Wave Motion in Multilayered Liquid Films

Abstract

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.