Modelling multi-phase flows in magmatic systems

Magmatic systems in the Earth's mantle and crust range from melt-poor partially molten rock, to mush bodies at intermediate melt fractions, and lenses of melt-rich, eruptible magma suspensions. Previous process-based models, however, have represented magmatic systems as either porous flows at low melt fractions (<20%) or suspension flows at high melt fractions (>60%). A lack of theoretical basis to represent mush flows at intermediate phase fractions has thus far hindered investigations into the dynamics of crustal mush bodies. Previous theories were formulated specifically for two-phase flows of melt-solid mixtures, hence not allowing for the inclusion of a third, volatile or other fluid phase. My contribution addresses this gap by presenting a comprehensive theoretical model [1] of magmatic multi-phase flows across all phase fractions at the system scale, rooted in mixture theory. I substantiate its applicability with a numerical implementation utilising a finite-difference staggered-grid approach [2]. 

 

Numerical experiments replicate expected behaviours for two-phase flows 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. In the mush regime, numerical experiments show strong melt localisation into lenses and stress-aligned melt-shear bands. A further application to a three-phase flow problem of immiscible melt segregation from a crystallising magma body demonstrates the versatility of the theoretical model and its numerical implementation. The model code is available open source at github.com/kellertobs/pantarhei.

 

References

[1] Keller & Suckale, GJI, 2019. https://doi.org/10.1093/gji/ggz287.

[2] Wong & Keller, GJI, 2022. https://doi.org/10.1093/gji/ggac481.