Interplay of bulk soluble surfactants and interfacial kinetics governs the stability of two-layer channel flows

The linear stability of two-layer channel flows in the presence of bulk-soluble surfactants is investigated here, taking into account the rheological properties of the interface. The interfacial stresses are quantified using the Boussinesq-Scriven model, while the surfactant kinetics is assumed to follow the Frumkin isotherm, which accounts for their non-ideal behavior. Our results show that in general, the bulk solubility of surfactants has a stabilizing effect on the interface, both with and without the presence of inertia. On the other hand, the interfacial viscosities play a more complex role, depending on the viscosity ratios of the two fluids, the thickness of the fluid layers, the strength of the surface tension gradients, and the extent of inertia. We show that depending on the strength of inertia and the variability in the surface tension, the interfacial rheology may either stabilize or destabilize the base flow. However, for sufficiently small Reynolds numbers, the surface viscosity always has a stabilizing influence. Our results may be used to better design stable co-flow systems with applications in various processes such as surface coating, preparation of fluid lenses, as well as in a host of multi-purpose microfluidic devices.