Effect of a soluble surfactant on the linear stability of two-phase flows in a finite-length channel

We study numerically the effect of a soluble surfactant on the stability of two-phase flow in a finite-length microchannel. We calculate the steady base flow and its global eigenmodes for experimentally relevant choices of material, kinetic, and flow parameters. The results show that the system is unstable for capillary numbers above a critical value. The surfactant surface concentration takes values of the order of the maximum packing density over the whole interface, even for very small volume concentrations. The two streams drag the surfactant molecules toward the downstream end of the interface against the action of the Marangoni stress. The sharp reduction of the interfacial tension at that end enhances the interface deformation and considerably destabilizes the system, translating into a sharp reduction of the critical capillary number.