Ying Qi Wong , Tobias Keller

Magmatic systems in the Earth's mantle and crust contain multiple phases including solid crystals, liquid melt and low viscosity fluids. Depending on depth, tectonic setting and chemical composition, magmatic systems can range from partially molten rock at low melt fraction to magma mushes at intermediate melt fraction to magmatic suspensions at high melt fraction. However, the theories underpinning most process-based models of magmatic systems describe magma as a single-phase fluid, or as a two-phase mixture either in the porous flow regime at low melt fractions or the suspension flow regime at high melt fractions. Connections between the two-phase endmember theories are poorly established and hinder investigations into the dynamics of mush flows at intermediate phase fractions, leaving a significant gap in bridging trans-crustal magma processing from source to surface. To address this knowledge gap and unify two-phase magma flow models, we develop a two-dimensional system-scale numerical model of the fluid mechanics of an n-phase system at all phase proportions, based on a recent theoretical model for multi-phase flows in igneous systems. We apply the model to two-phase, solid-liquid mixtures by calibrating transport coefficients to theory and experiments on mixtures with olivine-rich rock and basaltic melt using a Bayesian parameter estimation approach. We verify the model using the Method of Manufactured Solutions and test the scalability for high resolution modelling. We then demonstrate 1D and 2D numerical experiments across the porous, mush and suspension flow regimes. The experiments replicate known phenomena from endmember regimes, including rank-ordered porosity wave trains in 1D and porosity wave breakup in 2D in the porous flow regime, as well as particle concentration waves in 1D and mixture convection in 2D in the suspension flow regime. By extending self-consistently into the mush regime, the numerical experiments show that the weakening solid matrix facilitates liquid localisation into liquid-rich shear bands with their orientation controlled by the solid stress distribution. Although the present model can already be used to investigate three-phase mixtures using conceptually-derived transport coefficients, more rigorous calibration to experiments and endmember theories is needed to ensure accurate time scales and mechanics. With a self-consistent way to examine multi-phase mixtures at any phase proportion, this new model transcends theoretical limitations of existing multi-phase numerical models to enable new investigations into two-phase or higher magma mush dynamics.