Oxygen Transport in the GDL

The functions c (z) and yo(z) in Equation 5.156 are the steady-state oxygen concentration in the channel and the local cell current density, respectively. These functions result from the solution of the steady-state problem for oxygen transport in the cathode channel (the section Oxygen Transport in the Channel ). 

After nondimensionalization with Equations 4.51,5.83, and 5.153, Equation 5.157 takes the form 

For the channel problem, the perturbation of the oxygen x flux will be needed at the channel/GDL interface. Differentiating Equation 5.160 over x, multiplying the result by bb, and substituting x = l + k, one finds 

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Substituting Eq. (23.30) into Eq. (23.11), we obtain the general polarization curve of the cathode side, which takes into account oxygen transport in the GDL ... 

Accounting for the oxygen transport in the GDL leads to the relation between ci and the oxygen concentration in the channel c/, (Equation 5.41). Inserting cj into an equation ju = Dci gives... 

Equation 4.189 can be used for the fitting at experimental polarization curves, provided that (i) the oxygen stoichiometry is large and (ii) the potential loss caused by oxygen transport in the GDL is minimal. The validity of the second condition is usually not known a priori. However, it can be easily relaxed by incorporating the respective transport loss into the polarization equation, as discussed in the section Oxygen Transport Loss in the Gas-Diffusion Layer in Chapter 5. 

Note that Cox,i is determined by the oxygen transport in the GDL (see below). The boundary conditions to Equation 4.199 are... 

The first term on the right describes the activation potential loss (the overpotential needed to activate the ORR). The second term represents the potential loss resulting from the oxygen transport in the GDL. As can be seen, when Ch = jo//C second logarithm tends to minus infinity and the cell potential tends to zero. Physically, this condition means that the oxygen concentration Ci at the CCL/GDL interface tends to zero (Figure 5.5), and the cell is not able to produce a higher current. In dimensional variables. Equation 5.43 reads... 

Again, the second logarithm describes the potential loss due to oxygen transport in the GDL. In the dimensional form, this equation reads... 

What is the effect of finite A, at high currents In this section, the case will be considered for poor oxygen diffusivity and ideal proton conductivity of the CCL. In this case, the local polarization curve of the CCL is given by Equation 4.87. Substituting Equation 5.41 into Equation 4.87, one obtains the local polarization curve with the term describing oxygen transport in the GDL ... 

Substituting Equations 5.69 and 5.70 into the first term in Equation 5.68, results in the cell polarization curve under ideal oxygen transport in the GDL ... 

To take into account the oxygen transport in the GDL, the system (5.68) and (5.50) has to be solved numerically. Analysis shows that the numerical solution is well approximated by the following relation (Kulikovsky, 2011a) ... 

Springer et al. (1996) developed a physical model for the impedance of the cathode side of a PEFC, taking into account oxygen transport in the GDL. They fitted the... 

A physical-based impedance model of the PEFC cathode, which included oxygen transport in the GDL, has been developed by Bultel et al. (2005). The authors reported qualitative similarity of measured and calculated impedance spectra and analyzed the effect of GDL diffusion resistivity on the cell performance. 

In this section, a model for the PEFC cathode impedance is discussed, including oxygen transport in the channel (Kulikovsky, 2012d). The model is based on the transient CCL performance model from the section Basic Equations linked to the nonstationary extensions of the models for oxygen transport in the GDL and in the channel, discussed in the section Performance Modeling of a Fuel Cell. ... 

Generally, in each segment, three time-dependent processes run simultaneously oxygen transport in the GDL, oxygen transport in the CCL, and the double layer charging. The fourth time-dependent process is oxygen transport in the channel, which links the segments. To understand the contribution of each process to the local spectra, the respective time derivatives will be switched on one by one. 

Here, A is given by Equation 5.57. Comparing this to Equation 5.120, it is seen that the term 1 fj describes the CCL charge-transfer resistivity, and the last term/A,/(/jj -fxT), accounts for the combined resistivity of oxygen transport in the GDL and in the channel. 

It is easy to verify that in the limit of Mgx -> oo, the first term on the right-hand side of Equation 5.181 tends to 1//, while the third term tends to 1 /(/j — J)- Thus, the first term represents the total CCL charge transfer resistivity at a constant Mgx. By analogy to Equation 5.178, the last term in Equation 5.181 gives the combined resistivity, due to oxygen transport in the GDL and in the channel. 

To rationalize the effect, suppose that the local polarization curve of an individual segment is given by Equation 5.43, which contains Tafel activation overpotential (the first term) and the potential loss resulting from the oxygen transport in the GDL (the second term). 

Resistive limiting current density (A cm ). Equation 4.221 Methanol-limiting current density (A cm ). Equation 5.222 Limiting current density due to oxygen transport in the GDL at the channel inlet (mol cm ). Equation 4.210 Liquid water flux density (Acm )... 

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