Hydraulic permeation model current density

The theoretical analysis of the hydraulic permeation model, moreover, provided an expression for the current density, at which membrane dehydra-... 

The diffusion model and the hydraulic permeation model differ decisively in their predictions of water content profiles and critical current densities. The origin of this discrepancy is the difference in the functions D (T) and /Cp (T). This point was illustrated in Eikerling et al., where both flux terms occurring in Equation (6.46) were converted into flux terms with gradients in water content (i.e., VA) as the driving force and effective transport coefficients for diffusion, A), and hydraulic permeation,... 

The hydraulic permeation model predicts highly nonlinear water content profiles, with strong dehydration arising only in the interfacial regions close to the anode. Severe dehydration occurs only at current densities closely approaching/p,. The hydraulic permeation model is consistent with experimental data on water content profiles and differential membrane resistance, i i as corroborated in Eikerling et al. The bare diffusion models exhibit marked discrepancies in comparison with these data. 

PEM resistance in operational PEFC as a function of the fuel cell current density, comparing experimental data (dots) and calculated results from a performance model based on the hydraulic permeation model for various applied gas pressure differences between anode and cathode compartments. (Reprinted from S. Renganathan et al. Journal of Power Sources 160 (2006) 386-397. Copyright 2006, with permission from Elsevier.)... 

Membrane performance characteristics in the hydraulic and diffusion limits are compared to each other in Fig. 9. Figure 9(a) illustrates that in the diffusion model considerable deviations from the purely ohmic performance of the saturated membrane arise already at small jv/Jj, well below the critical current density. This is in line with the comparison of the water-content profiles calculated in the diffusion model, Fig. 9(b), with those from the hydraulic permeation model, in Fig. 7. Indeed, membrane dehydration is much stronger in the diffusion model, affecting larger membrane domains at given values of jp/./j. Moreover, the profiles exhibit different curvature from those in Fig. 7. 

Fig. 10 Membrane resistance in H2/O2 fuel cell as a function of proton current density. Experimental data, normalized to the resistance 9ts of the saturated membrane at various temperatures have been extracted from Ref. 94. They are compared to the values calculated in the hydraulic permeation model (main figure) and to the results of the diffusion model, taken from Ref. 7 (inset).

Fig. 9 Water content profiles in the membrane, calculated in the hydraulic permeation model, at various fuel-cell current densities. A typical value of the parameter / that determines the onset of membrane dehydration near the anode was estimated as / 5-10Acm for Nafion 117 [11,16]...

The hydraulic permeation model in Eikerling et al. (1998, 2007a) assumed a negligible contribution of diffiisional water flux. It is valid at sufficiently high water content. The model helped rationalizing main dependences of the critical current density on membrane parameters. A 5-function-like pore size distribution dk r)/dr = itmaxS (r - ri), which is completely determined by the maximum water uptake A- ax. and by the first moment of the pore size distribution (i.e., the average pore size), r, provided an explicit expression for jpc. ... 

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