Dynamics of thin films - Frank Müller
The most familiar process in this scope is the rupture of a soap bubble, a process which is well known to everyone. But what happens from the hydrodynamical point of view? A similar phenomenon are the detachment of a water drop from the tab. Such processes have been in the focus of scientists for more than one hundred years, with Lord Rayleigh being one of the first who investigated e.g. the rupture of planar soap films and the instabilities of jets qualitatively. In fact, progress in technology allows nowadays a more detailed study of these very fast processes. We use a fast camera (up to 100.000 frames per secons) in order to make dynamics visible that are far too fast for the naked eye.
Break-up of catenoids
A catenoid is a film with a minimal surface spanned between two rings. When a critical distance of the rings (D = 1.325R; R ... radius of the rings) is exceeded, the catenoid becomes instable and starts to collapse:
These images are taken with the fast camera. The time axis runs from left to right. The upper row shows the collapse of a catenoid with a film thickness of approximately 200 nm, the film thickness of the catenoid in the lower sequence is about 4300 nm. It turns out that for films thinner than 500 nm, there appears a so called satellite bubble in the center, if the film is thicker, there is a filament inbetween. Furthermore, the thinner film collapses much faster. For more details see the following movies: formation of satellite bubble (0.4 MB), formation of filament (1.0 MB), and our publication in Europhys. Lett. The following diagrams illustrate the dynamics of the collapse process. Several contributions, such as inertia of air and liquid and viscosity of both, may play a crucial role during collapse.
The left hand diagram shows the dependence of the waist radius r0 on time. This dependence is depicted for four films of different film thickness. It can clearly be seen that the inward velocity v/R increases with decreasing film thickness. In the right diagram, the dependence of the slope (red line in the left diagram), which represents the inward velocity at the minimal radius on the film thickness is shown. Measurements have been performed at ambient pressure and at 0.1 bar in order to separate the influence of the air inertia and viscosity from the liquid. It is clear from the right hand diagram that the air cannot be neglected for films thinner than about 2 micrometers.
This image shows an expamle of a catenoid, which is illuminated with parallel, monochromatic (535 nm) light. Due to interference of light at the front and rear sides of the film, a ring-like structure appears that depends on the film thickness. These experimental images can be compared with calculated ones, in order to estimate the film thickness with an accuracy up to 10 nm.
Here one can see a bubble with a film thickness of approximately 1840 nm. Rupture is initiated with a needle. The part of the film, which is not collected in the rim remains widely undisturbed at the initial position. An astonishing phenomenon occuring during rupture is the darkening of the remaining bubble. Laser scattering experiments show that this darkening is related to structural changes in the film. Further, the formation of a brim is an interesting issue. The radial force competes with the surface tension, and thus the rim is forced outward. For more information see movie (0.2 MB) or publications.
This diagram shows the dependence of the rim velocity on the inverse square root of the film thickness. As proposed by Culick's model, the dependence is linear, on the other hand the measured values are about 20 % too low, compared with the model.
The rim becomes unstable if the film thickness is in a certain range (300 - 600 nm). There occurs a fingering and finally droplets are released from the rim. This droplet formation has already reported by Pandit et al. (1990). So far, this instability is not quite well understood.
This image sequence shows a blow-up of the same image sequence as above, here with the focus on the brim formation. This brim is the stronger pronounced, the thicker the film is.
2006
F. Müller and R. Stannarius: Collapse of catenoid-shaped smectic films (2006), Europhys. Lett. 76, 1102-1108
2007