An effective medium treatment of the transport properties of a Voronoi tesselated network

Vrettos, Nikolas A.; Imakoma, Hironobu; Okazaki, Morio

doi:10.1063/1.344192

Cited by 31 publications

(6 citation statements)

References 10 publications

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“…RR is given by which reduces to γ RR ) -2/Z given above when Z 1 ) Z 2 ) Z. Note that Vrettos et al (1989), who also attempted to derive an EMA for conduction in Voronoi networks, obtained an equation identical to (31), which in our opinion is incorrect.…”

Section: Effective-medium Approximations For Topologically-disordered...mentioning

confidence: 95%

Transient Diffusion and Conduction in Heterogeneous Media: Beyond the Classical Effective-Medium Approximation

Sahimi

Tsotsis

1997

Ind. Eng. Chem. Res.

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In this paper steady-state and transient diffusion and conduction in heterogeneous media, such as composite solids, are studied. The heterogeneities are of percolation type in the sense that a randomly-selected fraction of the system does not allow transport to take place. We present several new extensions of the classical effective-medium approximation (EMA) for diffusion and conduction in regular network models of heterogeneous media, including an EMA for topologically-random networks, such as the Voronoi network, for which we introduce a novel stochastic Green function, and a cluster (higher order) EMA for transient diffusion and other dynamical properties of heterogeneous media. In all cases the predictions are compared with the results of Monte Carlo simulations.

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Section: Effective-medium Approximations For Topologically-disordered...mentioning

confidence: 95%

Transient Diffusion and Conduction in Heterogeneous Media: Beyond the Classical Effective-Medium Approximation

Sahimi

Tsotsis

1997

Ind. Eng. Chem. Res.

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“…This is because porosity can be modified easily and independent of particle size and shape. Although the micro‐geometry of Voronoi cells in 2D have been used in modeling pore space networks relevant to bulk permeability and conductivity characteristics, essentially because the network of pores and throats is random [e.g., Vrettos et al , 1989; Nagaya and Ishibashi , 1998], it might however be a limitation if the simulations were to be used for modeling flows through the material.…”

Section: Simulation Of Granular Materialsmentioning

confidence: 99%

Advances in the simulation and automated measurement of well‐sorted granular material: 1. Simulation

Buscombe

Rubin

2012

J. Geophys. Res.

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[1] In this, the first of a pair of papers which address the simulation and automated measurement of well-sorted natural granular material, a method is presented for simulation of two-phase (solid, void) assemblages of discrete non-cohesive particles. The purpose is to have a flexible, yet computationally and theoretically simple, suite of tools with well constrained and well known statistical properties, in order to simulate realistic granular material as a discrete element model with realistic size and shape distributions, for a variety of purposes. The stochastic modeling framework is based on three-dimensional tessellations with variable degrees of order in particle-packing arrangement. Examples of sediments with a variety of particle size distributions and spatial variability in grain size are presented. The relationship between particle shape and porosity conforms to published data. The immediate application is testing new algorithms for automated measurements of particle properties (mean and standard deviation of particle sizes, and apparent porosity) from images of natural sediment, as detailed in the second of this pair of papers. The model could also prove useful for simulating specific depositional structures found in natural sediments, the result of physical alterations to packing and grain fabric, using discrete particle flow models. While the principal focus here is on naturally occurring sediment and sedimentary rock, the methods presented might also be useful for simulations of similar granular or cellular material encountered in engineering, industrial and life sciences.

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“…Numerical simulations have delivered useful information [16], but due to practical limitations they have usually simplified the studies to periodic lattices of polyhedral obstacles [17], which are inherently anisotropic and unrealistic. Effective medium approximations have been developed to describe the effective diffusion coefficient of porous media based on Voronoi and Delaunay tessellations [18][19][20]. Effective medium approximations imply a description over a length scale much larger than any characteristic geometrical length scale of the medium.…”

Section: Introductionmentioning

confidence: 99%

Local details versus effective medium approximation: A study of diffusion in microfluidic random networks made from Voronoi tessellations

Ponce

Cordero

2020

Phys. Rev. E

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We measured the effective diffusion coefficient in regions of microfluidic networks of controlled geometry using the FRAP (Fluorescence Recovery After Photobleaching) technique. The geometry of the networks was based on Voronoi tessellations, and had varying characteristic length scale and porosity. For a fixed network, FRAP experiments were performed in regions of increasing size. Our results indicate that the boundary of the bleached region, and in particular the cumulative area of the channels that connect the bleached region to the rest of the network, are important in the measured value of the effective diffusion coefficient. We found that the statistical geometrical variations between different regions of the network decrease with the size of the bleached region as a power law, meaning that the statistical error of effective medium approximations decrease with the size of the studied medium, although no characteristic length scale could be defined over which the porous medium is equivalent to an effective medium.

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An effective medium treatment of the transport properties of a Voronoi tesselated network

Cited by 31 publications

References 10 publications

Transient Diffusion and Conduction in Heterogeneous Media: Beyond the Classical Effective-Medium Approximation

Transient Diffusion and Conduction in Heterogeneous Media: Beyond the Classical Effective-Medium Approximation

Advances in the simulation and automated measurement of well‐sorted granular material: 1. Simulation

Local details versus effective medium approximation: A study of diffusion in microfluidic random networks made from Voronoi tessellations

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