An experimentally validated numerical model for bubble growth in magma

Volcanic eruptions are driven by the growth of gas bubbles in magma. The timing and rate of bubble growth are important because they determine whether enough gas pressure can develop to fragment the melt. Bubbles grow in response to decompression and diffusive transport of dissolved volatiles (predominantly H2O) that exsolve into the bubbles. Growth is resisted by the viscosity of the melt. Both melt viscosity and H2O diffusivity have non-linear dependence on the concentration of H2O dissolved in the melt, which necessitates a numerical approach to modelling bubble growth. Several bubble growth models have previously been published and applied, but none of them has been validated against continuous, in situ experimental data or provided as a user-friendly tool. Here we present a numerical bubble growth model, implemented in MATLAB, which allows for arbitrary temperature and pressure pathways, and accounts for the impact of spatial variations in dissolved H2O concentration on viscosity and diffusivity. We validate the model against two sets of experimental data: (1) New continuous data for gas-volume fraction as a function of time, collected using optical dilatometry of vesiculating hydrous obsidian samples which were heated from 930 °C to 1000 °C at atmospheric pressure. This dataset captures isobaric, isothermal bubble growth under strongly disequilibrium conditions. (2) Discrete data from published decompression experiments at 825 °C and pressures from 200 MPa to ~5 MPa with decompression rates from 0.1 MPa s−1 to 10 MPa s−1. These experiments represent isothermal, decompression-driven bubble growth spanning equilibrium to strongly disequilibrium conditions. The numerical model closely reproduces the experimental data across all conditions, providing validation against contrasting bubble growth scenarios. The validated model has a wide range of potential volcanological applications, including forward modelling of bubble growth phenomena, and inverse modelling to reconstruct pressure–temperature–time pathways from textures and volatile contents of eruptive products.