Fig. 2: Acoustic modes for a spherical (non-tethered) bubble.

The predicted eigen-frequencies for the acoustic modes of a 100-µm-radius bubble are indicated by the vertical lines. Results from a numerical solver (COMSOL), an analytical bubble model for radial modes only²⁰, and an analytical model for a spherical resonator with hard walls³¹ are indicated by the legend. The numerically predicted pressure distributions for the ten lowest-order modes are also shown, with the gas/liquid boundary indicated by the inner concentric circle. The mode labeled as ‘(i)’ is the Minnaert breathing mode, and the others are higher-order acoustic modes