Numerically Efficient Model for the Nucleation, Growth, and Coalescence of Bubbles in Magma

We present a numerical model to describe the nucleation, growth, and coalescence of bubbles in a decompressed magma. The new model enables us to calculate the bubble size distribution (BSD) at a low computational cost by taking the bubble mass as a variable. We propose an approximate solution of nonsteady diffusional growth and a new coalescence kernel based on the film drainage of growing bubbles. We validate the new model against three sets of experimental samples that were decompressed at constant rates. The developed model reproduces the experimental BSDs across variable conditions. The new findings of our model are summarized as follows. First, nonsteady volatile diffusion, which reduces supersaturation around the nucleation peak, decreases the bubble number density by an order of magnitude. This effect resolves the discrepancy between the numerical and experimental data when nucleation and growth are dominant. Second, bubble coalescence broadens the BSD depending on the decompression rate, melt viscosity, and vesicularity. Finally, a power‐law BSD observed in the 2008 Chaitén pumice cannot be created by constant decompression rates. The power‐law behavior requires an increasing decompression rate that enables bubbles to nucleate continuously during magma ascent. In such an accelerated magma, bubble coalescence has a negligible effect on BSD because the duration of magma ascent at high vesicularity is too short to allow bubbles to enter into contact. In conclusion, the proposed numerical model has a wide range of applications for assessing how magma ascends during an eruption.