Anomalous Diffusion in Fractal Porous Medium

WANG Zi-ting

Volume 21 Issue 10

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 2000 > 21(10): 1033-1038

WANG Zi-ting. Anomalous Diffusion in Fractal Porous Medium[J]. Applied Mathematics and Mechanics, 2000, 21(10): 1033-1038.

Citation:

WANG Zi-ting. Anomalous Diffusion in Fractal Porous Medium[J]. Applied Mathematics and Mechanics, 2000, 21(10): 1033-1038.

Citation:

WANG Zi-ting. Anomalous Diffusion in Fractal Porous Medium[J]. Applied Mathematics and Mechanics, 2000, 21(10): 1033-1038.

PDF( 2082 KB)

Anomalous Diffusion in Fractal Porous Medium

WANG Zi-ting

Department of Applied Mathematics, University of Petroleum, Dongying, Shandong 257062, P. R. China

Received Date: 1999-01-23
Rev Recd Date: 2000-06-29
Publish Date: 2000-10-15

Abstract

Abstract

Fractal media has many characteristics different from those of homogeneous media, it has a correlated self-similar structure. The particle diffusion in pore fractal is different from Ficks diffusion, and its mean-squared displacement follows fractal scaling law. The model of particle diffusion in pore fractal by means of the statistics method of stochastic process is structured and some fractal characteristics and non-Markov property are proved.
- fractal,
- anomalous diffusion,
- porous media

FullText(HTML)

References(3)

References

[1]	Cushman J H.Dynamics of Fluids in Hierachical Porous Media[M].New York:Academic Press,1990.
[2]	Bert Ksendal.Stochastic Differential Equations[M].New York:Springer-Verlag World Publishing Corp,1989.
[3]	Ioannis Karatzas,Steven E.Shreve Brownian Motion and Stochastic Calculus[M].New York:Springer-Verlag World Publishing Corp,1988.

Relative Articles

[1]	GAO Weiye, ZHANG Sai, ZHANG Jie, HU Shiwang, WANG Zhenyi. Thermo-Mass Coupling Fractal Study of Wet Phase-Change Rough Porous Materials[J]. Applied Mathematics and Mechanics, 2022, 43(5): 561-568. doi: 10.21656/1000-0887.420328
[2]	ZHANG Jie, ZHANG Sai, GAO Weiye, HU Shiwang, WANG Zhenyi. A Fractal Model for Thermal Dispersion Coefficients of Porous Media[J]. Applied Mathematics and Mechanics, 2022, 43(5): 553-560. doi: 10.21656/1000-0887.420314
[3]	WANG Yuning, ZHAO Baosheng. General Solutions of Elastodynamics for 2D Isotropic Porous Media[J]. Applied Mathematics and Mechanics, 2019, 40(9): 1025-1034. doi: 10.21656/1000-0887.390235
[4]	REN Shi-lei, HAN Fei-peng, XIE Bin, HUANG Bo, HAO Peng-fei. Numerical Simulation of Flow Fields in Porous Media Based on the 3D CFD-DEM[J]. Applied Mathematics and Mechanics, 2017, 38(10): 1093-1102. doi: 10.21656/1000-0887.370326
[5]	LU Wei, WANG Ting-ting, XU Hong-tao, CHEN Jian, YANG Mo. LBM Simulation of Double Diffusive Mixed Convection in a Porous Medium Composite Cavity[J]. Applied Mathematics and Mechanics, 2017, 38(7): 780-793. doi: 10.21656/1000-0887.370175
[6]	LI Bei-bei, YAN Zhen-rong, CHEN Jian, XU Hong-tao, YANG Mo. Lattice Boltzmann Simulation of Double Diffusive Natural Convection in a Square Enclosure Filled With Porous Medium[J]. Applied Mathematics and Mechanics, 2016, 37(2): 184-194. doi: 10.3879/j.issn.1000-0887.2016.02.007
[7]	WANG Ke-yong, WANG Da-zhong, LI Pei-chao. Two Decoupling Methods for the Heat Transfer Model of a Plate Channel Filled With a Porous Medium[J]. Applied Mathematics and Mechanics, 2015, 36(5): 494-504. doi: 10.3879/j.issn.1000-0887.2015.05.005
[8]	CHEN Wei-yun, XIA Tang-dai, CHEN Wei, ZHAI Chao-jiao. Propagation of Plane P-Waves at the Interface Between an Elastic Solid and an Unsaturated Poroelastic Medium[J]. Applied Mathematics and Mechanics, 2012, 33(7): 781-795. doi: 10.3879/j.issn.1000-0887.2012.07.001
[9]	Mohammed Q Al-Odat, Abdalmajeed Al-Ghamdi. Numerical Investigation of the Dufour and Soret Effects on Unsteady MHD Natural Convection Flow Past a Vertical Plate Embedded in a Non-Darcy Porous Medium[J]. Applied Mathematics and Mechanics, 2012, 33(2): 195-209. doi: 10.3879/j.issn.1000-0887.2012.02.005
[10]	J. C. Umavathi, I. C. Liu, J. Prathap Kumar, D. Shaik Meera. Unsteady Flow and Heat Transfer of Porous Media Sandwiched Between Viscous Fluids[J]. Applied Mathematics and Mechanics, 2010, 31(12): 1415-1434. doi: 10.3879/j.issn.1000-0887.2010.12.003
[11]	K. Hooman, A. Ejlali, F. Hooman. Entropy Generation Analysis of Thermally Developing Forced Convection in a Fluid-Saturated Porous Medium[J]. Applied Mathematics and Mechanics, 2008, 29(2): 209-216.
[12]	Hani I. Siyyam, M. H. Hamdan. Analysis of Particulate Behavior in Porous Media[J]. Applied Mathematics and Mechanics, 2008, 29(4): 463-468.
[13]	ZHAO Ji-sheng, TAO Xia-xin, SHI Li-jing, OU Jin-ping. Onset Condition of Strain Localization in Matrix of Saturated Porous Media[J]. Applied Mathematics and Mechanics, 2005, 26(11): 1337-1344.
[14]	Kamel Hooman, Mofid Gorji-Bandpy. Laminar Dissipative Flow in a Porous Channel Bounded by Isothermal Parallel Plates[J]. Applied Mathematics and Mechanics, 2005, 26(5): 541-546.
[15]	LI Xi-kui, ZHANG Jun-bo, ZHANG Hong-wu. Instability and Dispersivity of Wave Propagation in Inelastic Saturated/Unsaturated Porous Media[J]. Applied Mathematics and Mechanics, 2002, 23(1): 31-46.
[16]	LI Hong-da, YE Zheng-lin, GAO Hang-shan. On the Continuity and Differentiability of a Kind of Fractal Interpolation Function[J]. Applied Mathematics and Mechanics, 2002, 23(4): 422-428.
[17]	TONG Deng-ke, Zhang Hong-qing. The Flow Problem of Fluids Flow in a Fractal Reservoir With Double Porosity[J]. Applied Mathematics and Mechanics, 2001, (10): 1009-1016.
[18]	Tong Dengke, Chen Qinlei. Generalized Flow Analysis of Non-Newtonian Visco-Elastic Fluids Flow Through Fractal Reservoir[J]. Applied Mathematics and Mechanics, 1999, 20(12): 1267-1274.
[19]	Dao Zhengde, Guo Boling, Lin Guoguang. The Fractal Structure of Attractor for the Generalized Kuramoto-Sivashinsky Equations[J]. Applied Mathematics and Mechanics, 1998, 19(3): 243-256.
[20]	Cheng Dai-zhan. Fractal Sets in Control Systems[J]. Applied Mathematics and Mechanics, 1993, 14(8): 699-706.