2.2 Granular nature of crystal-rich magma reservoirs
Another obstacle towards our ability to accurately model compacting magmatic systems is whether the deformation of these systems is suitable for a continuum description, or if granular models which describe individual interactions between crystals are instead required. While magma mushes are often simplified as porous media for continuum calculations, in reality they are complex multiphase mixtures where forces can be transmitted at the particle-particle scale (Bergantzet al. , 2017). Such hydrogranular behavior leads to local energy dissipation and phase segregation such that the final state of the mixture cannot be predicted even if the initial conditions are constrained (Bergantz et al. , 2017, Philpotts et al. , 1998, Qin & Suckale, 2020, Schleicher & Bergantz, 2017). Numerical approaches to modeling magma mushes as granular media have been pursued by studies including Bergantz et al. (2017), who developed granular models capable of capturing such complex particle-particle behavior in magma mushes. However, one of the challenges for such models includes upscaling results to the magmatic (spatial and temporal) scale.
2 Derivation of a physics-based forward model
To explore the issues outlined above, we develop a numerical model of compaction and apply it first to the phase separation experiments of Hoyos et al. (2022). Hoyos et al. (2022) performed a series of analog “French Press” experiments on monodisperse (and in some cases, bi-disperse) particles immersed in corn syrup (Fig. 2a ). In these experiments, the bottom boundary of the experimental domain migrates upwards at a constant boundary velocity,\(\mathbf{v}_{\mathbf{h}}\), of 0.3 mm/min resulting in an applied force on the piston of the syringe (Fig. 2a ) and residual liquid being extracted. A full summary of the symbols and definitions used is provided in table 1 . The experimental setup is such that the average porosity in the suspensions, the displacement of the piston, and the applied force, are all recorded over the duration of the experiments. The experiments were performed on monodisperse particles shape distributions with aspect ratios of 1:1, 2:1, and 4:1. Only selected load curves are included in the main text of the manuscript, however, the load data for all the experiments can be found in the supplementary material.
Table 1 – Symbols and definitions.