Electro-osmotic drag water flux

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

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operation, mechanical equilibrium prevails locally to fix the water distribution, while chemical equilibrium is rescinded by the finite flux of water across the membrane surfaces.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. 

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... 

In the above, D rn is the water diffusion coefficient through the membrane phase only. Note also that the water fluxes through the membrane phase, via electro-osmotic drag and molecular diffusion, represent a source/sink term for the gas mixture mass in the anode and cathode, respectively. 

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. 

The water diffusive flux through the membrane is considered following the ideas in [4]. Water content (molecule per sulphonate group) Cwiy) is considered through the MEA. It is assumed to obey a simple diffusive mechanism and that the diffusive flux is not influenced by the electro-osmotic drag. The following equation is assumed ... 

Modeling approaches that explore membrane water management have been reviewed in [16]. Overall, the complex coupling between proton and water mobility at microscopic scale is replaced by a continuiun description involving electro-osmotic drag, proton conductivity and water transport by diffusion or hydraulic permeation. Essential components in every model are the two balance equations for proton flux (Ohm s law) and for the net water flux. Since local proton concentration is constant due to local electroneutrality of the membrane, only one variable remains that has to be solved for, the local water content. 

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] ... 

Studies of the dynamical behavior of water molecules and protons in PEMs rationalize the influence of random morphology and water uptake on effective physicochemical properties, that is, proton conductivity, water flux, and electro-osmotic drag. 

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 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 flux owing to electro-osmotic drag in a cell with operating current density i is given as... 

In Equation 11.50a, the water flux component based on electro-osmotic drag is computed on the basis of the fact that the proton flux is two times... 

For water transport through the Nafion polymer membrane in a PEM fuel cell, there is an additional driving force such as electro-osmotic drag, and the net water flux is given as... 

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... 

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... 

There may also be a phase change phenomena associated with the motion of water in the membrane nnder a temperature gradient, since Bradean et al. [22] showed an exponential relationship between liqnid flnx and the temperature gradient and heat flux, but the exact nature of this is not fully understood. This mode of transport has not commonly been inclnded in the analysis of normal operation, since this effect is obscnred by the net diffusive and electro-osmotic drag transfer. Under startup or shutdown conditions, however, where larger gradients in temperature can exist, the net water flux from this mode can be significant, and has been exploited to passively drain the DM on shutdown to a frozen state [22]. 

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