Skip to main content
SpringerLink
Log in

Analytical Models for the Permeabilities of Fibrous Ecomaterials

  • Living reference work entry
  • First Online:
Handbook of Ecomaterials

  • 350 Accesses

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Abbreviations

Df:

Area fractal dimension of micropores

d f :

Average fiber diameter

F :

Form factor

DT:

Tortuosity fractal dimension

K :

Intrinsic permeability

k rg :

Relative permeability for the wetting phase in fibrous ecomaterials

krw:

Relative permeability for non-wetting phase in fibrous ecomaterials

p :

Pressure

Δp:

Pressure difference

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

The capillary pressure of fibrous ecomaterials for wetting phase

P m :

Mechanical pressure or injection pressure

q(λ):

The flow rate through a single tortuous capillary

Q(λ):

The total fluids mass transfer rate

R:

Probability

Sw:

Saturation of the wetting phase

T :

Surface tension for wetting phase

θ :

Contact angle between the liquid and the solid

ϕ :

Porosity

λ :

Pore/capillary diameter

d f :

Fiber diameter

λ max :

Maximum diameter of micropores

λ min :

Minimum diameter of micropores

μ :

Viscosity of the fluid

max:

Maximum

min:

Minimum

References

  1. Cai JC, Luo L, Ye R, Zeng XF, Hu XY (2015) Recent advances on fractal modeling of permeability for fibrous porous media. Fractals 23(1):1540006

    Article  Google Scholar 

  2. Chen HX, Lu YJ, Ling T (2013) Fault identification of gearbox degradation with optimized wavelet neural network. Shock Vib 20:247–262

    Article  Google Scholar 

  3. Xiao BQ, Wang W, Fan JT, Chen HX, Hu XL, Zhao DX, Zhang X, Ren W (2017) Optimization of the fractal-like architecture of porous fibrous materials related to permeability, diffusivity and thermal conductivity. Fractals 25(3):1750030

    Article  MathSciNet  Google Scholar 

  4. Zhao Z, Xie M, Li Y, Chen A, Li G, Zhang J, Hu H, Wang X, Li S (2015) Formation of curcumin nanoparticles via solution-enhanced dispersion by supercritical CO2. Int J Nanomedicine 10:3171–3181

    Article  Google Scholar 

  5. Cai JC, Perfect E, Cheng C-L, Hu XY (2014) Generalized modeling of spontaneous imbibition based on Hagen–Poiseuille flow in tortuous capillaries with variably shaped apertures. Langmuir 30:5142–5151

    Article  Google Scholar 

  6. Chen HX, Shang YF, Sun K (2013) Sequential hypothesis testing for reflected signal recognition of time-of-flight estimation in ultrasonic defect detection. Insight-Non-Destructive Test Cond Monit 55:66–71

    Article  Google Scholar 

  7. Xiao BQ, Fan JT, Ding F (2014) A fractal analytical model for the permeabilities of fibrous gas diffusion layer in proton exchange membrane fuel cells. Electrochim Acta 134:222–231

    Article  Google Scholar 

  8. Zhao Z, Li Y, Xie MB (2015) Silk fibroin-based nanoparticles for drug delivery. Int J Mol Sci 16:4880–4903

    Article  Google Scholar 

  9. Cai JC, Yu BM, Zou MQ, Mei MF (2010) Fractal analysis of invasion depth of extraneous fluids in porous media. Chem Eng Sci 65(18):5178–5186

    Article  Google Scholar 

  10. Cai JC, Yu BM, Zou MQ, Luo L (2010) Fractal characterization of spontaneous co-current imbibition in porous media. Energy Fuel 24(3):1860–1867

    Article  Google Scholar 

  11. Cai JC, Yu BM (2011) A discussion of the effect of tortuosity on the capillary imbibition in porous media. Transp Porous Media 89(2):251–263

    Article  Google Scholar 

  12. Cai JC, Hu XY, Xiao BQ, Zhou YF, Wei W (2017) Recent developments on fractal-based approach to nanofluids and nanoparticle aggregation. Int J Heat Mass Transf 105:623–637

    Article  Google Scholar 

  13. Xiao BQ, Fan JT, Ding F (2012) Prediction of relative permeability of unsaturated porous media based on fractal theory and Monte Carlo simulation. Energy Fuel 26:6971–6978

    Article  Google Scholar 

  14. Xiao BQ, Yan HX, Xiao SX, Ren W, Fan JT, Pan ZH (2016) An analytical model for gas diffusion through fractal nanofibers in complex resources. J Nat Gas Sci Eng 33:1324–1329

    Article  Google Scholar 

  15. Xiao BQ, Fan JT, Wang ZC, Cai X, Zhao XG (2015) Fractal analysis of gas diffusion in porous nanofibers. Fractals 23(1):1540011

    Article  Google Scholar 

  16. Xiao BQ, Tu X, Ren W, Wang ZC (2015) Modeling for hydraulic permeability and Kozeny-Carman constant of porous nanofibers using a fractal approach. Fractals 23(3):1550029

    Article  Google Scholar 

  17. Xiao BQ, Chen HX, Xiao SX, Cai JC (2017) Research on relative permeability of nanofibers with capillary pressure effect by means of Fractal-Monte Carlo technique. J Nanosci Nanotechnol 17(9):6811–6817

    Article  Google Scholar 

  18. Yu BM, Cheng P (2002) A fractal permeability model for bi-dispersed porous media. Int J Heat Mass Transf 45(14):2983–2993

    Article  Google Scholar 

  19. Ahn KJ, Seferis JC, Berg JC (1991) Permeation measurements through prepreg aging in relation to tack. Polym Compos 12:146–152

    Article  Google Scholar 

  20. Chaitanya JB, Stefan TT (2008) Effect of anisotropic thermal conductivity of the GDL and current collector rib width on two-phase transport in a PEM fuel cell. J Power Sources 179(1):240–251

    Article  Google Scholar 

  21. Amico S, Lekakou C (2001) An experimental study of the permeability and capillary pressure in resin-transfer moulding. Compos Sci Technol 61:1945–1959

    Article  Google Scholar 

  22. Dana E, Skoczylas F (2002) Experimental study of two-phase flow in three sandstones. II. Capillary pressure curve measurement and relative permeability pore space capillary models. Int J Multiphase Flow 28:1965–1981

    Article  Google Scholar 

  23. Li KW, Hone RN (2001) Steam-water relative permeability by the capillary pressure method. In: International symposium of the society of the core analysts, Sept 17–19

    Google Scholar 

  24. Li KW, Hone RN (2001) An experimental and analytical study of steam/water capillary pressure. SPE Reservoir Evaluation & Engineering, Decision, pp 477–482

    Article  Google Scholar 

  25. Denn MM (1986) Process fluid mechanics. Prentice Hall, Englewood Cliffs

    Google Scholar 

  26. Yu BM, Lee LJ, Cao HQ (2001) Fractal characters of pore microstructures of textile fabrics. Fractals 9(2):155–163

    Article  Google Scholar 

  27. Kirsch AA, Fuchs NA (1967) Studies on fibrous aerosol filters, II. Pressure drops in systems of parallel cylinders. Annals Occup Hyg 10(1):23–30

    Google Scholar 

  28. Zobel S, Maze B, Tafreshi HV, Wang Q, Pourdeyhimi B (2007) Simulating permeability of 3-D calendered fibrous structures. Chem Eng Sci 62(22):6285–6296

    Article  Google Scholar 

Download references

Acknowledgments

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.

Author information

Authors and Affiliations

  1. School of Mechanical and Electrical Engineering, Sanming University, Sanming, People’s Republic of China

    Boqi Xiao

  2. School of Mechanical and Electrical Engineering, Wuhan Institute of Technology, Wuhan, People’s Republic of China

    Boqi Xiao

Authors
  1. Boqi Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Boqi Xiao .

Editor information

Editors and Affiliations

  1. Instituto de Ingeniería Civil, Universidad Autónoma de Nuevo León Instituto de Ingeniería Civil, San Nicolás de los Garza, Nuevo León, Mexico

    Leticia Myriam Torres Martínez

  2. Universidad Autónoma de Nuevo León , Monterrey, Mexico

    Oxana Vasilievna Kharissova

  3. Universidad Autónoma de Nuevo León , Monterrey, Mexico

    Boris Ildusovich Kharisov

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Xiao, B. (2018). Analytical Models for the Permeabilities of Fibrous Ecomaterials. In: Martínez, L., Kharissova, O., Kharisov, B. (eds) Handbook of Ecomaterials. Springer, Cham. https://doi.org/10.1007/978-3-319-48281-1_90-1

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-48281-1_90-1

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-48281-1

  • Online ISBN: 978-3-319-48281-1

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

Publish with us

Policies and ethics

Search

Navigation