Continuum Percolation

Balberg, I.

doi:10.1007/978-0-387-30440-3_95

Cited by 12 publications

(1 citation statement)

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“…A rich literature exists for effective medium theories of transport properties in heterogeneous media [1,2,[5][6][7][8], while much is known about diffusion on regular and disordered lattices [9] as well as anomalous diffusion in disordered media [10,11] from a stochastic process point of view. In addition, work on percolation theory and in particular continuum percolation has been directed at transport properties of random structures [12][13][14]. More recently, simulations of ballistic and diffusive transport using the Lorentz model of random overlapping spheres have been performed [15,16].…”

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Diffusion in Jammed Particle Packs

et al. 2015

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Using random walk simulations we explore diffusive transport through monodisperse sphere packings over a range of packing fractions, φ, in the vicinity of the jamming transition at φ c .Various diffusion properties are computed over several orders of magnitude in both time and packing pressure. Two well-separated regimes of normal, "Fickian" diffusion, where the mean squared displacement is linear in time, are observed. The first corresponds to diffusion inside individual spheres, while the latter is the long-time bulk diffusion. The intermediate anomalous diffusion regime and the long-time value of the diffusion coefficient are both shown to be controlled by particle contacts, which in turn depend on proximity to φ c . The time required to recover normal diffusion t * scales as (φ − φ c ) −0.5 and the long-time diffusivityIt is shown that the distribution of mean first passage times associated with the escape of random walkers between neighboring particles controls both t * and D ∞ in the limit φ → φ c .

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Diffusion in Jammed Particle Packs

et al. 2015

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Flow, Transport, and Reaction in Porous Media: Percolation Scaling, Critical‐Path Analysis, and Effective Medium Approximation

Hunt

Sahimi

2017

Reviews of Geophysics

134

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We describe the most important developments in the application of three theoretical tools to modeling of the morphology of porous media and flow and transport processes in them. One tool is percolation theory. Although it was over 40 years ago that the possibility of using percolation theory to describe flow and transport processes in porous media was first raised, new models and concepts, as well as new variants of the original percolation model are still being developed for various applications to flow phenomena in porous media. The other two approaches, closely related to percolation theory, are the critical‐path analysis, which is applicable when porous media are highly heterogeneous, and the effective medium approximation—poor man's percolation—that provide a simple and, under certain conditions, quantitatively correct description of transport in porous media in which percolation‐type disorder is relevant. Applications to topics in geosciences include predictions of the hydraulic conductivity and air permeability, solute and gas diffusion that are particularly important in ecohydrological applications and land‐surface interactions, and multiphase flow in porous media, as well as non‐Gaussian solute transport, and flow morphologies associated with imbibition into unsaturated fractures. We describe new applications of percolation theory of solute transport to chemical weathering and soil formation, geomorphology, and elemental cycling through the terrestrial Earth surface. Wherever quantitatively accurate predictions of such quantities are relevant, so are the techniques presented here. Whenever possible, the theoretical predictions are compared with the relevant experimental data. In practically all the cases, the agreement between the theoretical predictions and the data is excellent. Also discussed are possible future directions in the application of such concepts to many other phenomena in geosciences.

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2011

Flow and Transport in Porous Media and Fractured Rock

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Continuum Percolation

Cited by 12 publications

References 122 publications

Diffusion in Jammed Particle Packs

Diffusion in Jammed Particle Packs

Flow, Transport, and Reaction in Porous Media: Percolation Scaling, Critical‐Path Analysis, and Effective Medium Approximation

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