Electro-osmotic flux

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. 

If a small molecule not carrying a charge has a migration time /m = 5 min, deduce the value of the electro-osmotic flux //ros. 

If the internal lining is rendered neutral there would be no more electro-osmotic flux and as a result the compound will no longer migrate towards the cathode but will reappear in the anode compartment. 

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. 

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],... 

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.

Steady states, as we have seen in Part One, are obtained when fluxes in opposite directions are involved. In electro-osmosis, hydrodynamic flow is opposed by electro-osmotic flux. In thermo-osmosis, hydrodynamic flow is opposed by thermo-osmotic flux. In case of chemical reactions, such situations can arise when positive feedback is opposed by negative feedback. For example, when autocatalysis is opposed by inhibitory reaction, steady state can be attained. However, the reaction rates are non-linear and have only non-linear steady states in practice. We illustrate this point by the following example. 

Attempts have been made to elucidate the mechanism of generation of such oscillations. Kim and Tarter suggested a mechanism based on (i) balancing of hydrodynamic and electro-osmotic flux and (b) influence of these fluxes on the anion concentration gradient, which may influence the microscopic structure of the emulsion. However, the above tentative explanation is not tenable since hydrodynamic flux will have a fixed value on account of fixed pressure difference across the membrane. Another... 

To counteract Archimedes thrust, a long time ago, Quincke, Me Taggart, and Alty [25-28] placed the bubble in a cylindrical tube filled with an aqueous phase and rotating about its symmetrical axis. The difference between the centrifugal forces acting on the bubble and on the aqueous phase maintains the bubble along the axis of rotation. This system was later abandoned, as the electric field applied to displace the bubble created an electro-osmotic flux within the tube, which biased the results [29]. 

If the system is closed, an electro-osmotic reflux at the center of the cell takes place. This reflux can only be neglected when the cell is wide enough and its geometry is appropriate [22]. In aU the other cases, the velocity of the bubble will be the result of the electrophoretic velocity and the reflux velocity. The electrophoretic velocity of the bubble can only be determined without correction on the so-called stationary levels of the ceU, at which electro-osmotic flux and counterflux cancel each other [18,20,33-35]. 

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. ... 

For a typical one-molar methanol concentration, the electro-osmotic flux of methanol in the membrane is small as compared to the methanol diffusion. The expression for the crossover current follows from the methanol mass balance in the cell (Kulikovsky, 2002b)... 

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. 

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