The permeability of loose magma mush

Models for the evolution of magma mush zones are of fundamental importance for understanding magma storage, differentiation in the crust, and melt extraction processes that prime eruptions. These models require calculations of the permeability of the evolving crystal frameworks in the mush, which influences the rate of melt movement relative to crystals. Existing approaches for estimating the crystal framework permeability do not account for crystal shape. Here, we represent magma mush crystal frameworks as packs of hard cuboids with a range of aspect ratios, all at their maximum random packing. We use numerical fluid flow simulation tools to determine the melt fraction, specific surface area, and permeability of our three-dimensional digital samples. We find that crystal shape exerts a first-order control both on the melt fraction at maximum packing and on the permeability. We use these new data to generalize a Kozeny-Carman model in order to propose a simple constitutive law for the scaling between permeability and melt fraction that accounts for crystal shape in upscaled mush dynamics simulations. Our results show that magma mush permeability calculated using a model that accounts for crystal shape is significantly different compared with models that make a spherical crystal approximation, with key implications for crustal melt segregation flux and reactive flow.