Rogue nanowaves: A route to film rupture

Sufficiently thin liquid films on solid surfaces are often unstable to intermolecular forces and it is commonly assumed that their rupture occurs via a linear instability mechanism in the so-called spinodal regime. Here, a theoretical framework is created for the experimentally observed thermal regime, in which fluctuation-induced nanowaves rupture linearly stable films. Molecular simulations in a quasi-2D geometry identify these regimes and are accurately reproduced by stochastic simulations based on fluctuating hydrodynamics. Rare-event theory is then applied to, and developed for, this field to provide exceptional computational efficiency and accuracy that allows us to extend calculations deep into the thermal regime. Analysis of the rare-event theory reveals a picture of how and when “rogue nanowaves” are able to provide a route to film rupture. Finally, future applications of the new theoretical framework and experimental verification is discussed.

Figure 1

Schematic of our setup, with the upper panel showing a periodic MD domain of length $L^{*}$, containing a film of average/initial-flat height $h_0^{*}$. The lower panel shows a close up, with the free surface extracted from the MD and the evolving local height $h^{*}(x^{*},t^{*})$.

Figure 2

Snapshots from the molecular simulations as rupture is approached in the spinodal (upper) and thermal (lower) regimes for thin films of length $L^{*}=80\mathrm{nm}$, for which $H^{*}=2.35\mathrm{nm}$. Arrows denote rupture points. The central figure shows a comparison of ensemble-averaged profiles $\langle h\rangle$ from the MD and stochastic thin film equation (STF) for these cases. Symmetry about $x=1/2$ is used to further average the MD profile. Videos of these cases are provided as Supplemental Material and described in SM3.

Figure 3

Dependency of the expected rupture time $\langle \tau \rangle$ as a function of film height $h_0$; comparing MD data for two domain sizes with the stochastic thin-film equation and rare-event theory. For the MD, $\pm$ one standard error fits within the data point.

Figure 4

Saddle-point profiles showing larger deformation as $h_0$ increases, approaching the limiting case (a parabola), in which disjoining pressure is negligible. Inset figure shows the saddle point for $h_0=1.01$ and that ensemble-averaged STF calculations converge toward this state as $\epsilon \to 0$.

Figure 5

Influence of the noise parameter $\epsilon$ and nonzero slip length $\ell$ on the expected rupture times compared to the rare-event theory. Solid lines correspond to STF calculations while dashed lines are the predictions of the rare-event theory. The inset confirms the prediction of the rare-event theory that the rupture time scales as $\sim {(h_0^3+\ell h_0^2)}^{-1}$.

Figure 6

Probability distribution function for 1000 computations of the rupture at $\epsilon =0.34$ with the left panel corresponding to $h_0=1.3$ (thermal) and the right to $h_0=0.7$ (spinodal).