Oxygen Transport in the Channel

Voltage perturbation disturbs the oxygen concentration in the channel. Propagation of this perturbation is a time-dependent process, which affects the cell impedance spectrum. To take into account this effect, a time-dependent mass balance equation is written for the oxygen concentration in the channel Ch 

Equation 5.165 is linear thus, an equation for the small-amplitude perturbation 

The boundary condition at z = 0 means undisturbed inlet oxygen concentration. The diffusion term on the right-hand side of Equation 5.168 is given by Equation 5.163. 

The expression for/z contains the perturbation of cell current density jL Ohm s law 

The solution of the steady-state version of the problem (5.165), under the condition of equipotential cell electrodes, gives the undisturbed shapes of the oxygen concentration and local current density along the channel given by Equations 5.55 and 5.56, respectively. In the notations of this section. Equations 5.55 and 5.56 take the form 

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Voltage Loss due to Oxygen Transport in the Channel Oxygen Mass Conservation in the Channel... 

The equations of the previous section allow us to take a next step by taking into account the potential loss resulting from the oxygen transport in the channel. Suppose that the cell has a straight oxygen channel. Let the coordinate z be directed along the... 

The results of the section Voltage Loss due to the Oxygen Transport in the Channel are summarized in Tables 5.2 and 5.3. As ean be seen, the low-current polarization eurves contain neither Up nor D. Thus, in the low-current regime, the cell performance is not affected by the species transport in the CCL. The performance is determined by oxygen transport in channel and GDL and by reaction kinetics (through the parameters b and / ). 

An experiment (Makharia et al., 2005) has been performed with pure oxygen under large stoichiometry of the cathode flow. This, together with the low cell current, makes the resistivity due to oxygen transport in the channel and in the GDL vanishingly small. These conditions correspond to the model assumptions and they can be recommended for CCL characterization by means of EIS. 

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. ... 

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 ). 

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. 

In each frame, the innermost (dotted) semicircle is the local (average in the last frame) impedance spectrum, calculated assuming infinitely fast relaxation of oxygen transport in the channel and in the GDL. In other words, these spectra represent processes in the CCL only. Note that the local current density decays toward the channel outlet, which increases the radius of the local CCL spectrum (Figure 5.24). 

FIGURE 5.27 Average impedance spectra of the cell for the indicated oxygen stoichiometries. Dashed curves show the spectra calculated assuming steady-state oxygen transport in the channel. The intersection of low- and high-frequency arcs occurs at frequencies between 1 and 3 Hz. 

The impedance spectra of the whole cell for the three stoichiometries of the oxygen flow are shown in Figure 5.27. As expected, the resistivity due to oxygen transport in the channel increases with the decrease in X. Note that for all X, the low-frequency ( channel ) arc intersects the CCL-l-GDL arc at a frequency / in the range of 1-3 Hz (Figure 5.27). The measurements of Schneider et al. (2007a) show that the intersection is independent of X and, in their experiments, it occurs at/ 7.9 Hz. 

In this limit, the resistivity resulting from oxygen transport in the channel is zero and, hence, the last term in this equation is the resistivity because of the oxygen diffusion in the GDL. As it should be, this resistivity tends to infinity, as the cell current density J approaches the limiting current density... 

Several approximations can be made to take into account oxygen transport in the ceU. In the simplest case, the oxygen concentration in the cathode channel, Cf, can be assumed constant. This corresponds to a high stoichiometry k of the oxygen (air) flow. The transport term in the ceU polarization curve then depends on the transport properties of the GDL only (Sections 23.3.1-23.3.4). 

To reach the catalyst layer, oxygen on the cathode side must be transported through the channel and the GDL (Figure 23.9). In this section, we assume that the oxygen concentration in the channel is constant. Transport of oxygen through the GDL obeys the following equation ... 

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... 

In low-temperature cells, oxygen required for the ORR is transported to the CCL through the gas channels and the GDL. Understanding the potential losses resulting from oxygen transport in the cell components is one of the key issues for better cell design. 

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. 

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 )... 

Furthermore, all of the previous models consider oxygen transport in the gas diffusion layer solely as a result of concentration gradient, and they do not consider an interaction of the species in the channel with those in the gas diffuser due to velocity vector. Gurau et al. [21,22] presented the first unified approach by coupling the flow and transport governing equations in the flow channel and gas diffuser with no boundary conditions at the interface. The modeling domain of this model is shown in Figure 7-10, and it is different for different species, namely ... 

A typical PEFC, shown schematically in Fig. 1, consists of the anode and cathode compartments, separated by a proton conducting polymeric membrane. The anode and cathode sides each comprises of gas channel, gas diffusion layer (GDL) and catalyst layer (CL). Despite tremendous recent progress in enhancing the overall cell performance, a pivotal performance/durability limitation in PEFCs centers on liquid water transport and resulting flooding in the constituent components.1,2 Liquid water blocks the porous pathways in the CL and GDL thus causing hindered oxygen transport to the... 

Apply 1 m/s as flow velocity so that the total contact time in the channel is 500 seconds. The modeling should be done as Id transport model with 10 cells (dispersivity 0.1 m) and last over 750 seconds. Also take into account the contact with the atmosphere. Therefore, ran the model once with a C02 partial pressure of 0.03 Vol% and a second time with 1 Vol%, both times assuming an oxygen partial pressure of 21 Vol% 02. The latter case corresponds rather to a closed carbonate channel. 

Fig. 42. Schematic of regions considered in PEFC air electrode modeling, including (from left to right) gas flow channel, gas-diffusion backing, and cathode catalyst layer. Oxygen is transported in the backing through the gas-phase component of a porous/tortuous medium and through the catalyst layer by diffusion through a condensed medium. The catalyst layer also transports protons and is assumed to have evenly distributed catalyst particles within its volume [100]. (Reprinted by permission of the Electrochemic Society).

The approach described in Sections 8.2.3 and 8.2.4.5.3 was used to construct quasi-2D (Q2D) analytical and semi-analytical models of PEFC [246, 247] and DMFC [248, 249], The Q2D model of a PEFC [246] takes into account water management effects, losses due to oxygen transport through the GDL, and the effect of oxygen stoichiometry. The model is fast and thus suitable for fitting however, the systematic comparison of model predictions with experiment has yet not been performed. Q2D approaches have been employed to construct a model of PEFC performance degradation [250], to explain the instabilities of PEFC operation [251, 252] and to rationalize the effect of CO2 bubbles in the anode channel on DMFC performance [253, 254],... 

Here, S is the specific surface area of the catalyst, a is the conversion and F is the gas flow. The term FjS is the area velocity. The rate constant depends on the type of catalyst material, the oxygen concentration, and the temperature. Additionally, it was found that the rate constant depends on the velocity in the channels, which implies that transport phenomena have an effect on the NO conversion. 

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