Self-similarity of bubble size distributions in the aging metastable foams

Abstract The quantitative approach to self-similar growth of gas bubbles in slowly evolving metastable liquid foams is provided using a solution to an evolution equation in the form of the non-linear Fokker–Planck equation. The obtained self-similar solution is compared to the experimental data obtained using the image analysis of liquid films at the container wall and the low-coherence reflectometry of foam samples. In addition, the modeled data are compared to the results of x-ray tomographic study of slowly aging foams, which were taken from the work of J. Lambert et al. The analyzed size distributions for surface film cells and bulk bubbles in the isolated samples of modeled liquid foams (Gillette shaving cream) allow for fitting with good accuracy using the self-similar solutions to the non-linear Fokker–Planck equation at the various aging times and various temperatures. The relationship between probability distributions for the normalized radii of the film cells and bulk bubbles is established. It is shown that the temperature-dependent rate factor of self-similar growth of the film cells and bulk bubbles can be considered in terms of the Arrhenius equation.