Possible mechanism for the spontaneous rupture of thin, free liquid films

TLDR

Thin liquid films are unstable to thickness fluctuations with wavelengths exceeding a critical value Λc determined by interfacial tension and the curvature of the interaction free energy, which can include van der Waals attraction and double‑layer repulsion. This study investigates the stability of free, thin liquid films against spontaneous thickness fluctuations. The authors model fluctuation growth by assuming laminar flow between rigid surfaces at constant viscosity, deriving expressions for the critical wavelength Λc and fastest‑growing time constant τm from van der Waals forces, and calculating the film lifetime and critical thickness hc for microscopic circular films, comparing with experimental data. They find that certain fluctuation modes grow exponentially with a characteristic time τm, that Λc ranges from 0.6 to 600 µm and τm from fractions of a second to hours for typical parameters, and that calculated critical thicknesses for water and aniline films (410 Å and 750 Å) are close to experimental values (270 Å and 410 Å).

Abstract

The stability of a free, thin liquid film against small, spontaneous thickness fluctuations is explored. The film is unstable with respect to fluctuations with wavelengths larger than a critical wavelength Λc=[–2π2γ/(d2V/dh2)]½, where γ is the interfacial tension and V(h) the free energy of interaction as a function of the film thickness h. V(h) may include van der Waals attraction and double-layer repulsion. The kinetics of the growing fluctuations is obtained by assuming a laminar liquid flow between rigid film surfaces at a constant viscosity. There are stable fluctuation-modes, which grow exponentially with time, each with a characteristic time constant τ, and modes with certain wavelengths grow faster than all others (τ=τm). If the van der Waals forces predominate Λc and τm are given by eqn. (4.2) and (4.3) respectively. For A= 10–14-10–12erg, γ= 30 dyne/cm and h= 100–1000 Å, Λc ranges from 0.6–600 µ and τm from a fraction of a second to several hours. The life-time and critical thickness hc of an unstable film are also calculated; they depend on the time constant τm and on the time of draining. The critical thickness is calculated for microscopic, circular films and compared with measurements of Scheludko and Exerowa. For water and aniline films, the calculated hc are 410 and 750 Å respectively, whereas the experimental values are 270 and 410 Å.