Electro-osmotic flux of water

Another problem is the flooding of the cathode CL due to the high electro-osmotic flux of water through the PEM, largely studied in the context of hydrogen-feed PEMFCs [22],... 

The first term on the right side of Eq. (1.46) is the stoichiometric flux of water due to the ORR. The second term is the electro-osmotic flux of water through the membrane, where is the effective transfer coefficient of water molecules through the MEA. ... 

The balance between the electro-osmotic drag of water from anode to cathode and back diffusion from cathode to anode yields the net water flux through the membrane [44] ... 

Electro-osmotic Drag Electro-osmotic drag of water is the mass flux resulting from a polar attraction of the water molecules to the positively charged protons moving from the anode to the cathode through the electrolyte, as illustrated in Figure 6.23. As each proton... 

Under fuel cell operation, a finite proton current density, 0, and the associated electro-osmotic drag effect will further affect the distribution and fluxes of water in the PEM. After relaxation to steady-state operation, mechanical equilibrium prevails locally to fix the water distribution, while chemical equilibrium is rescinded by the finite flux of water across the membrane surfaces. External conditions defined by temperature, vapor pressures, total gas pressures, and proton current density are sufficient to determine the stationary distribution and the flux of water. 

The physical mechanism of membrane water balance and the formal structure of modeling approaches are straightforward. Under stationary operation, the inevitable electro-osmotic flux has to be compensated by a back flux of water from cathode to anode, driven by gradients in concentration, activity, or liquid pressure of water. The water distribution in PEMs that is generated in response to these driving forces decreases from cathode to anode. With increasing/o, the water distribution becomes more nonuniform. the water content near the anode falls below the percolation threshold of proton conduction, X < X. This leaves only a small conductivity due to surface transport of water. As a consequence, increases dramatically this can lead to failure of the complete cell. 

There are three main fluxes through the membrane. A proton flux that goes from anode to cathode, a water electro-osmotic flux that develops along with the proton flux, and a water-gradient flux. This last flux is sometimes known as the water-back flux or back-diffusion flux it is due to a difference in the chemical potential of water at the two sides of the membrane and may be in either direction although the direction is typically from cathode to anode due to water production at the cathode. In addition to the above three fluxes, there are also fluxes due to crossover of oxygen and hydrogen, which are described in Section 5.9. 

The basic mechanisms of membrane operation in an operating fuel cell are shown in Fig. 8. Proton flow, as the primary membrane process, induces water transport from anode to cathode by electro-osmosis. Stationary operation implies that the electro-osmotic water flux has to be balanced by an internal backflux. This requires an appropriate gradient in water content across the membrane as a driving force. The stationary balance between electro-osmotic flux and backflux, thus, establishes to a profile of water across the membrane. 

According to Eq. 6.11, the DMFC determination of the methanol permeability requires the knowledge of the methanol drag factor, because the electro-osmotic flux could afford for a considerable fraction of the methanol flow, particularly at high methanol concentrations. An important drawback of this method is that the methanol drag coefficient is not well known, so Ren et al. [299] assumed that it was similar to the water drag coefficient ( =2.5). However, some recent NMR [300] and electro-osmosis [301] studies would indicate that this assumption is not valid, leading to considerable uncertainties in the methanol permeability coefficients determined by this method. 

Figure 7.1. Dependence of electro-osmotic flux (Jv)ap=o on potential difference A(f> for Zeokarb 225 (Na+ form)/methano 1-water system.

Figure 7.2. Non-Linear dependence of electro-osmotic flux on potential difference for IRC-50 (H+ form)/methanol-water system.

Suppose that the net flux of water in the membrane is zero, i.e. the electro-osmotic drug is fuUy compensated for by the back diffusion. Equating N, Eq. (1.69) to zero we get... 

Under steady-state operation, local mechanical equilibrium prevails at all microscopic and macroscopic interfaces in the membrane. It fixes the stationary distribution of absorbed water. The condition of chemical equilibrium is, however, lifted to allow for the flux of water. Continuity of the net water flux in the PEM and across its interfaces with adjacent media adjusts the gradients in water activity or pressure in the system. Water fluxes occur by diffusion, hydraulic permeation, and electro-osmotic drag. At external interfaces, vaporization and condensation proceed at rates that match the net water flux. These mechanisms apply to PEM operation in a working cell, as well as to ex situ water flux measurements that are conducted in order to investigate the transport properties of PEMs. 

The success of such a program of water flux measurements hinges on a number of conditions (i) the availability of theoretical models that account for the coupling of various water transport mechanisms, (ii) the development of model-based diagnostic tools to separate and isolate electro-osmotic flux from other fluxes, and (hi) experiments that can be conducted under controlled conditions. 

The most complete description of variations in local distributions and fluxes of water is provided by combination models, which allow for concurrent contributions of diffusion and hydraulic permeation to the water backflux that competes with the electro-osmotic drag. The main conclusions from these models for membrane water management under operation are... 

Water transport by electro-osmotic drag is always from the anode to the cathode. Since the drag is proportional to the current (protons), an expression for the flux of water by... 

What are the mechanisms and the transport coefficients of water fluxes (diffusion, convection, hydraulic permeation, electro-osmotic drag) ... 

In reality, this behavior is only observed in the limit of small jg. At currents o 1 A cm-2 that are relevant for fuel cell operation, the electro-osmotic coupling between proton and water fluxes causes nonuniform water distributions in PEMs, which lead to nonlinear effects in r/p M- These deviations result in a critical current density, p at which the increase in r/pp j causes the cell voltage to decrease dramatically. It is thus crucial to develop membrane models that can predicton the basis of experimental data on structure and transport properties. 

N effective number of polymer chains in resin N molar flux of liquid water in the membrane number of SO3 groups in the dry membrane ng. electro-osmotic drag coefficient in PEM... 

Table 2.1 lists the measured value of the DMFC current density, the equivalent current density of methanol crossover, the total water flux at a DMFC cathode and the calculated water electro-osmotic drag coefficient from Equation 2.2 at various DMFC operating temperatures. 

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