Water transport in membranes

Yet another mechanism for water transport in membranes is through hydrauHc permeation, which is driven by the liquid pressure difference between the anode and cathode. The permeation flux is controlled by the membrane permeabihty K , and the liquid pressure gradient across the membrane [22] ... 

An extensive hterature is devoted to the physics of water channels formation and to the mechanism of proton and water transport in membranes. In this section, we give a brief overview relevant to the analytical modelling of fuel cells. A detailed review of phenomenological membrane transport models is given in (Weber and Newman, 2007). Atomistic modelling and experiments on proton transport in membranes are reviewed in (Kreuer et al., 2004). Recent advances in mesoscopic membrane modelling are discussed in (Promislow and Wetton, 2009). The reader is referred to these works for a detailed discussion of the transport processes in polymer membranes. 

AG Thombre, GM Zentner, KJ Himmelstein. Mechanism of water transport in controlled porosity osmotic devices. J Membrane Sci 40 279-310, 1989. 

G. J. M. Janssen and M. L. J. Overvelde. Water transport in the proton-exchange-membrane fuel cell Measurements of the effective drag coefficient. Journal of Power Sources 101 (2001) 117-125. 

Notwithstanding any particular structural model, water transport in PEMs, in general, should be considered a superposition of diffusion in gradients of activity or concentration and hydraulic permeation in gradients of liquid or capillary pressure. Hydraulic permeation is the predominant mechanism xmder conditions for which water uptake is controlled by capillary condensation, whereas diffusion contributes significantly if water strongly interacts with the polymeric host. The molar flux of liquid water in the membrane, N, is thus given by... 

With the increased computational power of today s computers, more detailed simulations are possible. Thus, complex equations such as the Navier—Stokes equation can be solved in multiple dimensions, yielding accurate descriptions of such phenomena as heat and mass transfer and fluid and two-phase flow throughout the fuel cell. The type of models that do this analysis are based on a finite-element framework and are termed CFD models. CFD models are widely available through commercial packages, some of which include an electrochemistry module. As mentioned above, almost all of the CFD models are based on the Bernardi and Verbrugge model. That is to say that the incorporated electrochemical effects stem from their equations, such as their kinetic source terms in the catalyst layers and the use of Schlogl s equation for water transport in the membrane. 

Eikerling et al. ° used a similar approach except that they focus mainly on convective transport. As mentioned above, they use a pore-size distribution for Nafion and percolation phenomena to describe water flow through two different pore types in the membrane. Their model is also more microscopic and statistically rigorous than that of Weber and Newman. Overall, only through combination models can a physically based description of transport in membranes be accomplished that takes into account all of the experimental findings. 

Figure 33. Visualization of liquid water transport in an operating transparent PEFC (45 /rm membrane with EW < 1000 GDL, Toray paper TGPH 090 with 20 wt % PTFE loading with a microporous layer).

Nielsen S, Nagelhus EA, Amiry-Moghaddam M, Bourque C, Agre P, Ottersen OP (1997) Speciahzed membrane domains for water transport in gUal cells high-resolution immunogold cytochemistry of aquaporin-4 in rat brain. I Neurosci 17 171-180... 

The q-space imaging method, which deals with signals only after long diffusion times, discards all information relevant to dynamic aspects of water diffusion and transport, especially the restriction of water transport by membrane and cell wall permeability barriers in cellular tissues. This information is contained in the functional dependence of the pulsed gradient spin echo amplitude S(q,A,x) on the three independent variables q, A, and x (x is the 90-180 degree pulse spacing) [53]. As the tool to explore the q and A dependence of S(q,A,x), generalized diffusion times and their associated fractional populations are introduced and a multiple exponential time series expansion is used to analyze the dependence [53]. 

In the case of 100% selective membrane and negligible water transport, the membrane potential is given by the Nemst equations (46), respectively (47). 

In PEMFC systems, water is transported in both transversal and lateral direction in the cells. A polymer electrolyte membrane (PEM) separates the anode and the cathode compartments, however water is inherently transported between these two electrodes by absorption, desorption and diffusion of water in the membrane.5,6 In operational fuel cells, water is also transported by an electro-osmotic effect and thus transversal water content distribution in the membrane is determined as a result of coupled water transport processes including diffusion, electro-osmosis, pressure-driven convection and interfacial mass transfer. To establish water management method in PEMFCs, it is strongly needed to obtain fundamental understandings on water transport in the cells. 

Water transport in electrodialysis from the diluate to the concentrate process stream can affect the process efficiency significantly. If a convective flux as a result of pressure differences between flow streams can be excluded there are still two sources for the transport of water from the diluate to the concentrate solution. The first one is the result of osmotic-pressure differences between the two solutions, and the second is due to electro-osmosis that results from the coupling of water to the ions being transported through the membrane due to the driving force of an electrical potential. 

Figure 6.21 shows the AC impedance spectra for the cathodic ORR of the cell electrodes prepared using the conventional method and the sputtering method. It can be seen that the spectra of electrodes 2 and 3 do not indicate mass transport limitation at either potentials. For electrode 1, a low-frequency arc develops, due to polarization caused by water transport in the membrane. It is also observable that the high-frequency arc for the porous electrode is significantly depressed from the typical semicircular shape. Nevertheless, the real-axis component of the arc roughly represents the effective charge-transfer resistance, which is a function of both the real surface area of the electrode and the surface concentrations of the species involved in the electrode reaction. 

Two stationary states in the coupled processes can be identified as the level flow where A = 0, and the static head where J, = 0. Examples of the static head are open-circuited fuel cells and active transport in a cell membrane, while examples of the level flow are short-circuited fuel cells and salt and water transport in kidneys. 

Water transport from the vasculature into the ventricle is facilitated by aquaporin-1 (AQPl) highly expressed in the apical (ventricular-facing) membrane of the choroid plexus, and via AQP4 in the ependymal lining of the ventricles (Zador et al., 2007). Deletion of AQPl reduces by fivefold osmotically induced water transport in the choroid plexus (Oshio et al., 2005). CSF production is significantly reduced in AQPl-deficient mice, but only by 20-25%, indicating a substantial contribution of extrachoroidal fluid production by the brain parenchyma (Zador et al.,... 

The water transport in OMD is a simultaneous heat and mass transfer process. Evaporation cools the feed and condensation warms the brine solution. This results in a temperature gradient across the membrane, which adversely affects the driving force and in turn the mass flux. 

Courel, A.M., et al. Modelling of water transport in osmotic distillation using asymmetric membrane, J. Membr. Sci., 173, 107, 2000. 

Mok YS, Lee SC, and Lee WK. Water transport in water-in-oil-in-water liquid emulsion membrane system for the separation of lactic acid. Sep Sci Techrwl 1994 29 743-764. 

X. Ren, T.A. Zawodzinski, and S. Gottesfeld. Water and methanol transport in membranes for direct methanol fuel cells. Abstracts of Papers of the American Chemical Society 217, U490 1999. 

Zelsmann and co-workers [88] have reported tracer diffusion coefficients for water in Nafion membranes exposed to water vapor of controlled activity. These were determined by various techniques, including isotopic exchange across the membrane. They reported apparent self-diffiision coefficients of water much lower than those determined by Zawodzinski et al. [64], with a weaker dependence on water content, varying from 0.5 x 10 cm to 3 x 10 cm /s as the relative humidity is varied from 20 to 100%. It is likely that a different measurement method generates these large differences. In the experiments of Zelsmaim et al., water must permeate into and through the membrane from vapor phase on one side to vapor phase on the other. Since the membrane surface in contact with water vapor is extremely hydrophobic (see Table 7), there is apparently a surface barrier to water uptake from the vapor which dominates the overall rate of water transport in this type of experiment. 

The initial emphasis on evaluation and modeling of losses in the membrane electrolyte was required because this unique component of the PEFC is quite different from the electrolytes employed in other, low-temperature, fuel cell systems. One very important element which determines the performance of the PEFC is the water-content dependence of the protonic conductivity in the ionomeric membrane. The water profile established across and along [106]) the membrane at steady state is thus an important performance-determining element. The water profile in the membrane is determined, in turn, by the eombined effects of several flux elements presented schematically in Fig. 27. Under some conditions (typically, Pcath > Pan), an additional flux component due to hydraulic permeability has to be considered (see Eq. (16)). A mathematical description of water transport in the membrane requires knowledge of the detailed dependencies on water content of (1) the electroosmotic drag coefficient (water transport coupled to proton transport) and (2) the water diffusion coefficient. Experimental evaluation of these parameters is described in detail in Section 5.3.2. 

The water distribution within a polymer electrolyte fuel cell (PEFC) has been modeled at various levels of sophistication by several groups. Verbrugge and coworkers [83-85] have carried out extensive modeling of transport properties in immersed perfluorosulfonate ionomers based on dilute-solution theory. Fales et al. [109] reported an isothermal water map based on hydraulic permeability and electro-osmotic drag data. Though the model was relatively simple, some broad conclusions concerning membrane humidification conditions were reached. Fuller and Newman [104] applied concentrated-solution theory and employed limited earlier literature data on transport properties to produce a general description of water transport in fuel cell membranes. The last contribution emphasizes water distribution within the membrane. Boundary values were set rather arbitrarily. 

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