Linear stability and nonlinear dynamics of two-layer flow in the presence of surfactants


The event is taking part on the Tuesday, Nov 13th 2018 at 15:30
Theme/s: Applied Mathematics
Location of Event: Alan Turing Building, Room 306
This event is a: other

Abstract: A two-fluid shear flow in the presence of surfactants is considered. The flow configuration comprises two superposed layers of viscous and immiscible fluids confined in a long horizontal channel. The two fluids can have in general different densities, viscosities and thicknesses. The surfactants can be insoluble, i.e. located at the interface between the two fluids only, or soluble in the lower fluid. A primary aim of this study is to investigate the effect of surfactants on the stability of the interface, and in particular surfactants in high concentrations and above the critical micelle concentration (cmc). An asymptotic model valid in the approximation of a thin fluid layer is also derived, comprising a set of nonlinear PDEs to describe the evolution of the film thickness and surfactant concentration.

Interfacial instabilities are induced due to the acting forces of gravity and inertia, as well as the action of Marangoni forces generated as a result of the dependence of surface tension on the interfacial surfactant concentration. The underlying physical mechanism responsible for the formation of interfacial waves will be discussed, together with the complex flow dynamics (typical nonlinear phenomena associated with thin-film flows include travelling waves, solitary pulses, quasi-periodic and chaotic dynamics).

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External Speakers

Anna Kalogirou, (University of East Anglia)