HYDRODYNAMIC MODES OF VISCOELASTIC SOAP FILMS

We discuss the dispersion relation of the undulation modes of a soap f ilm containing a viscoelastic Maxwell fluid modeling a water soluble p olymer. Two types of modes exist, bending modes and squeezing modes. I n addition to the modes existing for a usual viscous soap film, we fin d Rayleigh waves driven by the bulk elasticity E of the liquid. The di spersion relation of the undulation modes strongly depends on the valu e of the surface elastic modulus of the surfactant layers epsilon(s). We study in detail the limit where the surface elastic modulus vanishe s and the limit where it is of the same order of magnitude as the surf ace tension. In this last case the Rayleigh waves are observed if Eh > > epsilon(s) where h is the thickness of the film. We also discuss bri efly the existence of higher harmonics due to the coupling of the undu lation modes to compressional elastic modes of the film.