Propagation of ultrasound in aqueous foams: bubble size dependence and resonance effects

We report experimental results on the propagation of ultrasonic waves (at frequencies in the range of 40 kHz) in aqueous foams. Monitoring the acoustics of the foams as they age, i.e. as the mean bubble radius increases by coarsening, we recover at short times some trends that are already known: decrease of the speed of sound and increase of attenuation. At long times, we have identified, for the first time, robust non-monotonic behaviors of the speed of sound and attenuation, associated with a critical bubble size, which decreases at increasing frequency. The experimental features appear to be surprisingly reminiscent of the Minnaert resonance known for a single isolated bubble in a fluid. Transposing the Minnaert theoretical framework to the limit of a dense packing of bubbles gives some qualitative agreement with the data, but still cannot explain quantitatively the measured properties.