The effects of surfactant solubility and concentration-dependant fluid density on the stability of inclined thin film flows

An analytical investigation of the stability of a surfactant-laden liquid film with a free surface, owing under the influence of gravity on an inclined plane, is conducted. This investigation focusses on the onset of instability of a steady equilibrium flow when the surfactant concentration along the surface affects surface tension, while at the same time, the concentration of surfactant in the bulk of the layer affects the mass density of the liquid. A linear stability analysis is carried out and an asymptotic solution is obtained for the growth rate of long perturbations. The results obtained reflect how the various control parameters influence the onset of instability.