Thin film instability with thermal noise

J. A. DIEZ; A. G. GONZÁLEZ

Tandil

Conferencia; FLUIDOS 2014 - XIII Meeting on Recent Advances in Physics of Fluids and its Applications; 2014

In this work we study theoretically and numerically the effect of thermal noise on the instability of a flat nanometric liquid film, under the action of capillary and intermolecular forces (van der Waals interaction). This noise is described by the addition of a stochastic term as a new driving force in the governing equation for the the film thickness, $h$, within the lubrication approximation. We consider that the noise amplitudes are correlated in space within a certain length, $\ell_c$, but have zero correlation in time. Therefore, the noise is white in time, but coloured in space. We develop here a linear stability analysis from which the evolution of the spatial spectrum can be obtained. The non-linear effects on this evolution is studied with numerical simulations. Interesting, we obtain that for sufficiently large $\ell_c$, we recover the deterministic (non noisy) time evolution of the instability. On the other limit, we note that $\ell_c$ cannot be made smaller the space discretization, $\Delta x$, so that the spatially white noise is only a theoretical limit, which cannot strictly be reached in the numerical simulations. One of the main effects of the noise term is to increase the breakup time of the film, while it practically does not affect the dewetting process leading to the formation of drops.