Water transport coefficient

Figure 18. Profile of the net water transport coefficient through the membrane in the midchannel cross-section of a 36-channel fuel cell at 1/ceii = 0.65V and /avg = 0.91 A/cm. ...

K = water transport coefficient = permeability / thickness of the membrane active layer... 

Note that the water transport coefficient is unique to a given membrane and is not a constant it varies directly with temperature. The coefficient for some newer polyamide membranes also varies with pH. 

The electroosmotic transport coefficient for water through Nafion 295 and 1150 membranes is typical and is shown to be highly dependent on the anolyte concentration to the exclusion of all the other variables studied. The water transport coefficient varies almost linearly with anolyte concentration from 6 to 17 molar caustic, giving 2.9 to 0.8 moles/F, as shown in Figure 3. The sodium ion transport number goes through a maximum of 0.82 eq/F in the 7 to 13 molar caustic range (27). 

Reported values of effective pore-water transport coefficients, referred to hereafter as D, for biogenic reworking range from 1 to 2 X 10 cmVsec (Goldhaber et al., 1977 Aller, 1978). 

The water transport coefficient (A) is not a constant in that it varies with temperature. The product flow as a function of temperature may be estimated6 by using the following equation ... 

Current density As current density increases, the cell voltage increases linearly, and the current efficiency and the water transport coefficient remain essentially constant. 

The example assumed a constant water transport coefficient (WTC). This is not a realistic assumption, because the coefficient depends, among other things, on the NaOH concentration. The extent of this dependence is a function of other variables and on the type of membrane used. A single relationship between WTC and operating variables cannot be assumed. 

The effect of a change in the water transport coefficient can, however, be evaluated separately. The required recycle flow varies linearly and inversely with the water transport coefficient. The relationship is a strong one ... 

Q = inlet flow rate, weight/time W = water transport coefficient Mw - molecular weight of water Me - molecular weight of caustic P = production rate of caustic, same units as Q Co = concentration of caustic leaving cells Ci = concentration of caustic entering cells = cathode current efficiency... 

Section 6.5 mentioned that the transport coefficients are much lower in KOH service than in NaOH production. KOH production therefore requires higher recirculation pumping rates. In NaOH service, the water transport coefficient is higher, but it depends on a number of variables, not least the type of membrane. Membrane suppliers are the best source of information on water transport coefficients. In the extreme case of a reduction from 4.0 to 2.0, the required brine feed rate increases by about 25% and that of 30.3% caustic more than doubles. 

An opposite effect holds on the brine side. Electrolysis continuously depletes the anolyte. The brine feed, which is more concentrated, serves to keep the concentration at the chosen level. Transportation of water through the membranes also helps to keep the concentration higher. As the water transport coefficient becomes smaller, less water leaves the anolyte through the membranes, reducing this contribution to a higher concentration. More strong brine is then necessary to offset this effect. A reduction in WTC therefore requires higher inlet flows on both sides of the cell. 

Figure 23 shows the results of a recent TMSC experiment in MGM-41-S confined water with (p = 2.4 and 1.8 nm. Note that there is a close similarity between these data and the data obtained from adiabatic calorimetry. Their interpretation, however, is completely different. Taking into account the results obtained for the water transport coefficients, represented by the NMR and neutron data, the results obtained for the dynamic fragile-to-strong glass crossover (Fig. 9), and the violation of the Stokes-Einstein relation (Fig. 10) we can assume that these maxima in Cp at about 225K are related to the crossover phenomenon and not a GT process. 

Hydranautics ROData program includes the normalized water transport coefficient and the normalized salt transport coefficient. The water transport coefficient corresponds to the permeability coefficient, A, in equation 4.1. The salt transport coefficient corresponds to the permeability coefficient, K, in equation 4.2. The coefficients should remain constant over normal (ambient) operating conditions. Changes in the... 

Bottom water currents in sluggish streams (i.e., bayous), lakes, estuaries, and other near-shore marine waters are moved by the wind at the surface. Both thermal and salinity stratification in these waters is a factor influencing the magnitudes of the bottom-water transport coefficients. Although this subject of MTCs has received limited study, some estimation methods are proposed. For unstratified water bodies. Equation 12.10 is useful wind speed is a key independent variable. For stratified lakes surface winds cause seiches that generate bottom water currents. Equations 12.11 through 12.13 can be used with seiche water displacement heights. To estimate bottom currents, these values are converted to bottom friction velocities with Equation 12.8, Equation 12.1 is then used for the MTC estimate. Bed characteristics can be used as proxies for bottom currents see Table 12.5. 

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