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

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

doi:10.1016/j.chroma.2011.07.066

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 journal › Article › peer-review

52 Scopus citations

Abstract

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=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 (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, (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.

Original language	English (US)
Pages (from-to)	6489-6497
Number of pages	9
Journal	Journal of Chromatography A
Volume	1218
Issue number	37
DOIs	https://doi.org/10.1016/j.chroma.2011.07.066
State	Published - Sep 16 2011
Externally published	Yes

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 ( http://www.deisa.eu/ ), 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).

Keywords

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

Access to Document

10.1016/j.chroma.2011.07.066

Cite this

@article{59fdb4371a3b4424bd4e2f86f370e367,

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

abstract = "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.",

keywords = "Degree of heterogeneity, Delaunay tessellation, Effective diffusion and tortuosity, Packing method and disorder, Porosity scaling, Voronoi volume distribution",

author = "Siarhei Khirevich and Alexandra H{\"o}ltzel and Anton Daneyko and Andreas Seidel-Morgenstern and Ulrich Tallarek",

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 {\textregistered} /P platforms were provided by “Genius” at RZG (Rechenzentrum Garching, Germany) and “Jugene” at FZJ (Forschungszentrum J{\"u}lich, Germany). We thank the DEISA Consortium ( http://www.deisa.eu/ ), 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 J{\"u}lich Supercomputing Centre (JSC) for allocation of a special CPU-time grant (project HMR10).",

year = "2011",

month = sep,

day = "16",

doi = "10.1016/j.chroma.2011.07.066",

language = "English (US)",

volume = "1218",

pages = "6489--6497",

journal = "Journal of Chromatography A",

issn = "0021-9673",

publisher = "Elsevier",

number = "37",

}

TY - JOUR

T1 - Structure-transport correlation for the diffusive tortuosity of bulk, monodisperse, random sphere packings

AU - Khirevich, Siarhei

AU - Höltzel, Alexandra

AU - Daneyko, Anton

AU - Seidel-Morgenstern, Andreas

AU - Tallarek, Ulrich

N1 - 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 ( http://www.deisa.eu/ ), 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).

PY - 2011/9/16

Y1 - 2011/9/16

N2 - 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.

AB - 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.

KW - Degree of heterogeneity

KW - Delaunay tessellation

KW - Effective diffusion and tortuosity

KW - Packing method and disorder

KW - Porosity scaling

KW - Voronoi volume distribution

UR - http://www.scopus.com/inward/record.url?scp=80051864716&partnerID=8YFLogxK

U2 - 10.1016/j.chroma.2011.07.066

DO - 10.1016/j.chroma.2011.07.066

M3 - Article

C2 - 21831382

AN - SCOPUS:80051864716

SN - 0021-9673

VL - 1218

SP - 6489

EP - 6497

JO - Journal of Chromatography A

JF - Journal of Chromatography A

IS - 37

ER -

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this