Polyhedral Bubble Vibrations

Abstract

Underwater bubbles are extremely good acoustic resonators, but are freely evolving and dissolving. Recently it was found that bubbles can be stabilized in frames, but the influence of the frame shape is still undocumented. Here we first explore the vibration of polyhedral bubbles with a low number of faces, shaped as the five Platonic solids. Their resonance frequency is well approximated by the formula for spherical bubbles with the same volume. Then we extend these results to shapes with a larger number of faces using fullerenes, paving the way to obtain arbitrary large resonant bubbles.

Post-buckling dynamics of spherical shells

“…The apparition of a second frequency invalidates the previous models where the oscillations come from the sole contribution of gas compressibility. Note that we cannot expect more complex behaviour, like the apparition of a second frequency, to emerge from a bubble yet having a non-spherical shape: it has been shown recently [47], in agreement with [48], that the generalized Minnaert model, where the radius of the spherical bubble is replaced by the effective radius extracted from the volume, is robust against geometry changes.…”

“…The result is that in the meantime, the frequency decreases. One can question this observation by extrapolating, in a first approach, that the contribution of the gas to the frequency would scale like the Minnaert frequency ωM of a free spherical bubble: ωM2∝Pe/Ve3/2, where we have simply replaced the usual radius of the original Minnaert expression by a generalized radius based on the volume, as in [47,48]. Since the volume at equilibrium Ve is an increasing function of internal pressure Pe, it is not clear a priori that the Minnaert frequency increases with pressure.…”

Post-buckling Dynamics of Spherical Shells

“…The apparition of a second frequency invalidates the previous models where the oscillations come from the sole contribution of gas compressibility. Note that we cannot expect more complex behavior, like the apparition of a second frequency, to emerge from a bubble yet having a non-spherical shape: it has been shown recently [46], in agreement with [47], that the generalized Minnaert model, where the radius of the spherical bubble is replaced by the effective radius extracted from the volume, is robust against geometry changes.…”

“…, where we have simply replaced the usual radius of the original Minnaert expression by a generalized radius based on the volume, as in [46,47]. Since the volume at equilibrium V e is an increasing function of internal pressure P e , it is not clear a priori that the Minnaert frequency increases with pressure.…”

Interferometric detection of hydrodynamic bubble–bubble interactions

“…However, well-controlled experiments are difficult to devise. A major pitfall is the lack of control on bubble positions, and hence on inter-bubble distances, as well as geometry of larger ensembles; this issue is generally addressed by tethering the bubbles to solid supports (Hsiao et al 2001;Chew et al 2011;Combriat et al 2020;Boughzala et al 2021) or by optical trapping (Garbin et al 2007). In the case of micrometric bubbles, coalescence and/or dissolution are common phenomena, which can be limited, for instance, by stabilising adsorbed shells on the bubbles ( Van der Meer et al 2007).…”