Contents 4 Membranes 1 Transport Models

Often, as in Figure 4.3b, the conductivity is measured as a function of the activity of the solvent with which the membrane is equilibrated. In order to relate these measurements to the actual water content, one can use experimentally determined sorption isotherms as shown in Figure 4.4 for Nafion and a sulfonated polyaromatic membrane. The sorption isotherms will be revisited in more detail to discuss their critical role in membrane transport models [21]. 

Membrane Water Content. Whether the dilute solution or concentrated solution theory equations are used to model the membrane system, functional forms for the transport parameters and the concentration of water are needed. The properties are functions of temperature and the water content, In the models, empirical fits are... 

Balaz and Lukacova (1999) attempted to model the partitioning of 36 non-ionizable compounds in 7 tissues. Amphiphilic compounds, or those possessing extreme log Kow values, tended to show complex distribution kinetics because of their slow membrane transport. However for the non-amphiphilic, non-ionizable compounds with non-extreme log Kow values studied it should be possible to characterize their distribution characteristics based on tissue blood PCs. Distribution is dependent on membrane accumulation, protein binding, and distribution in the aqueous phase. As these features are global rather than dependent on specific 3D structure, distribution is not expected to be structure-specific. In this study, tissue compositions in terms of their protein, lipid, and water content were taken from published data. This information was used to generate models indicating that partitioning was a non-linear function of the compound s lipophilicity and the specific tissue composition. 

There are different approaches that incorporate the water balance in the membrane into models of fuel cell performance. They rest on different concepts of membrane microstructure. As a common feature they use local values of transport parameters which are functions of the local water content, w (volume fraction of water relative to the total membrane volume). 

Macroscopic models can be classified into two broad categories (i) membrane conductivity models and (ii) mechanistic models, typically for fuel cell water management purposes. The latter usually require the use of a conductivity model, a fit to empirical data, or the assumption of constant conductivity (e.g. fully hydrated membrane at all times), and can be further classified into hydraulic models, in which a water transport is driven by a pressure gradient, and diffusion models, in which transport is driven by a gradient in water content. 

Fig. 19.5a, b. Counter-ion transport model in a cationic exchange membrane activation energy of the elementary process and equivalent electrical circuit a, in a high water content range b, in a low water content range (with permission). 

Perfluorosulfonated membranes have a microscopic phase-separated structure with hydrophobic regions and hydrophilic domain. Hydrophobic regions provide the mechanical support and hydrophilic ionic domains provide proton transport channel. Many morphological models for PFSA have been developed based on SAXS and wide-angle x-ray scattering (WAXS) experiments of the membranes. However, because of the random chemical structure of the PFSA copolymer, morphological variation with water content and complexity of coorganized crystalline and ionic domains, limited characteristic detail proved by the SAXS and WAXS experiments, the structure of the PFSl has been still subject of debate. Here, a brief description of seven membrane structure models is provided. 

Hydrogen bonding and electrostatic interactions between the sample molecules and the phospholipid bilayer membranes are thought to play a key role in the transport of such solute molecules. When dilute 2% phospholipid in alkane is used in the artificial membrane [25,556], the effect of hydrogen bonding and electrostatic effects may be underestimated. We thus explored the effects of higher phospholipid content in alkane solutions. Egg and soy lecithins were selected for this purpose, since multicomponent mixtures such as model 11.0 are very costly, even at levels of 2% wt/vol in dodecane. The costs of components in 74% wt/vol (see below) levels would have been prohibitive. 

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. 

The first major CFD models were those by Liu and co-workers " at the University of Miami. They are nonisothermal and the first multidimensional models. They allowed for a more in-depth study of the effects along the channels than the models described above. While the original model by Gurau et al. did not include liquid-water transport, it did have a variable water content in the membrane. To study... 

Unlike the cases of the single-phase models above, the transport properties are constant because the water content does not vary, and thus, one can expect a linear gradient in pressure. However, due to Schroeder s paradox, different functional forms might be expected for the vapor- and liquid-equilibrated membranes. 

As mentioned above, impaired fluid absorption in kidney proximal tubule in AQPl deficiency indicates the need for high cell membrane water permeability for rapid, near-isosmolar fluid transport. The involvement of AQPs in fluid secretion by glands (salivary, submucosal, sweat, lacrimal), and by the choroid plexus and the ciliary body has been investigated using appropriate knockout mouse models. The general conclusion is that AQPs facilitate active fluid (secretion and absorption) when sufficiently rapid, in which case AQP deletion is associated with reduced volume and increased ion/solute content of secreted fluid. AQPs appear not to be needed when fluid secretion rate (per unit epithelial surface area) is low, as AQP-independent water permeability is high enough to support slow fluid secretion (or absorption). 

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