A model of bubble growth during decompression of supersaturated melt was developed in order to explore the conditions for preservation of gas overpressure in bubbles or for maintaining supersaturation of the melt. The model accounts for the interplay of three dynamic processes: decompression rate of the magma, deformation of the viscous melt around the growing bubble, and diffusion of volatiles into the bubble. Generally, these processes are coupled and the evolution of bubble radius and gas pressure is solved numerically. For a better understanding of the physics of the processes, we developed some analytical solutions under simplifying assumptions for cases where growth is controlled by viscous resistance, diffusion or linear decompression rate. We show that the solutions are a function of time and two dimensionless numbers, which are the ratios of either the diffusive or viscous time scales over the decompression time scale. The conditions for each growth regime are provided as a function of the two governing dimensionless parameters. Analytical calculations for some specific cases compare well with numerical simulations and experimental results on bubble growth during decompression of hydrated silicic melts. The model solutions, including the division to the growth regimes as function of the two parameters, provide a fast tool for estimation of the state of erupting magma in terms of gas overpressure, supersaturation and gas volume fraction. The model results are in agreement with the conditions of Plinian explosive eruption (e.g. Mount St. Helens, 18 May 1980), where high gas overpressure is expected. The conditions of effusion of lava domes with sudden onset of explosive activity are also in agreement with the model predictions, mostly in equilibrium degassing and partly in overpressure conditions. We show that in a situation of quasi-static diffusion during decompression the diffusive influx depends on the diffusivity away from the bubble, insensitive to the diffusivity profile.
- Bubble growth