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Cited by 1,368Fuel Cells and Related MaterialsAdvancements in Solid Oxide Fuel CellsElectrocatalysts for Energy Conversion

A Mathematical Model of the Solid‐Polymer‐Electrolyte Fuel Cell

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Bernardi, Dawn M., Verbrugge, Mark W.·1992·Journal of The Electrochemical Society
DOI 10.1149/1.2221251
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Abstract

We present a mathematical model of the solid‐polymer‐electrolyte fuel cell and apply it to ( i ) investigate factors that limit cell performance and ( ii ) elucidate the mechanism of species transport in the complex network of gas, liquid, and solid phases of the cell. Calculations of cell polarization behavior compare favorably with existing experimental data. For most practical electrode thicknesses, model results indicate that the volume fraction of the cathode available for gas transport must exceed 20% in order to avoid unacceptably low cell‐limiting current densities. It is shown that membrane dehydration can also pose limitations on operating current density; circumvention of this problem by appropriate membrane and electrode design and efficient water‐management schemes is discussed. Our model results indicate that for a broad range of practical current densities there are no external water requirements because the water produced at the cathode is enough to satisfy the water requirement of the membrane. Inefficiencies due to the transport of unreacted hydrogen or oxygen through the membrane are shown to be insignificant at practical operating current densities. The transport of gases dissolved in the membrane phase, however, limits the utilization of catalyst. Predictions of cell performance with different types of membranes are also examined, and the model results compare favorably with experimental data.

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  • In Meng et al., liquid saturation evolves according to a capillary diffusion equation with Dcap set as a constant 2 × 10−5 kg m−1 s−1 and κp set as 1.8 × 10−18 m2 following Bernardi and Verbrugge.

    “In turn the liquid saturation evolves according to a capillary diffusion equation:(98)∇⋅(Dcap∇SL)−∇⋅(SL3κpvw∇p)=Rw where Dcap is capillary diffusivity (set as a constant = 2 × 10−5 kg m−1 s−1) and κp is a permeability for the membrane (set = 1.8 × 10−18 m2 following Bernardi and Verbrugge [142]).”

    From Modelling the Proton-Conductive Membrane in Practical Polymer Electrolyte Membrane Fuel Cell (PEMFC) Simulation: A Review (2020) · cites this paper as [142]

  • The quasi-empirical Schlögl equation used for water transport in the works of Bernardi and Verbrugge assumes the presence of liquid water filling the membrane pores.

    “The quasi-empirical Schlögl equation used for water transport in the works of Bernardi and Verbrugge assumes the presence of liquid water filling the membrane pores, and sets [116,142]:(100)μMwρwNw=−κp∇p−κϕcfF∇ϕ”

    From Modelling the Proton-Conductive Membrane in Practical Polymer Electrolyte Membrane Fuel Cell (PEMFC) Simulation: A Review (2020) · cites this paper as [142]

  • Bernardi and Verbrugge expressed the gas diffusion coefficients directly in the temperature-dependent form Dgas = Dgas,0 exp(−θdiff,gas/T).

    “Bernardi and Verbrugge expressed the gas diffusion coefficients directly, in the following temperature-dependent form (coefficient data are tabulated in Table 11) [142]:(123)Dgas=Dgas,0exp(−θdiff,gasT)”

    From Modelling the Proton-Conductive Membrane in Practical Polymer Electrolyte Membrane Fuel Cell (PEMFC) Simulation: A Review (2020) · cites this paper as [142]

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Authors
Bernardi, D. M., & Verbrugge, M. W.
Affiliations
General Motors (United States) (US)
ORCID
Verbrugge, Mark W.
Venue
Journal of The Electrochemical Society
Publisher
The Electrochemical Society
Published
1992-09-01
Volume
139
Issue
9
Pages
2477-2491
ISSN
  • 0013-4651 (ISSN-L)
  • 1945-7111
DOI
10.1149/1.2221251
OpenAlex
W1980196589
Cited by
1,368
References
0
Citations by year
2026: 19 · 2025: 24 · 2024: 29 · 2023: 38 · 2022: 37 · 2021: 40 · 2020: 29 · 2019: 40 · 2018: 32 · 2017: 30 · 2016: 34 · 2015: 29 · 2014: 44 · 2013: 40 · 2012: 60
FWCI
6.09
Type
journal article
Language
en
Open access
Licence
Locations
Journal of The Electrochemical Society (publishedVersion)
Topics
  • Physical Sciences › Engineering › Electrical and Electronic Engineering › Fuel Cells and Related Materials
  • Physical Sciences › Materials Science › Materials Chemistry › Advancements in Solid Oxide Fuel Cells
  • Physical Sciences › Energy › Renewable Energy, Sustainability and the Environment › Electrocatalysts for Energy Conversion
Keywords
proton exchange membrane fuel cells, mathematical modeling, cell polarization, species transport, gas transport, membrane dehydration, water management (fuel cells), catalyst utilization, current density

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