Role of Viscosity Stratification and Insoluble Surfactant in Instability of Two-Layer Channel Flow

We study, for the case of the two layer plane Poiseuille flow, the effect of viscosity stratification and interfacial surfactant on the flow instability. Considering a normal mode of the streamwise wave number α, both the linear and energy analyses are presented. The expressions of perturbation energy supplied at the interface are derived. The result demonstrates that the jumps of horizontal velocity and tangential stress of the perturbed flow across the interface could be induced by the presence of viscosity stratification and surfactant. This is expected to be responsible for the Yih and Marangoni instability.