Surface dynamics of noisy viscoelastic films by adiabatic approximation

Surface dynamics is sometimes used to determine the rheological properties of soft materials. In typical data analyses, surface capillary waves are included without incorporating thermal noise. A phenomenological expression for the time-dependent power spectral density has been proposed to account for thermal noise and shown to agree well with experiment. In this paper, we investigate the surface dynamics of viscoelastic films with thermal noise by using an adiabatic approximation involving fast quasi-equilibrium elastic vibrations to derive the power spectral density. Our result justifies the use of the phenomenological expression.