Metallic-thin-film instability with spatially correlated thermal noise

R. FERNÁNDEZ; A. G. GONZÁLEZ; J. A. DIEZ

PHYSICAL REVIEW E - STATISTICAL PHYSICS, PLASMAS, FLUIDS AND RELATED INTERDISCIPLINARY TOPICS

American Physical Society

Lugar: New York; Año: 2016 vol. 93 p. 131201 - 1312012

1063-651X

We study the effects of stochastic thermal fluctuations on the instability of the free surface of a flatliquid metallic film upon a solid substrate. These fluctuations are represented by a stochastic noiseterm added to the deterministic equation for the film thickness within the long wave approximation.Unlike the case of polymeric films, we find that this noise, while remaining white in time, mustbe colored in space at least in some regimes. The corresponding noise term is characterized by anonzero correlation length, c , which combined with the size of the system, leads to a dimensionlessparameter β that accounts for the relative importance of the spatial correlation (β ∼ −1c ). Weperform the linear stability analysis (LSA) of the film both with and without the noise term, andfind that for c larger than some critical value (depending on the system size), the wavelength of thepeak of the spectrum is larger than that corresponding to the deterministic case, while for smallerc this peak corresponds to smaller wavelength than the latter. Interestingly, whatever the valueof c , the peak always approaches the deterministic one for larger times. We compare LSA resultswith the numerical simulations of the complete non-linear problem and find a good agreement in thepower spectra for early times at different values of β. For late times, we find that the stochastic LSApredicts well the position of the dominant wavelength, showing that nonlinear interactions do notmodify the trends of the early linear stages. Finally, we fit the theoretical spectra to experimentaldata from a nanometric laser-melted copper film, and find that at later times, the adjustmentrequires smaller values of β (larger space correlations).