Extended Data Fig. 4: Simulation of free bubble dissolution.

The kinetics of gas bubble dissolution were calculated based on the modified-EP (Epstein and Plesset) equation, following the analysis in [25]: \(- \frac{{{{{\mathbf{dr}}}}}}{{{{{\mathbf{dt}}}}}} = \frac{{{{\mathbf{L}}}}}{{{{{\mathbf{r}}}}/{{{\mathbf{D}}}}_{{{\mathbf{w}}}}}}\left( {\frac{{1 + 2\sigma /{{{\mathbf{P}}}}_a{{{\mathbf{r}}}} - {{{\mathbf{f}}}}}}{{1 + 3\sigma /4{{{\mathbf{P}}}}_a{{{\mathbf{r}}}}}}} \right)\), where P_a = 101.3 kPa is the hydrostatic pressure outside the bubble and r is the bubble radius. Here, L = 0.02 is Ostwald’s coefficient, D_w = 2 × 10⁻⁵ cm² s⁻¹ is the gas diffusivity in water, σ = 72 mNm⁻¹ is the surface tension, and f = 1 is the ratio between the gas concentration in the medium versus that at saturation. This model assumes a perfectly spherical geometry and neglects the potentially stabilizing effects of the nearby collapsed GV shell. However, it provides useful simulations that illustrate the time constants relevant to the process of GV cavitation. (a) Radius-time curves of free air-filled bubbles of different initial sizes. The gas liberated from a collapsed GV occupied the volume of a sphere with a radius of 89 nm under atmospheric conditions and no surface tension, and is expected to have an initial radius slightly larger than 20 nm when surface tension between air and water is assumed across its surface. The actual initial radius is expected to be somewhere between these two values, depending on the degree of stabilization by collapsed GV shells or other solution components. (b) Time before 50% volume reduction for free air-filled bubbles of different sizes. These time constants support the ability of nanobubble to survive the half-cycle between GV collapse (peak pressure) and peak rarefaction. In addition, they can guide the selection of the pulse repetition interval after the initial bubble growth.