Vapor-equilibrated transport mode content

As in the case for the vapor-equilibrated transport mode, the properties of the liquid-equilibrated transport mode depend on the water content and temperature of the membrane. For a fully liquid-equilibrated membrane, the properties are uniform at the given temperature. This is because the water content remains constant for the liquid-equilibrated mode unlike in the vapor-equilibrate one. From experimental data, the value of A, for liquid-equilibrated Nafion is around 22, assuming the membrane has been pretreated correctly [6, 7, 52]. In agreement with the physical model, the water content is only a very weak function of temperature for extended (E)-form membranes (as assumed in our analysis) and can be ignored [6]. For other membrane forms, this dependence is much stronger and cannot be ignored, as discussed in the Section 5.10.1. 

In summary, the transport mode of a vapor-equilibrated membrane is that of a single membrane phase in which protons and water are dissolved. The chemical-potential gradient is used directly since it precludes the necessity of separating it into pressure and activity terms. Thus, Eqs. (5.8-5.11) are used directly without any modifications. Although it makes sense to use the chemical-potential driving force, most of the experimental data are a function of water content or X. Thus, a way is needed to relate X to the chemical potential. 

To examine the transport-mode-transition region in more detail, simulations were run at different current densities [71]. The resultant membrane water profiles are shown in Figure 5.11 where a vapor-equilibrated membrane at unit activity has a water content of L = 8.8 as calculated by the modified chemical model (see Section 5.5.1). The profiles in the figure demonstrate that the higher the current density the sharper the transition from the liquid-equilibrated to the vapor-equilibrated mode as well as the lower the value of the water content at the anode GDL/membrane interface. The reason why the transition occurs at the same point in the membrane is that the electro-osmotic flow and the water-gradient flow are both proportional to the current... 

If the membrane itself is partially in contact with liquid and vapor, as can commonly be the case in an operating fuel cell, the water content and uptake in the membrane can vary with location, although in equilibrium the water content in the membrane will become homogeneous with uptake depending on the overall water avadabihty. Transport in this case can be modeled as occurring in parallel between gas and liquid equilibrated modes, with a suitable fraction denoting the liquid and gas phase fractions of contact with the membrane. 

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