WAVE MOTION IN MULTILAYERED LIQUID-FILMS

The governing equation of the linear interfacial wave motion in an n-layered liquid film, which possesses n degree of freedoms, flowing steadily down an inclined plane is obtained- The effects of density, viscosity, and thickness variations on the various modes of wave motion are elucidated with aid of some numerical experiments for a three-layered system. It is found that the wave speed of the interfacial mode is much smaller than that of the free-surface mode. The interfaces seem to oscillate in phase for the free-surface mode but can be either out-of-phase or in-phase for the interfacial modes. It is shown that a limited control of wave speeds can be achieved by adjusting the variation in thickness, viscosity, and density of each layer. © 1978 by ASME.