Steady two-layer thin-film planar flow under gravity is investigated theoretically in this study. The film is assumed to emerge out of a channel and flow over a straight plate. The interplay among inertia, viscous and surface or interfacial tension is emphasized. It is found that the film and interface profiles, as well as the flow field, are strongly influenced by the viscosity ratio, film thickness ratio at inception, and surface-to-interfacial tension ratio. In the absence of surface and interfacial tension, the profiles of the film layers vary monotonically streamwise. The surface tension effect leads to waviness in layer profiles, with increasing wave number as the surface tension effect is reduced.

SUMMARYThe transient two-layer thin-film planar flow is investigated theoretically in this study. The interplay among inertia, viscous and surface/interfacial tension is emphasized. It is found that the film and interface profiles, as well as the flow field, are strongly influenced by the viscosity ratio, velocity and film thickness ratios at inception, and the surface-to-interfacial tension ratio. The nonlinear stability of the steady state reveals the formation of a solitary wave after flow inception, which propagates in the form of a convective instability, with the steady state recovered only in the tail (upstream) region of the wave. In the presence of surface/interfacial tension, surface modulation appears, which grows in wavelength and amplitude with position. The flow is found to be particularly stable for higher viscosity of the lower film layer.