(varicose) waves can develop, as depicted in Figure 13.14b. If now the
amplitudeabecomes almost as large asd/2, the film will rupture according
to the de Vries mechanism. However, the waves may be damped. A theory
for film stability has been worked out based on wave formation and
damping, for the most part by Vrij and by Sheludko. Two kinds of forces
determine whether the wave is damped or not. (a)Colloidal interaction.If
only van der Waals attraction acts across the film, the amplitude will always
tend to grow, because the attractive force is largest where the film is thinnest
(see Section 12.2.1). If also repulsive forces act, which is the common
situation, growth of the amplitude will be slowed down. (b) TheLaplace
pressurein the film will be greater where the surface is concave than where it
is convex. This means that liquid will stream from the thick parts of a film to
the thin parts, damping the wave. For the same amplitude, the local
curvature of the film surfaces, and hence the difference in Laplace pressure
and the damping tendency, will be greater for a shorter wavelengthl. The
balance of these forces will determine whether the amplitude will tend to
keep increasing or not. Vrij derived thatawould grow, and the film be
FIGURE13.14 Cross section through a part of film of (average) thicknessd. (a)
Illustration of hole formation. (b) Properties of a varicose wave on the film.