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On thermal fluctuations in thin film flow

In bulk fluids hydrodynamic Navier–Stokes equations are proven to be valid down to the nanometre scale. However, during the dewetting process of thin liquid films of nanometre thickness the interplay of surface tension γ, substrate potential and thermal noise can lead to qualitatively different behaviour on laterally much larger scales up to microns. By deriving a stochastic thin film equation with a conserved noise term we show that the spectrum of capillary waves changes from an exponential decay to a power law kBT/(γq2) for large wavevectors q due to thermal fluctuations at temperature T. Also the time evolution of film roughness σ(t) and of the typical wavevector k(t) of unstable perturbations changes qualitatively. Whereas a deterministic Navier–Stokes equation in the lubrication approximation predicts in the linear regime a constant k(t) = k0, one finds a coarsening due to thermal noise.