An expansion–coalescence model to track gas bubble populations in magmas

Abstract

We propose a kinetic model that statistically describes the growth by decompression, exsolution and coalescence of a polydisperse population of gas bubbles in a silicate melt. The model is homogeneous in space and its main variable is a distribution function representing the probability to find a bubble of volume v and mass m at time t. The volume and mass growth rates are described by a simplification of the classical monodisperse bubble growth model. This simplification, which shortens computational time, removes the coupling between mass evolution and an advection–diffusion equation describing the behavior of the volatile concentration in the melt. We formulate three coalescence mechanisms: thinning of the inter-bubble planar films, film deformation by differential bubble pressure, and buoyancy-driven collision. Numerical simulations based on a semi-implicit numerical scheme show a good agreement between the coalescence-free runs and the monodisperse runs. When coalescence is introduced, numerical results show that coalescence kernels based on different physical mechanisms yield distinct evolutions of the size distributions. A preliminary comparison between runs and experimental data suggests a qualitative match of two out of the three proposed kernels. This kinetic model is thus a powerful tool that can help in assessing how bubble growth and coalescence occur in magmas.