Permeability of polydisperse magma foam

Effective models for the evolution of magma permeability are key to understanding shallow magma ascent and eruption dynamics. Models are generally empirical constructs, commonly focused on monodisperse systems, and unable to cope with the foam limit at high porosity. Here, we confirm that bubble size distributions in high-porosity pyroclasts are highly polydisperse. We combine collated experimental data and numerical simulations to test and validate a theoretically grounded percolation model for isotropic magma permeability, which accounts for the effect of polydispersivity of bubble sizes. We find that the polydispersivity controls the percolation threshold. It also serves as essential input into the scaling of permeability that is required to achieve universality in the description of permeability. Our model performs well against collated published data for the permeability of high-porosity volcanic rocks. We then extend this model to predict the viscous and inertial contributions to fluid flow that are required to model magma outgassing in all regimes. Our scaling relationship holds across the full range of porosity, from the percolation threshold to the open-foam limit.