CPC H01M 8/1067 (2013.01) [H01M 4/861 (2013.01); H01M 8/04149 (2013.01)]  8 Claims 
1. A method for producing a gas diffusion layer (“GDL”) for a fuel cell which comprises the GDL, wherein the GDL, has a length (xaxis; ), thickness (yaxis; h) and width (zaxis; 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 xaxis of the GDL meets boundary condition (6):
where p_{g }is gas density, p_{in }is inlet pressure, p_{out }is outlet pressure, is length of the gas diffusion layer, and x is a space variable;
where c_{o }is oxygen mass fraction, wherein ε is porosity of the gas diffusion layer, x is a space variable, c_{in }is inlet oxygen mass fraction, and c_{out }is outlet oxygen mass fraction, 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:
wherein c_{o }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 ε_{n }is represented by ε_{n+1}=ε_{n}=δ_{n}∂_{ε}E(ε_{n}, U_{n}),
herein a local minimizer (ε*, U*, Λ*) of the Lagrangian L that satisfies
∇L(ε*, U*, Λ*)=;
meets the conditions:
∂_{ε}L(ε*, U*, Λ*)=∂_{ε}E(ε*;U*)+Λ*∂_{ε}A(ε*;U*)=0;
∂_{W}L(ε*, U*, Λ*)=∂_{W}E(ε*;U*)+Λ*∂_{W}A(ε*; U*)=0; and
∂_{Λ}L(ε*, U*, Λ*)=A(ε*;U*)=0.
wherein porosity ε_{n }is in a range of from 0.4 to 0.8 and parameter δ_{n }selected to keep porosity within this range,
wherein a ratio of width to thickness
of the GDL is in a range of from 10:1 to 100:1, and
wherein a ratio of length to thicknes
of the GDL is in a range of from 50:1 to 70:1.
