Transport in Porous Media

, Volume 121, Issue 2, pp 437–458 | Cite as

Modeling the Effect of Fibre Surface Morphology on Liquid Water Transport in Polymer Electrolyte Membrane Fuel Cell Gas Diffusion Layers

  • Hang Liu
  • James Hinebaugh
  • Stéphane Chevalier
  • Rupak Banerjee
  • ChungHyuk Lee
  • Aimy BazylakEmail author


In this work, we present a novel methodology for incorporating the effect of fibre surface morphology on liquid water transport in polymer electrolyte membrane fuel cell gas diffusion layers (GDLs). Roughness features presented on the surface of the fibre are analysed using atomic force microscopy and are found to significantly impact the capillary pressure of liquid water pathways propagating through the GDL. A threshold capillary pressure was defined as the largest capillary pressure exhibited by the liquid water phase during the invasion of the throat. The threshold capillary pressures observed in the presence of roughness features are significantly greater than those in the absence of roughness features. Two-dimensional circumferential roughness models in cylindrical and converging-diverging throats are established, and an interfacial meniscus advancing algorithm is presented to determine the resulting threshold capillary pressures required for liquid water penetration. Revised Young–Laplace equations, which are particularly useful for pore network modeling, are suggested for calculating threshold capillary pressures that account for the effect of the roughness of throats with intrinsic contact angles greater than \(90^{\circ }\).


Liquid–gas interfaces Nanoscale roughness Threshold capillary pressure Roughness model Pore network modeling 

List of symbols

\(\alpha \)

Angle of inclination (\(^{\circ }\))

\(\beta \)

Filling angle (\(^{\circ }\))

\(\beta _\mathrm{t}\)

Critical filling angle at threshold capillary pressure (\(^{\circ }\))

\(\theta \)

Intrinsic contact angle (\(^{\circ }\))

\(\theta _\mathrm{e}\)

Effective contact angle (\(^{\circ }\))

\(\sigma \)

Surface tension (\(\hbox {N}/\hbox {m}\))

\(A_{{\text {AFM}}}\)

Cross-sectional area of the partially imaged carbon fibre (\(\upmu \hbox {m}^{2}\))


Cross-sectional area of the carbon fibre in the absence of roughness features (\(\upmu \hbox {m}^{2}\))


Cross-sectional area of fibre roughness features protruding from the carbon fibre section (\(\upmu \hbox {m}^{2}\))


Length of the chord defining the base of the partial fibre (arc) (\(\upmu \hbox {m}\))


Length between the centres of meniscus curvature and the adjacent roughness features (\(\upmu \hbox {m}\))


Interfacial meniscus radius (\(\upmu \hbox {m}\))


Carbon fibre radius (\(\upmu \hbox {m}\))


Effective throat radius (\(\upmu \hbox {m}\))


Unit roughness radius (\(\upmu \hbox {m}\))


Throat radius in absence of roughness features (\(\upmu \hbox {m}\))


Capillary pressure (\(\hbox {Pa}\))

\(P_{{\text {defending}}}\)

Pressure in the defending phase (\(\hbox {Pa}\))

\(P_{{\text {invading}}}\)

Pressure in the invading phase (Pa)


Carbon fibre height profile (\(\upmu \hbox {m}\))



Financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC), the NSERC Discovery Accelerator Program, the NSERC Canada Research Chairs Program, and the Canada Foundation for Innovation are gratefully acknowledged. Graduate scholarships to Hang Liu from the University of Toronto Connaught International Scholarship for Doctoral Students is gratefully acknowledged. Graduate scholarships to ChungHyuk Lee from the Pierre Rivard Hydrogenics Graduate Fellowship, C. W. Bowman Graduate Scholarship, William Dunbar Memorial Fellowship in Mechanical Engineering, and the Ontario Graduate Scholarship are also gratefully acknowledged. The authors would like to thank Dr. Roswitha Zeis for her valuable discussions. The authors also acknowledge Mr. Peter Krolla-Sidenstein at the Karlsruhe Institute of Technology in Karlsruhe, Germany, for his generous assistance in AFM imaging.


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Authors and Affiliations

  1. 1.Thermofluids for Energy and Advanced Materials (TEAM) Laboratory, Department of Mechanical and Industrial Engineering, University of Toronto Institute for Sustainable Energy, Faculty of Applied Science and EngineeringUniversity of TorontoTorontoCanada

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