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

Siarhei Khirevich, Alexandra Höltzel, Anton Daneyko, Andreas Seidel-Morgenstern, Ulrich Tallarek*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

51 Scopus citations


The mass transport properties of bulk random sphere packings depend primarily on the bed (external) porosity e{open}, 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 (e{open}=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.

Original languageEnglish (US)
Pages (from-to)6489-6497
Number of pages9
JournalJournal of Chromatography A
Issue number37
StatePublished - Sep 16 2011
Externally publishedYes

Bibliographical note

Funding Information:
This work was supported by the Deutsche Forschungsgemeinschaft DFG (Bonn, Germany) under grants TA 268/4-1 and TA 268/5-1 . Computational resources on IBM BlueGene ® /P platforms were provided by “Genius” at RZG (Rechenzentrum Garching, Germany) and “Jugene” at FZJ (Forschungszentrum Jülich, Germany). We thank the DEISA Consortium ( ), co-funded through the EU FP6 project RI-031513 and the FP7 project RI-222919, for support within the DEISA Extreme Computing Initiative. We are also grateful to the Jülich Supercomputing Centre (JSC) for allocation of a special CPU-time grant (project HMR10).


  • Degree of heterogeneity
  • Delaunay tessellation
  • Effective diffusion and tortuosity
  • Packing method and disorder
  • Porosity scaling
  • Voronoi volume distribution

ASJC Scopus subject areas

  • Analytical Chemistry
  • Biochemistry
  • Organic Chemistry


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