Structure-transport correlation for the diffusive tortuosity of bulk, monodisperse, random sphere packings

The mass transport properties of bulk random sphere packings depend primarily on the bed (external) porosity^ε, but also on the packing microstructure. We investigate the influence of the packing microstructure on the diffusive tortuosity τ = D_m/D_eff, which relates the bulk diffusion coefficient (D_m) to the effective (asymptotic) diffusion coefficient in a porous medium (D_eff), by numerical simulations of diffusion in a set of computer-generated, monodisperse, hard-sphere packings. Variation of packing generation algorithm and protocol yielded four Jodrey-Tory and two Monte Carlo packing types with systematically varied degrees of microstructural heterogeneity in the range between the random-close and the random-loose packing limit (^ε = 0.366–0.46). The distinctive tortuosity-porosity scaling of the packing types is influenced by the extent to which the structural environment of individual pores varies in a packing, and to quantify this influence we propose a measure based on Delaunay tessellation. We demonstrate that the ratio of the minimum to the maximum void face area of a Delaunay tetrahedron around a pore between four adjacent spheres, (A_min/A_max)D, is a measure for the structural heterogeneity in the direct environment of this pore, and that the standard deviation σ of the (A_min/A_max)D-distribution considering all pores in a packing mimics the tortuosity-porosity scaling of the generated packing types. Thus, σ(A_min/A_max)D provides a structure-transport correlation for diffusion in bulk, monodisperse, random sphere packings. Copyright © 2011 Elsevier B.V. All rights reserved. [accessed August 10th 2011