Thermal fluctuations in capillary thinning of thin liquid films

Abstract

Thermal fluctuations have been shown to influence the thinning dynamics of planar thin liquid films, bringing predicted rupture times closer to experiments. Most liquid films in nature and industry are, however, non-planar. Thinning of such films not just results from the interplay between stabilizing surface tension forces and destabilizing van der Waals forces, but also from drainage due to curvature differences. This work explores the influence of thermal fluctuations on the dynamics of thin non-planar films subjected to drainage, with their dynamics governed by two parameters: the strength of thermal fluctuations, θ, and the strength of drainage, κ. For strong drainage (κ κ tr ), we find that the film ruptures due to the formation of a local depression called a dimple that appears at the connection between the curved and flat parts of the film. For this dimple-dominated regime, the rupture time, t r , solely depends on κ, according to the earlier reported scaling, t r ∼ κ −10/7 . By contrast, for weak drainage (κ κ tr ), the film ruptures at a random location due to the spontaneous growth of fluctuations originating from thermal fluctuations. In this fluctuations-dominated regime, the rupture time solely depends on θ as t r ∼ −(1/ω max ) ln( √ 2θ ) α , with α = 1.15. This scaling is rationalized using linear stability theory, which yields ω max as the growth rate of the fastest-growing wave and α = 1. These insights on if, when and how thermal fluctuations play a role are instrumental in predicting the dynamics and rupture time of non-flat draining thin films.

Thermal capillary wave growth and surface roughening of nanoscale liquid films

“…A long-wave approximation for thin films, and also for jets, has been used to derive stochastic lubrication equations (SLE) from FH: the jet SLE by Moseler & Landman (2000), and the planar-film SLE by Grün, Mecke & Rauscher (2006), Davidovitch, Moro & Stone (2005) and Durán-Olivencia et al (2019). Notably, numerical solutions to the jet SLE (Moseler & Landman 2000;Eggers 2002;Zhao, Lockerby & Sprittles 2020) and the planar-film SLE (Grün et al 2006;Nesic et al 2015;Diez, González & Fernández 2016;Durán-Olivencia et al 2019;Shah et al 2019) demonstrated that noise can accelerate the rupture process, in agreement with experimental analyses (Becker et al 2003).…”

Influence of initial film radius and film thickness on the rupture of foam films

“…while the lower bound is dictated by the region where curvature goes from practically zero in the flat part to 2/R c in the curved part. This leads to R pb √ h o R c , as discussed in more detail in Shah et al [35]. We now perform a scaling analysis to demonstrate that the problem is governed by two dimensionless parameters.…”

“…The mobility term (rh 3 ) is discretized as per the positivity-preserving scheme discussed in Diez et al [34]. Based on our previous work [35], we use r = 0.05 and t = r 2.25 , and confirm that the presented simulation results for lifetimes are grid and time-step size independent.…”

“…To turn to the dimensional quantities, one should then use the following choices of scales: h 0 and film radius R film . The lower limit of the film radius (40 μm) was chosen based on the experimentally observed values [25,36], while the upper limit (4000 μm) was chosen to approach the semi-infinite film asymptote [29,35,37]. The range of initial film thicknesses studied in this work is representative of the drainage experiments reported in the literature [7,36].…”

“…We start with a description of films with the largest radius (R film = 4000 μm) considered in this work, connecting their behavior to the well-known behavior of semi-infinite films [29,35,37]. The features of thinning of large films are the same for thin (h 0 = 300 nm) and thick (h 0 = 2000 nm) films.…”