Thin film instability with thermal noise

TL;DR

This paper investigates how thermal noise influences the instability of thin liquid films on solid substrates, combining linear stability analysis, numerical simulations, and experimental data fitting to understand the role of spatially correlated thermal fluctuations.

Contribution

It introduces a model incorporating spatially correlated thermal noise into thin film instability analysis and validates it through simulations and experimental data fitting.

Findings

Thermal noise affects the dominant wavelength of film instability.

The model's predictions align well with numerical simulations at early times.

Experimental data from copper films support the theoretical spectra.

Abstract

We study the effects of stochastic thermal fluctuations on the instability of the free surface of a flat liquid film upon a solid substrate. These fluctuations are represented as a standard Brownian motion that can be added to the deterministic equation for the film thickness within the lubrication approximation. Here, we consider that while the noise term is white in time, it is coloured in space. This allows for the introduction of a finite correlation length in the description of the randomized intermolecular interaction. Together with the expected spatial periodicity of the flow, we find a dimensionless parameter, $\beta$, that accounts for the relative importance of the spatial correlation. We perform here the linear stability analysis (LSA) of the film under the influence of both terms, and find the corresponding power spectra for the amplitudes of the normal modes of the instability. We compare this theoretical result with the numerical simulations of the complete non-linear problem, and find a good agreement for early times. For late times, we find that the stochastic LSA predictions on the dominant wavelength remains basically valid. We also use the theoretical spectra to fit experimental data from a nanometric melted copper film, and find the corresponding times of the evolution as well as the values of the parameter, $\beta$.