Surfactant destabilization and non-linear phenomena in two-fluid shear flows at small Reynolds numbers.

The flow of two superposed fluids in a channel in the presence of an insoluble surfactant is studied. Asymptotic analysis when one of the layers is thin yields a system of coupled weakly non-linear evolution equations for the film thickness and the local surface surfactant concentration. Film and main flow dynamics are coupled through a non-local term, and in the absence of surfactants the model is non-linearly stable with trivial large time solutions. Instability arises due to the presence of surfactants and the pseudo-differential non-linear system is solved numerically by implementing accurate linearly implicit methods. Extensive numerical experiments reveal that the dynamics are mostly organized into travelling or time-periodic travelling wave pulses, but spatiotemporal chaos is also supported when the length of the system is sufficiently large.