Distribution of soap molecules in flowing soap films

Flowing soap films are useful tools to simulate two-dimensional flows. The Marangoni elasticity due to the presence of soap molecules not only stabilizes the soap film but also imparts it compressibility to the two-dimensional flow in the soap film. Therefore, it is desirable to measure the surface concentration $c_s$ of soap molecules to understand the physics flowing soap films. In this study, we present an indirect measurement of $c_s$, by making a direct measurement of the surface tension and the Marangoni elasticity. Using a two-stage model for soap distribution in the flows, the range of $c_s$ is calculated for different thickness and the soap solution concentration. Our model shows that the soap film will have the same $c_s$ for the range of parameters in popular use and in agreements with experimental data.