Hydraulic permeation model results

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.)... 

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. 

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).

Structural models emerge from the notion of membrane as a heterogenous porous medium characterized by a radius distribution of water-filled pores. This structural concept of a water-filled network embedded in the polymer host has already formed the basis for the discussion of proton conductivity mechanisms in previous sections. Its foundations have been discussed in Sect. 8.2.2.1. Clearly, this concept promotes hydraulic permeation (D Arcy flow [80]) as a vital mechanism of water transport, in addition to diffusion. Since larger water contents result in an increased number of pores used for water transport and in larger mean radii of these pores, corresponding D Arcy coefficients are expected to exhibit strong dependencies on w. 

A permeate flux declines in the presence of solute due to membrane fouling. A decrease in flux is a result of several phenomenons including adsorption of macromolecules to membrane surface involving pore blocking, concentration polarization, and formation of a gel-like cake layer within the membrane pores (50). Several models have been used to describe solute fouling, among them are hydraulic resistance, osmotic pressure, gel polarization, and film models (51,52). 

An effect not considered in the above models is the added resistance, caused by fouling, to solute back-diffusion from the boundary layer. Fouling thus increases concentration polarization effects and raises the osmotic pressure of the feed adjacent to the membrane surface, so reducing the driving force for permeation. This factor was explored experimentally by Sheppard and Thomas (31) by covering reverse osmosis membranes with uniform, permeable plastic films. These authors also developed a predictive model to correlate their results. Carter et al. (32) have studied the concentration polarization caused by the build-up of rust fouling layers on reverse osmosis membranes but assumed (and confirmed by experiment) that the rust layer had negligible hydraulic resistance. 

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