Nonuniversal conductivity exponents in continuum percolating Gaussian fractures

Flukiger, Frédérique; Plouraboué, Franck; Prat, Marc

doi:10.1103/physreve.77.047101

Cited by 5 publications

(1 citation statement)

References 12 publications

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“…It has also permitted the study of the hydraulic and electrical percolation conductivity exponents by Flukiger et al (2006). The relevance of such a network for modeling two-phase flows in random rough fracture in contact is the purpose of the present study.…”

Section: Introductionmentioning

confidence: 97%

Critical point network for drainage between rough surfaces

et al. 2007

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In this paper, we present a network method for computing two-phase flows between two rough surfaces with significant contact areas. Low-capillary number drainage is investigated here since one-phase flows have been previously investigated in other contributions. An invasion percolation algorithm is presented for modeling slow displacement of a wetting fluid by a non wetting one between two rough surfaces. Short-correlated Gaussian process is used to model random rough surfaces.The algorithm is based on a network description of the fracture aperture field. The network is constructed from the identification of critical points (saddles and maxima) of the aperture field. The invasion potential is determined from examining drainage process in a flat mini-channel. A direct comparison between numerical prediction and experimental visualizations on an identical geometry has been performed for one realization of an artificial fracture with a moderate fractional contact area of about 0.3. A good agreement is found between predictions and observations.

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Section: Introductionmentioning

confidence: 97%

Critical point network for drainage between rough surfaces

et al. 2007

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Dependency of percolation critical exponents on the exponent of power law size distribution

Sadeghnejad

Masihi

King

2013

Physica A: Statistical Mechanics and its Applications

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Non-universality of the dynamic exponent in two-dimensional random media

Cho

Yethiraj

Sung

2019

Sci Rep

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The diffusion of solutes in two-dimensional random media is important in diverse physical situations including the dynamics of proteins in crowded cell membranes and the adsorption on nano-structured substrates. It has generally been thought that the diffusion constant, D, should display universal behavior near the percolation threshold, i.e., D ~ (ϕ − ϕc)μ, where ϕ is the area fraction of the matrix, ϕc is the value of ϕ at the percolation threshold, and μ is the dynamic exponent. The universality of μ is important because it implies that very different processes, such as protein diffusion in membranes and the electrical conductivity in two-dimensional networks, obey similar underlying physical principles. In this work we demonstrate, using computer simulations on a model system, that the exponent μ is not universal, but depends on the microscopic nature of the dynamics. We consider a hard disc that moves via random walk in a matrix of fixed hard discs and show that μ depends on the maximum possible displacement Δ of the mobile hard disc, ranging from 1.31 at Δ ≤ 0.1 to 2.06 for relatively large values of Δ. We also show that this behavior arises from a power-law singularity in the distribution of transition rates due to a failure of the local equilibrium approximation. The non-universal value of μ obeys the prediction of the renormalization group theory. Our simulations do not, however, exclude the possibility that the non-universal values of μ might be a crossover between two different limiting values at very large and small values of Δ. The results allow one to rationalize experiments on diffusion in two-dimensional systems.

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Nonuniversal conductivity exponents in continuum percolating Gaussian fractures

Cited by 5 publications

References 12 publications

Critical point network for drainage between rough surfaces

Critical point network for drainage between rough surfaces

Dependency of percolation critical exponents on the exponent of power law size distribution

Non-universality of the dynamic exponent in two-dimensional random media

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