Modeling and simulation of bubble nucleation in magma
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Volcanic eruptions are triggered by magma degassing, whose critical first step is the nucleation of bubbles. The pressure decrease during magma ascent makes the melt supersaturated in volatiles such as water, leading to the nucleation of supercritical fluid bubbles that subsequently grow and coalesce. The mechanism is not yet fully understood, not only because bubbles nucleate at depth and therefore cannot be directly observed, but also because their critical radii can be as small as a few nanometers, making experimental studies of bubble nucleation extremely difficult. Another major challenge is the determination of surface tension, since comparisons between experimental measurements of the nucleation rate and predictions of classical nucleation theory reveal discrepancies spanning several orders of magnitude. Here, we develop an asymmetric free energy model for a binary mixture of silicate melt and water, following the same ideas that recently led to a symmetric model. We calibrate the model parameters by fitting experimental phase diagrams. We then augment the free energy using square-gradient theory, thereby introducing a diffuse interface. The capillary coefficient is calibrated to reproduce the (planar) surface tension measured in experiments. The model allows us to calculate curvature corrections to the planar surface tension, such as the Tolman length, as well as the thickness of the melt-water interface. Finally, we couple the free energy with a rare-event technique and carry out simulations of water-bubble nucleation under different thermodynamic conditions. We measure critical radii, the nucleation energy barriers, and the associated nucleation rates.
