Impact of microstructure on the effective diffusivity in random packings of hard spheres

We present results of computer simulations of the effective diffusion coefficient in bulk random packings of hard monosized spheres with solid volume fraction between 0.54 (random-loose packing) and 0.634 (maximally random jammed). Six types of sphere packings were generated with different protocols and parameters resulting in a systematically varied degree of microstructural heterogeneity. The packing morphology is qualitatively characterized by statistical analyses of Voronoi cells obtained from spatial tessellation of the packing space. Diffusive transport of point-like tracers in the pore space of the packings was simulated with a random-walking particle-tracking technique. Our results indicate that the effective transport characteristics of the random sphere packings are not fully defined from the solid volume fraction but also depend on the packing microstructure. For the first time, we compared (i) the values of the effective diffusion coefficient D_eff simulated in packings with different morphologies, and (ii) the corresponding values of D_eff obtained from an approximate analytical formula involving the three-point microstructural parameter ζ₂. This analysis reveals that this approximation involving ζ₂ clearly reflects key morphological specificity of individual sphere packings and provides a sufficiently accurate estimate of the effective diffusion coefficient.