Please wait a minute...
Chin. Phys. B, 2012, Vol. 21(10): 100201    DOI: 10.1088/1674-1056/21/10/100201
GENERAL   Next  

Simulation of the relationship between porosity and tortuosity in porous media with cubic particles

Tang Xiao-Wu, Sun Zu-Feng, Cheng Guan-Chu
MOE Key Laboratory of Soft Soils and Geoenvironmental Engineering, Department of Civil Engineering, Zhejiang University, Hangzhou 310058, China
Abstract  Tortuosity is an important parameter used in areas such as vascular medicine, neurobiology, and the field of soil permeability and diffusion to express the mass transport in porous media. It is a function of the porosity and the shape and distribution of particles. In this paper, the tortuosity of cubic particles is calculated. With the assumption that the porous medium is homogeneous, the problem is converted to the micro-level over a unit cell, and geometry models of flow paths are proposed. In three-dimensional (3D) cells, the flow paths are too complicated to define. Hence, the 3D models are converted to two-dimensional (2D) models to simplify the calculation process. It is noticed that the path in the 2D model is shorter than that in the 3D model. As a result, triangular particles and the interaction are also taken into consideration to account for the longer distance respectively. We have proposed quadrate particle and interaction (QI) and quadrate and triangular particle (QT) models with cubic particles. Both models have shown good agreement with the experimental data. It is also found that they can predict the toruosities of some kinds of porous media, like freshwater sediment and Negev chalk.
Keywords:  tortuosity      porosity      porous media      cubic particles     
Received:  17 February 2012      Published:  01 September 2012
PACS:  02.10.-v (Logic, set theory, and algebra)  
  02.30.-f (Function theory, analysis)  
Fund: Project supported by the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20090101110075) and the Key Innovation Team Support Project of Zhejiang Province, China (Grant No. 2009R50050).
Corresponding Authors:  Tang Xiao-Wu     E-mail:  tangxiaowu@zju.edu.cn

Cite this article: 

Tang Xiao-Wu, Sun Zu-Feng, Cheng Guan-Chu Simulation of the relationship between porosity and tortuosity in porous media with cubic particles 2012 Chin. Phys. B 21 100201

[1] McDuff R E and Ellis R A 1979 Am. J. Sci. 279 666
[2] Epstein N 1989 Chem. Eng. Sci. 44 777
[3] Boudreau B P 1996 Geochim. Cosmochim. Ac. 60 3139
[4] Sweerts J P, Kelly C A, Rudd J W, Hesslein R and Cappenberg T E 1991 Limnol. Oceanogr. 36 335
[5] Weissberg H 1963 J. Appl. Phys. 34 2636
[6] Ullman W J and Aller R C 1982 Limnol. Oceanogr. 27 552
[7] Maxwell J C 1873 Treatise on Electricity and Magnetism 2nd edn. (Oxford: Clarendon Press) p. 40
[8] Rayleigh L and Brusseau M L 1997 Philosophical Magazine 34 481
[9] Petersen E E 1958 Am. Inst. Chem. E. J. 4 343
[10] Comiti J and Renaud M 1989 Chem. Eng. Sci. 44 1539
[11] Koponen A, Kataja M and Timonen J 1996 Phys. Rev. E 54 406
[12] Koponen A, Kataja M and Timonen J 1997 Phys. Rev. E 56 3319
[13] Yu B M and Li J H 2004 Chin. Phys. Lett. 21 1569
[14] Maciej M, Arzhang K and Zbigniew K 2008 Phys. Rev. E 78 026306
[15] Pisani L 2011 Transp. Porous. Med. 88 193
[16] Wyllie M R J and Gregory A R 1955 Eng. Des. Process. Dev. 47 1379
[17] Iversen N and Jorgensen B B 1993 Geochim. Cosmochim. Ac. 57 571
[18] Currie J A 1960 Brit. J. Appl. Phys. 11 318
[19] Polak A, Nativ R and Wallach R 2002 J. Hydrol. 268 203
[20] Shackelford C D 1991 J. Contam. Hydrol. 7 177
[1] Modeling of microporosity formation and hydrogen concentration evolution during solidification of an Al-Si alloy
Qingyu Zhang, Dongke Sun, Shunhu Zhang, Hui Wang, Mingfang Zhu. Chin. Phys. B, 2020, 29(7): 078104.
[2] Frequency-dependent reflection of elastic wave from thin bed in porous media
Hong-Xing Li, Chun-Hui Tao, Cai Liu, Guang-Nan Huang, Zhen-An Yao. Chin. Phys. B, 2020, 29(6): 064301.
[3] Numerical study on permeability characteristics of fractal porous media
Yongping Huang, Feng Yao, Bo Zhou, Chengbin Zhang. Chin. Phys. B, 2020, 29(5): 054701.
[4] Se substitution and micro-nano-scale porosity enhancing thermoelectric Cu2Te
Xiaoman Shi, Guoyu Wang, Ruifeng Wang, Xiaoyuan Zhou, Jingtao Xu, Jun Tang, Ran Ang. Chin. Phys. B, 2018, 27(4): 047204.
[5] Molecular dynamics simulation of decomposition and thermal conductivity of methane hydrate in porous media
Ping Guo, Yi-Kun Pan, Long-Long Li, Bin Tang. Chin. Phys. B, 2017, 26(7): 073101.
[6] Experimental study and theoretical analysis of fluid resistance in porous media of glass spheres
Tong Wang, Kun-Can Zheng, Yu-Peng Jia, Cheng-Lu Fu, Zhi-Jun Gong, Wen-Fei Wu. Chin. Phys. B, 2017, 26(7): 074701.
[7] A fractal approach to low velocity non-Darcy flow in a low permeability porous medium
Cai Jian-Chao. Chin. Phys. B, 2014, 23(4): 044701.
[8] Unsteady MHD flow and heat transfer near stagnation point over a stretching/shrinking sheet in porous medium filled with a nanofluid
Sadegh Khalili, Saeed Dinarvand, Reza Hosseini, Hossein Tamim, Ioan Pop. Chin. Phys. B, 2014, 23(4): 048203.
[9] K2S-activated carbons developed from coal and their methane adsorption behaviors
Feng Yan-Yan, Yang Wen, Chu Wei. Chin. Phys. B, 2014, 23(10): 108201.
[10] A steady solution of the gasar eutectic growth in directional solidification
Li Xiang-Ming, Li Wen-Qiong, Jin Qing-Lin, Zhou Rong. Chin. Phys. B, 2013, 22(7): 078101.
[11] Cross-diffusive effects on the onset of the double-diffusive convection in a horizontal saturated porous fluid layer heated and salted from above
Rajib Basu, G. C. Layek. Chin. Phys. B, 2013, 22(5): 054702.
[12] The light-enhanced NO2 sensing properties of porous silicon gas sensors at room temperature
Chen Hui-Qing,Hu Ming,Zeng Jing,Wang Wei-Dan. Chin. Phys. B, 2012, 21(5): 058201.
[13] Tortuosity for streamlines in porous media
Kou Jian-Long,Tang Xue-Ming,Zhang Hai-Yan,Lu Hang-Jun,Wu Feng-Min,Xu You-Sheng,Dong Yong-Sheng. Chin. Phys. B, 2012, 21(4): 044701.
[14] Acousto-electric well logging by eccentric source and extraction of shear wave
Cui Zhi-Wen, Wang Ke-Xie, Hu Heng-Shan, Sun Jian-Guo. Chin. Phys. B, 2007, 16(3): 746-752.
[15] A method of solving the stiffness problem in Biot's poroelastic equations using a staggered high-order finite-difference
Zhao Hai-Bo, Wang Xiu-Ming, Chen Hao. Chin. Phys. B, 2006, 15(12): 2819-2827.
No Suggested Reading articles found!