nonlinearly 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. © The authors 2012.

Citation

Kalogirou, A., Papageorgiou, D. T., & Smyrlis, Y.-. S. (2011, July). Surfactant destabilization and non-linear phenomena in two-fluid shear flows at small Reynolds numbers. Presented at The IMA Conference on Nonlinearity and Coherent Structures, Reading, UK

• Presentation Conference Type: Conference Paper (published)
• Conference Name: The IMA Conference on Nonlinearity and Coherent Structures
• Start Date: Jul 6, 2011
• End Date: Jul 8, 2011
• Acceptance Date: Mar 28, 2012
• Online Publication Date: Jun 4, 2012
• Publication Date: Jun 4, 2012
• Deposit Date: Jun 4, 2019
• Journal: IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
• Print ISSN: 0272-4960
• Electronic ISSN: 1464-3634
• Publisher: Oxford University Press
• Peer Reviewed: Peer Reviewed
• Volume: 77
• Issue: 3
• Pages: 351-360
• DOI: https://doi.org/10.1093/imamat/hxs035
• Keywords: Applied Mathematics
• Public URL: https://nottingham-repository.worktribe.com/output/2138192