Analytical Models for the Permeabilities of Fibrous Ecomaterials

  • Boqi XiaoEmail author
Reference work entry


The fibrous ecomaterials have a variety of applications in various areas including tissue engineering, fuel cells, fiber-reinforced composite, thermal insulation, filtration, textile fabric, apparel products, medical science, and paper products in recent years. Generally, fibrous ecomaterials can serve as a porous media, through which photons, electrons, particles, fluids, and heat pass through in most of the above applications. So, it can be of importance to study the permeabilities of fibrous ecomaterials. Based on the well-known fractal feature of micropores in fibrous ecomaterials, this chapter presents an investigation for the permeabilities of fibrous ecomaterials. For this purpose, the first section was aimed at studying the relative permeability with the effect of capillary pressure by means of Fractal-Monte Carlo technique in the fibrous ecomaterials. In the second part, the permeability of the fibrous gas diffusion layer is investigated in proton exchange membrane fuel cells based on fractal geometry.


Fibrous ecomaterials Fractal Permeability Relative permeability Porosity 



Area fractal dimension of micropores


Average fiber diameter


Form factor


Tortuosity fractal dimension


Intrinsic permeability


Relative permeability for the wetting phase in fibrous ecomaterials


Relative permeability for non-wetting phase in fibrous ecomaterials




Pressure difference

\( \overline{P_{c,w}} \)

The capillary pressure of fibrous ecomaterials for wetting phase


Mechanical pressure or injection pressure


The flow rate through a single tortuous capillary


The total fluids mass transfer rate




Saturation of the wetting phase


Surface tension for wetting phase

Greek Letters


Contact angle between the liquid and the solid




Pore/capillary diameter


Fiber diameter


Maximum diameter of micropores


Minimum diameter of micropores


Viscosity of the fluid








This work was supported by the National Natural Science Foundation of China (Grant No. 51576114), the Science Fund for Distinguished Young Scholars of Hubei Province of China (Grant No. 2018CFA066), the Natural Science Foundation of Fujian Province of China (Grant No. 2016J01254), and the Program for Young Top-notch Innovative Talents of Fujian Province of China.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Mechanical and Electrical EngineeringSanming UniversitySanmingPeople’s Republic of China
  2. 2.School of Mechanical and Electrical EngineeringWuhan Institute of TechnologyWuhanPeople’s Republic of China

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