Spontaneous rupture of thin liquid films

TLDR

Hydrodynamic stability theory has been applied to study rupture of thin liquid films on solid surfaces and free films, which are typically less than several hundred Ångström thick. The study examines how a small perturbation of the free interface generates film motion that can be described by the Navier–Stokes equations. By adding a body force derived from London–van der Waals interactions to the Navier–Stokes equations, the authors determine the unstable wavelength range, rupture time, and the effect of soluble and insoluble surface‑active agents on film rupture. The resulting model accounts for experimental observations of condensation on solid surfaces and bubble coalescence.

Abstract

The rupture of a liquid film on a solid surface and of a free liquid film have been studied using hydrodynamic stability theory. The films are not thicker than several hundred Ångström. A small perturbation applied to the free interface generates motions in the film, and the assumption is made that the Navier–Stokes equations can be used to describe them. The difference in forces acting upon an element of liquid in a thin film and in a bulk fluid is accounted for by introducing a body force in the Navier–Stokes equations. This force is calculated from the potential energy per unit volume in the liquid caused by the London–van der Waals interactions with the surrounding molecules of the liquid and with those of the solid. If the perturbation grows, it leads to the rupture of the film. The range of wavelengths of the perturbation for which instability occurs is established and the time of rupture is evaluated. The effect of insoluble and soluble surface active agents is analyzed. Available experimental data concerning condensation on a solid surface and coalescence of bubbles are explained on the basis of the obtained results.