US 11,658,323 B2
Method for making a hydrogen fuel cell gas diffusion layer having tailored porosity
Jamal Hussain Al-Smail, Dhahran (SA)
Assigned to King Fahd University of Petroleum and Minerals, Dhahran (SA)
Filed by King Fahd University of Petroleum and Minerals, Dhahran (SA)
Filed on Sep. 30, 2019, as Appl. No. 16/588,166.
Prior Publication US 2021/0098808 A1, Apr. 1, 2021
Int. Cl. H01M 8/1067 (2016.01); H01M 8/04119 (2016.01); H01M 4/86 (2006.01)
CPC H01M 8/1067 (2013.01) [H01M 4/861 (2013.01); H01M 8/04149 (2013.01)] 8 Claims
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1. A method for producing a gas diffusion layer (“GDL”) for a fuel cell which comprises the GDL, wherein the GDL, has a length (x-axis; custom character), thickness (y-axis; h) and width (z-axis; w) and is adjacent a channel in the fuel cell which has an inlet and an outlet through which oxygen flows, the method comprising:
forming the GDL, to have a porosity gradient to permit flow of oxygen through the GDL such that the oxygen mass fraction along the length or x-axis of the GDL meets boundary condition (6):

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where pg is gas density, pin is inlet pressure, pout is outlet pressure, custom character is length of the gas diffusion layer, and x is a space variable;
where co is oxygen mass fraction, wherein ε is porosity of the gas diffusion layer, x is a space variable, cin is inlet oxygen mass fraction, and cout is outlet oxygen mass fraction, custom character is length of the gas diffusion layer, and x is a space variable;
solving the porosity of the GDL along its length ε=ε(x) by minimizing cost functional E:

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wherein co is obtained from solution of boundary condition (6), a and b are scalar, and M is the catalyst layer,
wherein the GDL meets the condition:
E(ε*;U*)=minE(ε;U),
subject to
A(ε;U)=0
wherein the solution is a minimizer of Langrangian L, defined as
(ε, W, Λ):=E(ε;W)+ΛA(ε; W); and
wherein εn is represented by εn+1nnεE(εn, Un),
herein a local minimizer (ε*, U*, Λ*) of the Lagrangian L that satisfies
L(ε*, U*, Λ*)=;
meets the conditions:
εL(ε*, U*, Λ*)=∂εE(ε*;U*)+Λ*∂εA(ε*;U*)=0;
WL(ε*, U*, Λ*)=∂WE(ε*;U*)+Λ*∂WA(ε*; U*)=0; and
ΛL(ε*, U*, Λ*)=A(ε*;U*)=0.
wherein porosity εn is in a range of from 0.4 to 0.8 and parameter δn selected to keep porosity within this range,
wherein a ratio of width to thickness

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of the GDL is in a range of from 10:1 to 100:1, and
wherein a ratio of length to thicknes

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of the GDL is in a range of from 50:1 to 70:1.