A unified numerical model for two-phase porous, mush and suspension flow dynamics in magmatic systems

Abstract

SUMMARYMagmatic 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 in the suspension flow regime at high melt fractions. Connections between the two-phase end-member 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 2-D system-scale numerical model of the fluid mechanics of an n-phase system at all phase proportions, based on a recent theoretical model for multiphase 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 1-D and 2-D numerical experiments across the porous, mush and suspension flow regimes. The experiments replicate known phenomena from end-member regimes, including rank-ordered porosity wave trains in 1-D and porosity wave breakup in 2-D in the porous flow regime, as well as particle concentration waves in 1-D and mixture convection in 2-D in the suspension flow regime. By extending self-consistently into the mush regime, the numerical experiments show that the weakening solid matrix facilitates liquid localization 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 end-member theories is needed to ensure accurate timescales and mechanics. With a self-consistent way to examine multiphase mixtures at any phase proportion, this new model transcends theoretical limitations of existing multiphase numerical models to enable new investigations into two-phase or higher magma mush dynamics.