CONICET | Buscador de Institutos y Recursos Humanos

The thermal fluctuations effects on the instability of the free surface of a flat liquid metallic film upon a solid substrate are considered within the long wave approximation. Unlike the case of polymeric films, we find that this stochastic noise, while remaining white in time, must be colored in space at least in some regimes. The noise term has a nonzero correlation length, $ell_c$, which combined with the size of the system, leads to a dimensionless parameter $eta$ that accounts for the relative importance of the spatial correlation ($eta sim ell_c^{-1}$). The linear stability analysis (LSA) of the film shows that the wavelength of the peak of the spectrum is larger than that corresponding to the deterministic case when $ell_c$ is larger than a critical value that depends on the system size while, for all $ell_c$´s, the peak approaches the deterministic one for larger times. The numerical simulations of the complete non-linear problem are in good agreement with the LSA power spectra for early times at different values of $eta$. For late times, the stochastic LSA predicts well the position of the dominant wavelength, showing that nonlinear interactions do not modify substantially the trends of the early linear stages.We compared LSA predictions with the experimental data from the instability of laser-melted copper nanometric films on a silicon oxide substrate. As a result, we found that the early stages of the experiment evolved with an almost white noise in space, while a strong spatial correlation appeared in the spectra for later times. Thus, correlated noise seems to be an important factor in the central regions of the laser spot, i.e. those with larger liquid lifetimes. Taken together, our results provide a clear indication that the stochastic differential framework for metallic thin-film phenomena at the nanometric scale requires the inclusion of thermal noise with extended spatial correlation.