Abstract:  
Air flow through lungs may involve the presence of mucus which has much higher viscosity than air. To this end, we developed a model and examined the stability of two superimposed fluids with different viscosity in the two layers. Simple solutions of two-layer fluid flows with a high viscosity contrast can be unstable. This instability can be quite different than that occurring with a single fluid and in fact can shed some light on it when a perturbation approach is adopted. Our focus is on the limit of large viscosity contrast, which has not been fully analyzed or understood yet. Here the asymptotic properties of stability will be investigated. These results have a direct application in understanding air-driven mucus clearance mechanisms and the mucus transport phenomena in human lungs.