An expansion-coalescence model for bubble growth in viscous fluids

We statistically describe at a mesoscopic level the growth by decompres- sion, exsolution and coalescence of a population of gas bubbles immersed in a viscous fluid. The model treats in particular the case of water gas bubbles entrained in a viscous magma ascending in a volcano conduit. Bubbles are characterized both by their volume and mass, but are homogeneously dis- tributed in space and have no relative velocity. Volume and mass growth rates as well as the coalescence operator are defined starting from a micro- scopic model and by means of physical arguments. Numerical simulations show a good agreement of the computed volumes distributions with those measured in experiments, justifying the importance to consider coalescence in this framework and the need of more precise experiences in order to better validate the coalescence kernel