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 ɛ, but also on the packing microstructure. We investigate the influence of the packing microstructure on the diffusive tortuosity τ = Dm/Deff, which relates the bulk diffusion coefficient (Dm) to the effective (asymptotic) diffusion coefficient in a porous medium (Deff), 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 (ɛ = 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, (Amin/Amax)D, is a measure for the structural heterogeneity in the direct environment of this pore, and that the standard deviation σ of the (Amin/Amax)D-distribution considering all pores in a packing mimics the tortuosity–porosity scaling of the generated packing types. Thus, σ(Amin/Amax)D provides a structure–transport correlation for diffusion in bulk, monodisperse, random sphere packings.