Acoustics of Cubic Bubbles: Six Coupled Oscillators

Abstract

In this manuscript we introduce cubic bubbles that are pinned to 3D printed millimetric frames immersed in water. Cubic bubbles are more stable over time and space than standard spherical bubbles, while still allowing large oscillations of their faces. We found that each face can be described as a harmonic oscillator coupled to the other ones. These resonators are coupled by the gas inside the cube but also by acoustic interactions in the liquid. We provide an analytical model and 3D numerical simulations predicting the resonance with a very good agreement. Acoustically, cubic bubbles prove to be good monopole sub-wavelength emitters, with non-emissive secondary surfaces modes.

Acoustic interaction between 3D-fabricated cubic bubbles

“…We have previously shown 10 that the acoustic resonance frequency of a cubic bubble is very close to that of a spherical bubble of the same volume. In addition, the emitted field is spatially very close to that of a monopolar source, provided the distance d of the observation to the cube centre is larger than the cube size.…”

“…Thanks to the recent evolution of 3D-printing techniques, we have shown in a previous work 10 that it is possible to (i) maintain the position of a gas bubble in water, and (ii) stabilise its size, using a single cubic frame where a bubble is trapped.…”

Tunable Fluid-Type Metasurface for Wide-Angle and Multifrequency Water-Air Acoustic Transmission

“…For trapping the air layer successfully, the solid structure should obey two principles. First, the bubble size (a − w) should be smaller than the capillary length (about 2.7 mm) for the surface tension being dominated [33]. Besides, the maximum Laplace pressure at the bottom air-water interface should always exceed the liquid static pressure of ρ w ðe + d Þg during the formation process (Figure 4(d)), otherwise, water will penetrate into the cells [34,35].…”

The Acoustics of Liquid Foams

“…Those results may directly be exported to the modeling of macroscopic foam acoustic properties. More complex degrees of freedom and couplings, however, remain to be investigated to complete the whole picture, taking into account (i) the dynamics of the vertices at the junction between four Plateau borders [53], and (ii) the compressibility of the air in the bubbles, using an approach similar to the one used to model the vibration of a cubic air bubble in water [55].…”

“…Bubble metascreens can thus be used as ultrathin coatings for turning acoustic reflectors into perfect absorbers [76,77]. Harazi et al have shown that cubic bubbles (bubbles pinned to 3D solid frame) can be elementary building blocks for the design of acoustic metamaterials [55]. Other types of acoustic metamaterials have been designed from liquid emulsions which are then solidified by polymerization.…”