Molecular simulation of thin liquid films: Thermal fluctuations and instability

Abstract

The instability of a thin liquid film on a solid surface is studied both by molecular dynamics simulations (MD) and a stochastic thin-film equation (STF), which models thermal fluctuations with white noise. A linear stability analysis of the STF allows us to derive a power spectrum for the surface fluctuations, which is quantitatively validated against the spectrum observed in MD. Thermal fluctuations are shown to be critical to the dynamics of nanoscale films. Compared to the classical instability mechanism, which is driven by disjoining pressure, fluctuations (a) can massively amplify the instability, (b) cause the fluctuation wavelength that is dominant to evolve in time (a single fastest-growing mode does not exist), and (c) decrease the critical wavelength so that classically stable films can be ruptured.

Thermal capillary wave growth and surface roughening of nanoscale liquid films

“…Linear stability analysis of the SLE has provided time-dependent capillary wave spectra for both jets and planar films (Mecke & Rauscher 2005;Fetzer et al 2007;Zhang, Sprittles & Lockerby 2019;Zhao, Sprittles & Lockerby 2019). Importantly, in the recent article (Zhang, Sprittles & Lockerby 2020), new SLE have been derived for both planar and annular films (like those consider here), taking into account the slip effects at the solid-liquid interface, which are well-known to be significant for nanoflows (Lauga, Brenner & Stone 2005;Bocquet & Charlaix 2010).…”

Dynamics of liquid nanothreads: Fluctuation-driven instability and rupture

“…Numerical solutions to the SLE offer much broader applicability than the analytic results described above, and can be obtained at a small fraction of the computational cost of MD. A set of closely related stochastic equations are well studied for thin-film flows [26][27][28][29][30] and thermally activated vapor-bubble nucleation [31]. But, surprisingly, there are no detailed numerical SLE studies in the literature for liquid thread rupture.…”

Lattice Boltzmann simulations of stochastic thin film dewetting

“…To understand the influence of thermal fluctuations on the temporal evolution of the film height, we cursory recall the linear stability analysis of Eq. (3) [14,36]. Introducing the deviation δh from the mean height h 0 , such that h = h 0 + δh and δh h 0 , the linearized stochastic thin-film equation is obtained,…”

“…The disjoining pressure (h) is the derivative, with respect to the height h, of the interfacial potential, which incorporates the interactions between liquid and substrate (i.e., wetting properties). The advantage of this approach in comparison with molecule-resolved methods such as molecular dynamics [13][14][15][16] and density functional theory [17][18][19][20] is that these may quickly become computationally prohibitive, as the size of the film is increased above few nanometres in thickness and to the micrometric scale in the horizontal extension. However, when dealing with films of nanometric thickness, a hydrodynamic description may fall short due to thermal fluctuations.…”

“…For instance, in the context of dewetting, rupture times measured in experiments are shorter than predicted by simulations of the thin-film equation [21][22][23]. More in general, thermal fluctuations can accelerate the appearance of film instabilities [14,[24][25][26]. The first theoretical and experimental studies, by means of light scattering techniques, on film rupture influenced by thermal fluctuations date back to the 1960s [27].…”