Rupture of thinning liquid films. Influence of the surface wave's spatial correlations

According to the theory of stochastic processes, the presence of uncorrelated subdomains on the liquid film surface is demonstrated. The spectral density of the spatial correlation function of the surface wave amplitudes on a thin liquid film together with the corresponding root-mean-square amplitude A and number of uncorrelated subdomains N are obtained. It is shown that the presence of uncorrelated subdomains increases the film critical thickness of rupture hcr. Some numerical calculations for A, N and hcr at different film radii R are obtained, taking into account only van der Waals and capillary forces.