Hydraulic Permeation Comparison

The diffusion model and the hydraulic permeation model differ in their predictions of water content profiles and critical current densities. The origin of this discrepancy is the difference in the functions ZT (A.) and This point was illustrated in the original publication on this model (Eikerling et al., 1998), where both flux terms, occurring in Equation 5.28, were converted into flux terms with gradients in water content, VX, as the driving force and with effective transport coefficients for diffusion, D k), and hydraulic permeation, 

Direct comparison of D (A.) and confirmed that 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. Moreover, severe dehydration occurs only at current densities close to jpc. The hydraulic permeation model is consistent with experimental data on water content profiles and differential membrane resistance (Buechi and Scherer, 2001 Mosdale et al., 1996 Xu et al., 2007 Zhang et al., 2008). Bare diffusion models exhibit marked discrepancies in comparison with these data. 

Recently, it was shown that the hydraulic permeation model could explain why the membrane performance responds to variations in external gas pressures, observed in operating fuel cells by Renganathan et al. (2006). These authors analyzed the uniformity of water content distributions in operating PEMs by plotting the normalized PEM resistance 

Rpem/Rs beyond this point. These trends are in excellent agreement with experimental data for Nafion 112. A finite positive gas pressure gradient, = Pf — P 0, improves the internal humidification of the membrane, leading to a more uniform water distribution and a significantly reduced dependence of membrane resistance on k. The latter trends are consistent with predictions of the hydraulic permeation model. 

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Direct comparison of D (A)and Dj( jj,(A) showed that hydraulic permeation dominates at high A, whereas diffusion prevails at low A. 

Note that diffusion models and hydraulic permeation models have their own caveats the membrane is neither a homogeneous acid solution, nor is it the well-structured porous rock. Critical comparison of the results of the two approaches with each other and with experiments, is of crucial importance for understanding the membrane functioning within the cell and developing the strategies on water management and optimized membrane properties. 

Hydraulic Permeation versus Diffusion and Comparison with Experiments... 

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. 

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