Marangoni destabilization on a core-annular film flow due to the presence of surfactant

In this paper, the linear stability of a two-fluid, surfactant-laden core-annular flow is asymptotically examined in the thin-annulus limit. The instability of the system is determined by the interplay between interfacial tensions, Marangoni effects and viscosity stratification. A scaling analysis is developed to identify the dominant instability mechanisms in various parameter regimes. With proper scalings, the combined effects of Marangoni forces and viscosity stratification on the leading order stability are examined for both cases in the absence and the presence of the core inertia. For each case, a coupled set of linear evolution equations is derived for the interfacial deflection and the surfactant concentration. In the absence of the core inertia, the system with a more viscous film is always unstable due to the presence of surfactant. When the core fluid is more viscous, the stabilizing effect of the core inertia is compromised by the Marangoni destabilization. The resulting critical Reynolds number, beyond which the instability is completely suppressed by the core inertia, increases with surfactant elasticity.