Dispersion properties of waves on a surface of viscous fluid covered by an elastic film

A linear dispersion relation is derived for waves on the free surface of an infinitely deep viscous fluid covered by an elastic surfactant film. The solutions of the dispersion relation are studied over a wide range of variations of the fluid viscosity and the film elasticity. Dynamics of the Marangoni mode associated with the presence of the elastic film is considered in detail. Values of the film elasticity modulus corresponding to both wave motions in fluid and motions damped monotonically with time are found. The elasticity and viscosity parameters at which the nature of the fluid motion changes qualitatively are determined