The two series show the same kind of evolution of the number of bubbles per unit volume of glass, N , with decreasing pressure (Fig.  2 ): as soon as the nucleation pressure is crossed, N increases very rapidly (within a few MPa), and then it stabilizes to a value that is strongly sensitive to the decompression rate.

The detailed evolution of N with P_F in the 1,000 kPa/s series may be divided into three stages (Fig.  2 ): (1) the main nucleation stage, characterized by very high nucleation rates and a dramatic increase of N (from 0 mm ⁻³ at 64.5 MPa to 4,400 mm ⁻³ at 59.7 MPa); (2) the secondary nucleation stage (from P_F  = 59.7 to 39.9 MPa), corresponding to smaller nucleation rates and a slow increase of N (from 4,400 mm ⁻³ at 59.7 MPa to 5,900 mm ⁻³ at 39.9 MPa); and (3) the coalescence stage, during which N decreases slowly (from 5,900 mm ⁻³ at 39.9 MPa to 3,200 mm ⁻³ at 20.5 MPa).

( 2000 ) and a temperature dependency of 7.3 × 10 ⁻⁵  N/m/°C (from a best linear fit from the data points in their Fig.  2 ), we compute σ _LB  = 0.103 N/m for a rhyolitic melt at 200 MPa–800°C.

In our experiments, N was not controlled by N_XL for two reasons: (1) the numbers of bubbles are two orders of magnitude smaller than the numbers of crystals in the 1,000 kPa/s series ( N_XL  = 8.7 ± 2 × 10 ⁵  mm ⁻³ ; Figs.  2 , 3 ), and four orders of magnitude smaller in the 27.8 kPa/s series and (2) as the number density of crystals is the same in the two series, a control of N by N_XL cannot account for the strong correlation between N and $$ \left| {\left.