A new theory of bubble formation in magma

We have newly developed an accurate theoretical model of bubble formation in supersaturated magma with a relatively low viscosity under the formulation by Toramaru (1995). Such a model is essential in deriving considerable information from the data of bubble nucleation in the recent decompression experiments. We obtain analytical solutions for the time evolution of the nucleation rate and the number density of nucleated bubbles in cases with constant decompression rates and constant supersaturation pressures. Both the bubble number density and the duration time of nucleation obtained in this study are larger than those obtained by Toramaru by a factor of 10. We find that the uncertainty of several orders in the classical nucleation rate has little effect on the final number density of bubbles in cases of continuous decompression. In the formulation by Toramaru, a spatially uniform volatile concentration surrounding the growing bubbles is assumed. We also construct a nonuniform concentration model and subsequently show that an uniform concentration model is valid for the evaluation of the bubble number density. Finally, we apply our model to the recent decompression experiments and indirectly estimate the surface tensions of the rhyolitic melt with only H₂O and with H₂O and CO₂. Our indirect estimates indicate that the surface tensions for 7 wt % H₂O dissolved in melt are 0.08 ± 0.01 N m^-1 for samples with no CO₂ and 0.07 ± 0.01 N m^-1 for samples with a considerable amount of CO₂, respectively. These estimations are consistent with the available experimental values of the surface tension.