The permeability of loose magma mush

Abstract

<div><strong><strong>Large-volume rhyolitic eruptions are characteristically crystal-poor yet are thought to originate from crystal rich magma mush bodies. This contradiction is explained by the interstitial melt being extracted prior to the eruption, generating large volumes of crystal-poor magmas. The timescale for melt extraction is inversely correlated to the permeability of the mush, defined by the shape of the crystals. Yet, existing approaches for estimating the crystal framework permeability do not account for crystal shape. Here, we represent magma mush by using numerically generated packs of hard cuboids with a range of aspect ratios and at their maximally dense random packing. We use lattice-Boltzmann simulations to constrain the permeability of the cuboid packs, showing that crystal shape exerts a first-order control on both the melt fraction at maximum packing, and on the constitutive relationship between permeability and melt </strong>fraction. Using percolation theory and a validation dataset, we develop a predictive scaling framework to compute permeability for mush comprised of crystals that can be approximated by cuboids, valid at melt fractions down to, and including the random maximum packing of crystals. We show that for packs of prolate cuboids, the melt extraction timescale can be reduced by almost two orders of magnitude relative to a pack of oblate cuboids, implying that rejuvenation timescales leading to eruption</strong> <strong>could be much shorter than previously predicted, using our novel permeability model that is sensitive to crystal shape.</strong></div>

A Scaling for the Permeability of Loose Magma Mush Validated Using X‐Ray Computed Tomography of Packed Confectionary in 3D and Estimation Methods From 2D Crystal Shapes

“…Also shown are the data from Bretagne et al. (2023) for cuboid simulations, and the model (Equation 4) with C = 5 and for a best fit value of C = 4.01. For comparison, we also show hard sphere simulations from Vasseur et al.…”

“…We perform this minimization using all data (including the numerical cuboid data from Bretagne et al. (2023) or with each data set individually (Table 2, Figure 3b) and show the result with the best‐fit C for the combination of the fudge and sugar crystals (i.e., C = 4.01 ± 0.24). Zoomed in, the data fall closer to the model using C = 4.01 (Figure 3b).…”

“…This means a key parameter that can limit the rates and fluxes of melt through the system is the permeability of the mush. All crust‐scale models require permeability to compute fluxes (Bachmann & Bergantz, 2004; Jackson et al., 2018) and yet there is relatively little work constraining mush permeability and how it evolves (Bretagne et al., 2023; Cheadle et al., 2004; Hersum, 2009; Hersum et al., 2005).…”

“…Bretagne et al. (2023) showed that the values of ϕ τ and ϕ j depend on crystal shape, with important implications for the controls of mush mineralogy on the evolving properties of mush.…”

“…This approach encompasses the widely used Kozeny‐Carman formulation $$k={\phi }_{m}^{3}{a}^{2}/\left(150{\left(1-{\phi }_{m}\right)}^{2}\right)$$, for which $$\beta =1/\left(150{\left(1-{\phi }_{m}\right)}^{2}\right)$$ (e.g., Bachmann & Bergantz, 2004). In these models, complex crystal habits and multi‐component mushes are reduced to a single size parameter a , despite evidence that the shape of the objects defining the solid framework in a porous medium has a first‐order effect on the possible packing geometries (e.g., Liu et al., 2017) and the resulting permeability at those packings (Bretagne et al., 2023). Here, we move beyond idealized shapes and test more sophisticated permeability models against packs of realistic particles explicitly.…”