The effects of our three-dimensional world that influence the attempt to create a two-dimensional fluid are the thickness of the fluid, drag from the surrounding world "outside" the two dimensions, and deformations from a plane. It is important to reduce the influences of these effects to get as close to a purely two-dimensional fluid.
The thickness of the soap films, I used for my measurements, was on the order of , and the resolution of my measurements was , so there was a factor 100 in difference between the smallest scale I could discern in the film, and the thickness of the film. This is roughly equal to the ratio between the circumference of the Earth and the depth of the atmosphere, which on large scales shows two-dimensional behaviour.
The thinner you make the fluid, the less variations are possible in the third dimension, and the closer you get to the ideal approximation to a two-dimensional fluid - a one molecule thick film suspended in vacuum.
If the film was flowing on a fixed surface, there would be very large velocity variations through the film (the velocity would have to be zero at the bottom of the fluid layer). By suspending the film in air, we can move the large variations out of the soap film and into the surrounding air. The air just above and below the soap film is pulled along with the soap film, so the velocity at the two surfaces of the soap film will be (almost) the same.
Figure 3.1: Experimental set-up: (a) Feeding container. (b) Supporting wires. (c) Channel terminator. (d) Comb. (e) Funnel with particles. (f) Video camera. (g) DC lamp. (h) Backdrop of black cloth. The distance between the two wires that formed the "walls" of the channel was , and there was from the feeding container to the channel terminator.
Table 3.1: Details of the equipment used for the experiment.
Table 3.2: Soap film recipe.
Table 3.3: Physical properties of the water-glycerol mixture.
Figure 3.1 shows a drawing of the experimental set-up. The feeding container was an open rectangular box with a row of diameter holes in the bottom. The outermost holes were used for the two wires that suspended the film. The other end of the wires were wound around a rod that terminated the channel. The soap water mixture (see recipe in table 3.2) flowed from the rod into another container. The glycerol in the mixture increases the lifetime of the film. "Dawn" is a detergent that according to Hamid Kellay (and my own experience) makes more stable soap films than other detergents. A one-dimensional grid, in the shape of a comb, was put in the film to introduce turbulence on a small scale compared to the channel width. The centre-to-centre separation of the teeth was , and the diameter of the teeth was . I used small glass beads to visualise the flow. The diameter of the beads varied a factor 25 from to . The particles were fed a few at a time to the film from a small funnel placed just downstream of the comb. The hole in the funnel was so small that the particles would create an arch and thus block the flow (see ). A slight tap on the rack that held the funnel would cause the arch to break down and let some of the particles run out of the funnel before a new arch blocked the hole. The number of particles that came out of the funnel was more or less the same every time. A video camera placed above the channel, with the view axis perpendicular to the flow plane, recorded the positions of the particles. The section of the film that was in the field of vision of the camera was from the comb and approximately downstream. The video signal from the camera was fed to a video recorder for later analysis, and to a PC for display and real-time processing and analysis. The off-line data processing is described in detail in chapter 4. The particles in the film were illuminated by a DC lamp. The lamp was placed in such a way that there was no direct light on the backdrop, because the cloth could scatter enough light to disturb the image of the particles in the soap film.
Figure 3.2: Cross-section of a soap film. The hydrophilic head groups of the surfactant molecules, drawn as little filled circles, point into the film, while the hydrophobic tails point out of the film. The bulk of the film consists of a water-glycerol mixture with some balls of surfactant molecules. Please notice that the scale is not correct. The molecules are about 1000 times smaller than the thickness of the film.
Figure 3.3: Side view of the experimental set-up. The depth, d, in the feeding container was . The channel was long and the inclination of the channel was . The feeding container was tilted to keep the minimal surface between the wires and the container close to the holes that fed soap-water to the film.
The three of the five holes in the feeding container, that were not blocked by the wires that suspended the film, fed soap-water to the film. The level of soap water in the feeding container was kept at . At the feeding holes most of the soap-water was concentrated in three wide jets, but when you looked at the film downstream from the feeding container there were no visible traces of the jets (except that the film was flowing :-).