Universal scaling for the permeability of random packs of overlapping and nonoverlapping particles

Vasseur, Jérémie; Wadsworth, Fabian B.; Bretagne, Eloïse; Dingwell, Donald B.

doi:10.1103/physreve.105.l043301

Cited by 4 publications

(9 citation statements)

References 32 publications

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“…For comparison, Figure 3a also shows the data for hard sphere simulations and an associated model specifically for the permeability of hard spheres in a dilute system (Vasseur et al., 2021, 2022). This is shown here for completeness, and to demonstrate that solutions for spherical particles can, if scaled correctly, provide similar universal results as those for anisometric particles such as cuboids, fudge, and sugar.…”

Section: Results and Analysismentioning

confidence: 99%

“…Based on these arguments, the model applicability window is 0.35 ≤ ϕ m ≤ 0.60. Below these limits, a percolation model is required (e.g., Martys et al., 1994; Vasseur et al., 2021, 2022; Vasseur & Wadsworth, 2017; Wadsworth et al., 2016), and above these limits a dilute expansion model is required (Sangani & Acrivos, 1982; Vasseur et al., 2021, 2022).…”

Section: Discussionmentioning

confidence: 99%

“…LBflow has been validated or applied using sphere packs in cubic lattice arrangements (Llewellin, 2010b; Wadsworth et al., 2017), random overlapping sphere packs (Vasseur & Wadsworth, 2017; Vasseur et al., 2020), hard sphere packs (Vasseur et al., 2021, 2022), hexagonal arrays (Vasseur & Wadsworth, 2019), fibrous porous media (Nabovati et al., 2009), sintering systems (Wadsworth et al., 2017, 2021), and basalt pore spaces (Macente et al., 2022) among others. We calculate the specific surface area s of the particle packs using a marching cubes algorithm (Lorensen & Cline, 1987) from Python's scikit‐image toolbox (following Lewiner et al., 2003).…”

Section: Methodsmentioning

confidence: 99%

“…where ϕ m is the volume fraction of the non-particle phase, C is a constant, and s is the specific surface area of the pore space (Torquato, 2013;Röding et al, 2020;Wadsworth et al, 2017;Vasseur et al, 2021Vasseur et al, , 2022. In the case of magma mush, we can think of ϕ m as being the melt volume fraction, and then ϕ = 1 − ϕ m representing the crystal volume fraction (assuming a two-phase system).…”

Section: A Permeability Model For Loose Mushmentioning

confidence: 99%

“…The simplest and most widely used model for the permeability k of packed particles is the Kozeny‐Carman model (Ergun, 1952). While this model is given in a variety of forms, sometimes including additional parameters such as a pore network tortuosity, and the specific lengths of pores or particles, the more general form is

k=\frac{{\phi }_{m}^{3}}{C{s}^{2}}

where ϕ m is the volume fraction of the non‐particle phase, C is a constant, and s is the specific surface area of the pore space (Torquato, 2013; Röding et al., 2020; Vasseur & Wadsworth, 2017; Wadsworth et al., 2017; Vasseur et al., 2021, 2022). In the case of magma mush, we can think of ϕ m as being the melt volume fraction, and then ϕ = 1 − ϕ m representing the crystal volume fraction (assuming a two‐phase system).…”

Section: A Permeability Model For Loose Mushmentioning

confidence: 99%

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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

Bretagne,

Wadsworth,

Vasseur

et al. 2023

JGR Solid Earth

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Melt percolation through partially molten “mushy” regions of the crust underpins models for magma migration, accumulation, and processes that prime systems for eruption. Knowledge of the hydraulic properties of magma mush, specifically permeability, is required for accurate predictions of melt migration rates and accumulation timescales. Previous studies, validated for cuboidal crystal analogs, show that crystal shape exerts a first‐order control on the permeability, and is tested here for anisometric natural crystal shapes using X‐ray CT 3D data sets of magma mush analogs made from packed confectionary particles arranged randomly. We use a lattice‐Boltzmann fluid flow simulation tool to determine the permeability of the analogue melt phase network between the packed particles. We find excellent agreement with our data sets to within ∼0.1 log units, when the specific surface area is measured. To extend this to more typical cases where the specific surface area is unknown, we use the shape and size of the objects determined in both 3D and 2D to estimate the specific surface area assuming a cuboid approximation. These approximate solutions give good results to within ∼0.5 log units of the measured permeability and offer a method by which permeability could be estimated from a thin section of a cumulate or pluton sample. Our shape‐sensitive approach is more accurate than existing models for permeability of magma mush, most approximating natural crystal shapes to spheres. We therefore propose that these could be implemented in dynamic magma mush models for melt movement in the crust to produce more accurate flux predictions.

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Section: Results and Analysismentioning

confidence: 99%