A public study of the lifetime distribution of soap films
Eighth entry by Kelly Miller, AP225 Fall 2011
Authors: S. T. Tobin, A. J. Meagher, B. Bulfin, M. Möbius, and S. Hutzler
Journal: American Journal of Physics, Volume 79, Issue 8, August 2011, pg. 819
This paper presents data for over 2500 films that were gathered during a 2-month exhibition on the science of bubbles in Dublin's Science Gallery. Soap films were made out of commercial dish washing solution and sealed in acrylic containers. Visitors to the gallery were invited to create 10-20 parallel soap films in the acrylic containers which were then sealed with cork stoppers. The individual films burst at random and, each day the total number of remaining films in the tubes was recorded and a histogram of the bubble lifetimes was created. The histogram was found to be described by a "Weibull distribution", indicating that the failure rate is not constant and increases over time. The lifetime of the bubbles in sealed containers was compared to those in unsealed containers and it was found that unsealed containers contain bubbles that last significantly shorter periods of time compared to those found in sealed containers. This experiment was used to demonstrate and teach the difference between the unpredictability of the lifetime of individual films and the existence of a well-defined lifetime distribution when many bubbles are considered.
Experts in many fields, physics included, are becoming increasingly concerned that students are not taught statistics and probability well. This paper presents an example of a physical system that is governed by a probabilistic function - the decay and stability of soap films. Soap films provide a safe and simple medium in providing access to experiments that illustrate well the physics behind the stability of thin films and several interesting statistics concepts. The experiment described in this paper was part of a 2009 public exhibition called "BUBBLE", put on by the Science Gallery in Dublin in collaboration with the Trinity College Dublin Foams and Complex Systems group.
Lifetime of Soap Films
Visitors to the gallery filled acrylic cylindrical tubes with equally spaced parallel soap films (a "bamboo film"). The tubes were corked to isolate them from the environment and then, the number of circular films in each tube was counted every day. During the exhibition, 2586 soap films were made. The goal of the experiment was to determine a probability distribution of film lifetimes.
The apparatus used is described in Figure 1. A pump was used to blow air into a soap solution. The gas pressure was held constant so lead to the formation of equal-volume gas bubbles, which rose and were collected in a tube with a diameter of 16mm.
Each tube had between 10-20 thin films and was stoppered at both ends with cork stoppers which were wetted before in the same soap solution.
Every day, the total number of films in each tube was counted and the data was recorded and finally, a statistical analysis and data fitting was performed to determine what distribution or model best described it. To figure out which model best described the data, the authors used a two-sample Kolmogorov-Smirnov test which determines if two samples are drawn from the same distribution function. This test was used to compare the empirical distribution to the best fit of several candidate distributions (which appeared to be the best fits). The candidate distributions were the Weibull, Gamma, and log-normal distributions.
The Weibull distribution was the only one to pass the Kolmogorov test.
Figure 4 shows the distribution of the initial number of films in the tubes. A normal distribution model was fit to the data.
Towards the goal of understanding the distribution of the bursting of films as a function of time, a histogram of the number of occurrences of the different counts of film bursts was plotted on a log-linear scale. From this plot, it can be seen that approximately 90% of events involve only one or two bursts.
The authors also computed a lifetime distribution for the films and this data was fitted to a Weibull distribution. The difference between the fit and the data were found to follow a normal distribution suggesting that the differences can be attributed to random factors.
The shape parameter of k=1.55+/-0.05 corresponds to a failure rate that increases with time. As the films age, they become thinner and more delicate - possibly due to evaporation and drainage of liquid from the films. Evaporation is a function of the quality of the seal on the sample tubes and the ambient temperature and humidity. Drainage in bamboo foams occurs only in the thin wetting films along the tube walls and is therefore very limited. The authors noted that most films became black films (film thickness decreases to 20nm or less) after 2-3 weeks. This suggests that most of the liquid has drained or evaporated by then.
To try to figure out if there were interactions occurring between films (such as avalanches - where a bursting films triggers neighbouring films to burst) - the average lifetime as a function of the initial number of films in the sample tube was plotted together with the average of all film lifetimes. If interactions between films was an issue, the authors expected the average lifetime to change with the number of films in the sample (more film bursts when films are closer together). The authors found that the average lifetime appears constant with respect to the initial film count, suggesting a negligible effect from interactions.
To study the effects of exposure to the environment on the lifetime of the films, the authors did a small scale experiment where some tubes were left uncorked at one end, thereby exposing the films to several disruptive forces (evaporation, airborne contaminants and air flow).
All films in the uncorked tubes burst within 2 days (the average film lifetime in a corked tube was over 16 days).
What Causes the Thin Film to Rupture?
A thin film is stabilized by the balance between the attractive van der Waals forces and electrostatic repulsions. Thin films become thinner through drainage and evaporation until they reach a minimum thickness. The dependence of potential energy on film thickness is thought to have two minima (one at ~20 nm and another at ~5nm (referred to as a black film)). Black films are very fragile and can be ruptured easily by environmental factors. In this experiment these environmental conditions were minimized and yet - the films still burst. This begs the question, what causes the films to rupture?
One possible model to explain thin film rupture is thermally excited capillary waves on both surfaces of the film. The waves can move the interfaces temporarily closer together and the increased van der Waals attraction causes the films to rupture. This model is not universally accepted and recently, the importance of hydrodynamic interactions has been emphasized. How the models for film rupture explain the Weibull distribution found in this paper is still not well understood.