Thermal Noise Influences Fluid Flow in Thin Films during Spinodal Dewetting

Experiments on dewetting thin polymer films confirm the theoretical prediction that thermal noise can strongly influence characteristic time scales of fluid flow and cause coarsening of typical length scales. Comparing the experiments with deterministic simulations, we show that the Navier-Stokes equation has to be extended by a conserved bulk noise term to accomplish the observed spectrum of capillary waves. Because of thermal fluctuations the spectrum changes from an exponential to a power law decay for large wave vectors. Also the time evolution of the typical wave vector of unstable perturbations exhibits noise-induced coarsening that is absent in deterministic hydrodynamic flow.

Figure 1

Dewetting of a 3.9 nm polystyrene film as monitored by in situ AFM at $53°\mathrm{C}$.

Figure 2

Analysis of AFM experiments and of deterministic simulations ($T=0$): (a) The roughness ${\sigma }^2(t)$ and (b) the variance $k^2(t)$ of the local slope (only experiment 1 and simulations for clarity) as functions of time and fits based on the linearized TFEq. While ${\sigma }^2(t)$ can be fitted with the deterministic theory by adjusting the initial roughness ${\sigma }_0^2$ and the characteristic time scale $t_0$, this is not possible for the experimental $k^2(t)$. In the linear regime the deterministic $k^2(t)$ is constant in time.

Figure 3

Slope variance $k^2$ from the experiments plotted versus the roughness ${\sigma }^2$. The solid lines are fits based on the linearized stochastic TFEq, whereas the dash-dotted lines are asymptotic fits according to Eq. (2). The influence of noise is reduced for smoothed as well as for less resolved data (experiment 2). The inset shows the same data in a double logarithmic plot highlighting the validity of the asymptotic equation (2).