the break-up of free films pulled out of a pure liquid bath

THE BREAK-UP OF FREE FILMS PULLED OUT OF A PURE
LIQUID BATH
D. LORENE CHAMPOUGNY (LABORATOIRE DE PHYSIQUE DES SOLIDES. UNIVERSITE PARIS SUD & CNRS );
D. EMMANUELLE RIO (LABORATOIRE DE PHYSIQUE DES SOLIDES. UNIVERSITE PARIS SUD & CNRS ); D. FREDERIC
RESTAGNO (LABORATOIRE DE PHYSIQUE DES SOLIDES. UNIVERSITE PARIS SUD & CNRS ); D. BENOIT SCHEID (TIPS FLUID PHYSICS UNIT. UNIVERSITE LIBRE DE BRUXELLES )
Generating a stable soap film is an easy task, while pulling a thin film out of an oil bath is almost
impossible. Yet, even in the absence of surface active molecules, some natural or industrial processes
involve long-lived thin films made of viscous liquids (e.g. lava or molten glass). How high can a film
made of pure liquid be pulled out of a bath before breaking up? This is the question we address in this
work, from both the theoretical and experimental points of view.
We derive a lubrication model to describe the non-stationary free liquid film that is created when a
vertical frame is pulled out of a liquid reservoir at a given velocity (see figure 1). We here focus on the
case of a pure liquid of constant surface tension γ, corresponding to a stress-free boundary condition at
the liquid/air interfaces of the film, and thus employ an essentially extensional description of the flow.
Taking into account van der Waals interactions between the interfaces, we observe that film rupture is
well-defined in time as well as in space, which allows us to compute the critical thickness and the film
height at the moment of rupture. The theoretical predictions of the model turn out to be in quantitative
agreement with experimental measurements of the break-up height L* of silicone oil films in a wide
range of liquid viscosities η, pulling velocities U and supporting fiber diameters D, as shown in
dimensionless units in figure 2 (where ℓc is the capillary length and Ca = ηU/γ the capillary number).
Sketches of the liquid film under consideration.
Comparison between the experimental data (symbols) and the
predictions of the model (solid lines).