Scaling Laws in the Dynamics of Collapse of Single Bubbles and 2D Foams

Avalanches of rupturing bubbles play an important role in the dynamics of collapse of macroscopic liquid foams. We hypothesized that the occurrence of cascades of rupturing bubbles in foams depends, at least in part, on the power released during the rupture of a bubble. In this paper, we present results on the dynamics of single bubble bursting obtained by analyzing the pressure wave (sound) emitted by the bubble when collapsing. We found that the released energy varies linearly with bubble size, the frequency of the emitted sound follows a power law with exponent 3/2 (compatible with the Helmholtz resonator model) and the duration of a rupturing event seems to be independent of bubble size. To correlate the dynamics of individual bubbles with the dynamics of foams, we studied the occurrence of avalanches on bubble rafts and found that the phenomenon appears to be a self-organized criticality (SOC) process. The distribution functions for the size of the avalanches are a power law with exponents between 2 and 3, depending on the surfactant concentration. The distribution of times between ruptures also follows a power law with exponents close to 1, independently of the surfactant concentration.