TORTUOSIMETRIC OPERATOR FOR COMPLEX POROUS MEDIA CHARACTERIZATION
DOI:
https://doi.org/10.5566/ias.2039Keywords:
geodesic distance transform, geometric tortuosity, Monte Carlo algorithms, multi-scale porous networksAbstract
Geometric tortuosity is one of the foremost topological characteristics of porous media. Despite the various definitions in the literature, to our knowledge, they are all linked to an arbitrary propagation direction. This article proposes a novel topological descriptor, named M-tortuosity, by giving a more straightforward definition, describing the data regardless of physicochemical processes. M-tortuosity, based on the concept of geometric tortuosity, is a scalable descriptor, meaning that information of several dimensions (scalar, histograms, 3D maps) is available. It is applicable on complex disconnected structures without any arbitrary definition of entry and exit. Topological information can be represented by aggregation into a unique scalar descriptor for classification purposes. It is extended by iterative erosions to take into account porous structure narrowness, especially bottleneck effects. This new descriptor, called M-tortuosity-by-iterative-erosions, describes tortuosity of the porous part as seen by a spherical particle of given size walking along the network. Boolean models are used to simulate different porous media structures in order to test the proposed characterization.
References
Baddeley A, Jensen EBV (2004). Stereology for statisticians. Monographs on statistics and applied probability 103:03.
Berrocal CG, Löfgren I, Lundgren K, Görander N, Halldén C (2016). Characterisation of bending cracks in R/FRC using image analysis. Cement Concrete Res. 90:104--16.
Borgefors G (1986). Distance transformations in digital images. Comput. Vision Graph. 34(3):344--71.
Caflisch RE (1998). Monte Carlo and quasi-Monte Carlo methods. Acta Numer. 7:1--49.
Carman PC (1937). Fluid flow through granular beds. Trans. Inst. Chem. Eng. 15:150--66.
Chen-Wiegart YK, DeMike R, Erdonmez C, Thornton K, Barnett SA, Wang J (2014). Tortuosity characterization of 3D microstructure at nano-scale for energy storage and conversion materials. J. Power Sources 249:349--56.
Chiche D, Digne M, Revel R, Chanéac C, Jolivet J-P (2008). Accurate determination of oxide nanoparticle size and shape based on X-ray powder pattern simulation: application to boehmite AlOOH. J. Phys. Chem. C 112(23):8524--33.
Chiu SN, Stoyan D, Kendall WS, Mecke J (2013). Stochastic geometry and its applications. John Wiley & Sons.
Clennell MB (1997). Tortuosity: a guide through the maze. Geol. Soc. Spec. Publ. 122(1):299--344.
Criminisi A, Sharp T, Rother C, P{'e}rez P (2010). Geodesic image and video editing. ACM T. Graphic. 29(5):134--1.
Decker L, Jeulin D, Tovena I (1998). 3D morphological analysis of the connectivity of a porous medium. Acta Stereol. 17(1).
Ghanbarian B, Hunt AG, Ewing RP, Sahimi M (2013). Tortuosity in porous media: a critical review. Soil Sci. Soc. Am. J. 77(5):1461--77.
Ghanbarian B, Hunt AG, Sahimi M, Ewing RP, Skinner TE (2013). Percolation theory generates a physically based description of tortuosity in saturated and unsaturated porous media. Soil Sci. Soc. Am. J. 77(6):1920--29.
Gommes CJ, Bons A-J, Blacher S, Dunsmuir JH, Tsou AH (2009). Practical methods for measuring the tortuosity of porous materials from binary or gray-tone tomographic reconstructions. AIChE J. 55(8):2000--12.
Holzer L, Wiedenmann D, Münch B, Keller L, Prestat M, Gasser Ph, Robertson I, Grobéty B (2013). The influence of constrictivity on the effective transport properties of porous layers in electrolysis and fuel cells. J. Mater. Sci. 48(7):2934--52.
Jeulin D (1996). Modeling heterogeneous materials by random structures. Invited lecture, European Workshop on Application of Statistics and Probabilities in Wood Mechanics, Bordeaux , N-06/96/MM, Paris School of Mines Publication.
Jeulin D (1997). Advances in Theory and Applications of Random Sets. In : Advances In Theory And Applications Of Random Sets: Proceedings Of The Symposium. World Scientific 105.
Jeulin D, Moreaud M (2006). Percolation of multi-scale fiber aggregates. S4G (Stereology, Spatial Statistics and Stochastic Geometry) 6th International Conference, Prague, Czech Republic.
Jeulin D (2010). Multi scale random models of complex microstructures. Mater. Sci. Forum 638:81--6.
Kingman JFC (1993). Poisson Processes. Oxford Science Publications, Oxford Studies in Probability 3.
Lantuéjoul C, Beucher S (1981). On the use of the geodesic metric in image analysis. J. Microsc., Wiley Online Library, 121(1):39--49.
Lindquist WB, Lee S-M, Coker DA, Jones KW, Spanne P (1996). Medial axis analysis of void structure in three-dimensional tomographic images of porous media. J. Geophys. Res.-Sol. Ea. 101(B4):8297--8310.
Lohou C, Bertrand G (2005). A 3D 6-subiteration curve thinning algorithm based on P-simple points. Discrete Appl. Math. 151(1):198--228.
Matheron G (1975). Random sets and integral geometry. Wiley New York.
Moreaud M (2006). Propriétés morphologiques multi-échelles et pr'evision du comportement diélectrique de nanocomposites. Thèse Ecole des Mines de Paris.
Moreaud M, Chaniot J, Fournel T, Becker J-M, Sorbier L (2018). Multi-scale stochastic morphological models for 3D complex microstructures. 17th Workshop on Information Optics (WIO), Quebec, Canada, IEEE, 1--3.
Neumann M, Hirsch C, Stan{v{e}}k J, Bene{v{s}} V, Schmidt V (2018). Estimation of geodesic tortuosity and constrictivity in stationary random closed sets. Scand. J. Stat..
Neyman J (1934). On the two different aspects of the representative method: the method of stratified sampling and the method of purposive selection. J. R. Stat. Soc. 97(4):558--625.
Petersen EE (1958). Diffusion in a pore of varying cross section. AIChE J. 4(3):343--5.
Peyrega C, Jeulin D (2013). Estimation of tortuosity and reconstruction of geodesic paths in 3D. Image Anal. Stereol. 32(1):27--43.
Rosenfeld A, Pfaltz JL (1968). Distance Functions on Digital Pictures. Pattern Recogn. 1:33--61.
Rutovitz D (1968). Data structures for operations on digital images. Pictorial pattern recognition 105--33.
Savary L, Jeulin D, Thorel A (1999). Morphological analysis of carbon-polymer composite materials from thick sections. Acta Stereol. 18(3):297--303.
Serra J (1982). Image Analysis and Mathematical Morphology. Academic Press, London.
Tagliasacchi A, Delame T, Spagnuolo M, Amenta N, Telea A (2016). 3D Skeletons: A State-of-the-Art Report. Comput. Graph. Forum 35(2):573--97.
Toivanen PJ (1996). New geodesic distance transforms for gray-scale images. Pattern Recogn. Lett. 17(5):437--50.
Tran V-D, Moreaud M, Thiébaut E, Denis L, Becker J-M (2014). Inverse problem approach for the alignment of electron tomographic series. Oil & Gas Science and Technology--Revue d’IFP Energies nouvelles 69(2):279--91.
Yu B-M, Li J-H (2004). A geometry model for tortuosity of flow path in porous media. Chinese Phys. Lett. 21(8):1569.
Yun M, Yu B, Xu P, Wu J (2006). Geometrical Models for Tortuosity of Streamlines in Three-Dimensional Porous Media. Can. J. Chem. Eng. 84(3):301--9.
Wang H, Pietrasanta A, Jeulin D, Willot F, Faessel M, Sorbier L, Moreaud M (2015). Modelling mesoporous alumina microstructure with 3D random models of platelets. J. Microsc. 260(3):287--301.
”plug im!” an open access and customizable software for signal and image processing. https://www.plugim.fr (2018).
Downloads
Published
Issue
Section
License
Copyright (c) 2019 Image Analysis & Stereology
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
