Transport and elastic properties of fractal media

Roberts, Anthony P.; Knackstedt, Mark

doi:10.1016/s0378-4371(96)00198-7

Cited by 7 publications

(6 citation statements)

References 33 publications

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“…In the case r c or ξ → 0 a fractal surface results [25,33]. Cross-sections of six of the model microstructures obtained with r c =1, ξ=2 and d=2µm are illustrated in Fig.…”

Section: Model Composite Materialsmentioning

confidence: 99%

“…This can be partially attributed to the fact that percolation threshold of the reconstructed models is around 10% while the experimental systems had thresholds of less than 3% [3]. Recent work in microstructure modelling has led to a general scheme [5,[22][23][24][25][26][27] ( § I) which includes the model employed by Quiblier. Importantly, other models in the scheme can mimic the low percolation thresholds observed in sandstones (and many other materials [22]).…”

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confidence: 99%

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Statistical reconstruction of three-dimensional porous media from two-dimensional images

1997

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A method of modeling the three-dimensional microstructure of random isotropic two-phase materials is proposed. The information required to implement the technique can be obtained from two-dimensional images of the microstructure. The reconstructed models share two-point correlation and chord-distribution functions with the original composite. The method is designed to produce models for computationally and theoretically predicting the effective macroscopic properties of random materials ͑such as electrical and thermal conductivity, permeability and elastic moduli͒. To test the method we reconstruct the morphology and predict the conductivity of the well known overlapping sphere model. The results are in very good agreement with data for the original model. ͓S1063-651X͑97͒02309-X͔ PACS number͑s͒: 47.55. Mh, 44.30.ϩv, 81.05.Rm, 61.43.Bn Predicting the macroscopic properties of composite or porous materials with random microstructures is an important problem in a range of fields ͓1,2͔. There now exist largescale computational methods for calculating the properties of composites given a digital representation of their microstructure ͑e.g., permeability ͓3,4͔, conductivity ͓3-5͔, and elastic moduli ͓6͔͒. A critical problem is actually obtaining an accurate three-dimensional description of this microstructure ͓3,7,8͔. For particular materials it may be possible to simulate microstructure formation from first principles. Generally this relies on a detailed knowledge of the physics and chemistry of the system, the accurate modeling of each material requiring a significant amount of research. Where such information is unavailable an alternative is to directly ͓9-15͔ or statistically ͓3,4,8,16-21͔ reconstruct the microstructure from experimental images.Several techniques of direct reconstruction have been implemented. A composite can be repeatedly sectioned and imaged, and the results combined to reproduce a threedimensional digital image of the microstructure ͓9-11͔. For porous materials, time-consuming sectioning can be avoided by using laser microscopy ͓12͔ which can image pores to depths of around 150 m. Recent microtomography studies have also directly imaged the three-dimensional microstructure of porous sandstones ͓13,14͔ and magnetic gels ͓15͔. The complexity and restrictions of these methods provide the impetus to study alternative reconstruction methods.Based on the work of Joshi ͓16͔, Quiblier ͓17͔ introduced a method of generating a three-dimensional statistical reconstruction of a random composite. The method is based on matching statistical properties of a three-dimensional model to those of a real microstructure. A key advantage of this approach is that the required information can be obtained from a two-dimensional image of the sample. Recently the method was applied to the reconstruction of sandstone ͓4,8,18,19͔ and a material composed of overlapping spheres ͓3͔. Computations of the permeability and conductivity ͓3,4,18͔ of the reconstructed images underestimate experimental data by around a factor of ...

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“…In the case r c or ξ → 0 a fractal surface results [25,33]. Cross-sections of six of the model microstructures obtained with r c =1, ξ=2 and d=2µm are illustrated in Fig.…”

Section: Model Composite Materialsmentioning

confidence: 99%

mentioning

confidence: 99%

Statistical reconstruction of three-dimensional porous media from two-dimensional images

1997

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“…China e-mail: wqjxyf@sdu.edu.cn H. Qi School of Mathematics and Statistics, Shandong University at Weihai, Weihai 264209, P.R. China e-mail: htqi@sdu.edu.cn the property of a fractal structure [1][2][3][4][5]. These media may be called fractal media [6,7].…”

Section: Introductionmentioning

confidence: 99%

Analytical solutions for anomalous transport of volatile pollutants in nonaqueous-phase liquid contaminated soil

Jiang

2010

Nonlinear Dyn

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“…Models based on Gaussian random fields (GRFs) have been employed in the literature to study a variety of material systems [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. These GRF models are often constructed using the twopoint phase probability function S 2 (r), defined to be the probability that two points x and y with r = |x − y| both lie in the solid phase.…”

Section: Introductionmentioning

confidence: 99%

Versatility and robustness of Gaussian random fields for modelling random media

Quintanilla

Chen

Reidy

et al. 2007

Modelling Simul. Mater. Sci. Eng.

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One of the authors (JAQ) has recently introduced a method of modelling random materials using excursion sets of Gaussian random fields. This method uses convex quadratic programming to find the optimal admissible field autocorrelation function, providing both theoretical and computational advantages over other techniques such as simulated annealing. In this paper, we discuss the application of this algorithm to model various aerogel systems given small-angle neutron scattering data. We also present new results concerning the robustness of this method.

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Transport and elastic properties of fractal media

Cited by 7 publications

References 33 publications

Statistical reconstruction of three-dimensional porous media from two-dimensional images

Statistical reconstruction of three-dimensional porous media from two-dimensional images

Analytical solutions for anomalous transport of volatile pollutants in nonaqueous-phase liquid contaminated soil

Versatility and robustness of Gaussian random fields for modelling random media

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