Abstract
The permeability of packs of spheres is important in a wide range of physical scenarios. Here, we create numerically generated random periodic domains of spheres that are polydisperse in size and use lattice-Boltzmann simulations of fluid flow to determine the permeability of the pore phase interstitial to the spheres. We control the polydispersivity of the sphere size distribution and the porosity across the full range from high porosity to a close packing of spheres. We find that all results scale with a Stokes permeability adapted for polydisperse sphere sizes. We show that our determination of the permeability of random distributions of spheres is well approximated by models for cubic arrays of spheres at porosities greater than ∼0.38, without any fitting parameters. Below this value, the Kozeny-Carman relationship provides a good approximation for dense, closely packed sphere packs across all polydispersivity.
Highlights
AND BACKGROUNDUnderstanding the relationship between the microstructure of porous solids and their bulk properties is central to general descriptions of randomly assembled heterogeneous materials [1]
We find that all results scale with a Stokes permeability adapted for polydisperse sphere sizes
I) by a form of ks that is adapted to account for polydisperse sphere sizes by introducing s from Eq (6b)
Summary
Understanding the relationship between the microstructure of porous solids and their bulk properties is central to general descriptions of randomly assembled heterogeneous materials [1]. Perhaps the most widely used permeability model for real packed particulate or granular media is the so-called Kozeny-Carman equation [11,12] together with extensions or adaptations thereof [13,14].
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