The presence of surfactants in a fluid-fluid interface can have a substantial effect on the evolution of such an interface. The insoluble surfactants, in general, separate aqueous from non-aqueous media. The influence of surfactants on the interfacial dynamics goes in two ways. Firstly, most types of surfactants reduce the interfacial tension. Second, the presence of a gradient in concentrations of surfactants, introduces the Marangoni force. In general, the Marangoni force acts to oppose any external flow that causes an increase or excess of surfactants in regions along the interface. Studies on the influence of insoluble surfactants on core-annular flows have been done lately, where the core liquid is surrounded by other annular liquid. A mathematical model for core-annular flows confined in a cylindrical tube with insoluble surfactants at the interface between the two fluids has been developed, obtaining a system of two coupled nonlinear integro-partial-differential equations. Furthermore, in the absence of surfactants, the system reduces to the Kuramoto-Sivashinsky equation. This equation is very unstable and it is found a rich behavior of solutions ranging from steady-state waves, periodic in time waves with period doubling up to chaotic situations. In our research we found chaotic behavior by including dispersive terms, hence the importance of it.

Key words: Chaos, nonlinear interfacial stability, core-annular flows, surfactants.