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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 354701, 7 pages
Research Article

Fractal Derivative Model for Air Permeability in Hierarchic Porous Media

Jie Fan1,2,3,4 and Jihuan He2

1Key Laboratory of Advanced Textile Composites, Ministry of Education of China, 399 West Binshui Road, Tianjin 300387, China
2National Engineering Laboratory for Modern Silk, College of Textile and Engineering, Soochow University, 199 Ren-ai Road, Suzhou 215123, China
3Zhejiang Provincial Key Laboratory of Textile Research and Development, 138 Jiefang Road, Hangzhou 310001, China
4School of Textiles, Tianjin Polytechnic University, 399 West Binshui Road, Tianjin 300387, China

Received 7 August 2012; Revised 16 November 2012; Accepted 17 November 2012

Academic Editor: Chuandong Li

Copyright © 2012 Jie Fan and Jihuan He. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Air permeability in hierarchic porous media does not obey Fick's equation or its modification because fractal objects have well-defined geometric properties, which are discrete and discontinuous. We propose a theoretical model dealing with, for the first time, a seemingly complex air permeability process using fractal derivative method. The fractal derivative model has been successfully applied to explain the novel air permeability phenomenon of cocoon. The theoretical analysis was in agreement with experimental results.