Saturated liquids

Two additional illustrations are given in Figures 6 and 7 which show fugacity coefficients for two binary systems along the vapor-liquid saturation curve at a total pressure of 1 atm. These results are based on the chemical theory of vapor-phase imperfection and on experimental vapor-liquid equilibrium data for the binary systems. In the system formic acid (1) - acetic acid (2), <() (for y = 1) is lower than formic acid at 100.5°C has a stronger tendency to dimerize than does acetic acid at 118.2°C. Since strong dimerization occurs between all three possible pairs, (fij and not... 

When liquid content of the feed is high, a condenser and a separator are needed. The liquid-to-gas ratio can be as high, so that even at reaction temperatures a liquid phase is present. The reactor still performs as a CSTR, however the response time for changes will be much longer than for vapor phase alone. Much lower RPM will be needed for liquid-phase studies (or liquid and gas phase experiments) since the density of the pumped fluid is an order-of-magnitude greater than for vapor phase alone. In this case a foamy mixture or a liquid saturated with gas is recirculated. 

Residual liquid saturation of cake m (approximate, eonsidering the speeific cake resistance) = 0.5... 

Conversely, given the wetting-liquid saturation, or equivalently P of the permeable medium, the locus of marginally stable states... 

Figure 5. The critical absolute permeability necessary to sustain the stability of a static foam as a function of liquid saturation. Calculations are for the constant-charge electrostatic model.

Figure 26. The effect of liquid saturation on mean granule size (Ritala et al. 1988). (Reprinted from Drug Development and Industrial Pharmacy, p. 1048, courtesy of Marcel Dekker, Inc.)...

Van der Waals, whose theory has been further developed by Hulshoff and by Bakker, went one step further than Gibbs by assuming that there exists a perfectly continuous transition from one medium to the other at the boundary. This assumption limits him to the consideration of one particular case that of a liquid in contact with its own saturated vapour, and mathematical treatment becomes possible by the further assumption that the Van der Waals equation (see Chapter II.) holds good throughout the system. The conditions of equilibrium thus become dynamical, as opposed to the statical equilibrium of Laplace s theory. Van der Waals arrives at the following principal results (i) that a surface tension exists at the boundary liquid-saturated vapour and that it is of the same order of magnitude as that found by Laplace s theory (2) that the surface tension... 

The gas-liquid saturation value, Cj), will be assumed constant. Dimensionless variables can be defined as... 

The HTE characteristics that apply for gas-phase reactions (i.e., measurement under nondiffusion-limited conditions, equal distribution of gas flows and temperature, avoidance of crosscontamination, etc.) also apply for catalytic reactions in the liquid-phase. In addition, in liquid phase reactions mass-transport phenomena of the reactants are a vital point, especially if one of the reactants is a gas. It is worth spending some time to reflect on the topic of mass transfer related to liquid-gas-phase reactions. As we discussed before, for gas-phase catalysis, a crucial point is the measurement of catalysts under conditions where mass transport is not limiting the reaction and yields true microkinetic data. As an additional factor for mass transport in liquid-gas-phase reactions, the rate of reaction gas saturation of the liquid can also determine the kinetics of the reaction [81], In order to avoid mass-transport limitations with regard to gas/liquid mass transport, the transfer rate of the gas into the liquid (saturation of the liquid with gas) must be higher than the consumption of the reactant gas by the reaction. Otherwise, it is not possible to obtain true kinetic data of the catalytic reaction, which allow a comparison of the different catalyst candidates on a microkinetic basis, as only the gas uptake of the liquid will govern the result of the experiment (see Figure 11.32a). In three-phase reactions (gas-liquid-solid), the transport of the reactants to the surface of the solid (and the transport from the resulting products from this surface) will also... 

One contradictory point regarding how the MPL works is related to the water saturation in the CL of the cathode. Nam and Kaviany [150] stated that using an MPL near the CL means that the water condensed in the DL carmot enter the CL, thus reducing the overall saturation of the active catalyst zones. This idea was also presented by Pasaogullari and Wang [151], who concluded that in the presence of an MPL, the liquid saturation in the CL is reduced substantially. These concepts contradict those presented earlier because it is not clear whether the liquid saturation does in fact increase in the cathode catalyst layer. This may depend directly on the rate at which the water goes back (or is forced) to the anode. 

The structure-related statistical factors include the surface-to-volume atom ratio of Pf nanoparficles, fhe effecfiveness factor of cafalysf ufilizafion of mesoscopic agglomerates, T, and percolation and wetting effecfs af fhe macroscopic level, represented by the functions/(Xpjc,Xei) and g Sf, where S, is the liquid saturation. 

However, the above expression can underpredict the tortuosity at low porosities. Nam and Kaviany have a very good discussion of the appropriate function to use for the tortuosity, in which changing values due to liquid saturation are also accounted for. 

One of the most important aspects of the two-phase models is their ability to predict the liquid saturation as a function of position. The saturation. S, is defined as the amount of pore volume that is filled with liquid thus... 

The other way to incorporate flooding in the catalyst layers is to use the two-phase modeling approach described in section 4.3.2.1. This involves calculating the liquid saturation in the catalyst layer and then adjusting the interfacial area accordingly. This is done by a linear expression... 

Figure 19. Liquid saturation and current density of the cathode as a function of position for the case of dry air fed at 60 °C. (a) Liquid saturation in the gas-diffusion layer where the channel goes from x = 0 to 0.05 cm and the rib is the rest the total cathode overpotential is —0.5 V. (b) Current-density distributions for different channel/rib arrangements. (Reproduced with permission from ref 56. Copyright 2001 The Electrochemical Society, Inc.)...

Um et al. also examined a transient using their complex model. They saw that in a matter of tens of seconds the current density response reached steady state after a change in potential. However, their model did not include liquid water. The most complex model to examine transients is that of Natarajan and Nguyen. It should be noted that although the model of Bevers et al. has transient equations, they do not report any transient results. Natarajan and Nguyen included liquid saturation effects and water transport in their model. They clearly showed the flooding of the diffusion media and that it takes on the order of a couple of minutes for the profiles to develop. 

The single-phase model described herein considers the total water amount without distinguishing liquid water from water vapor. This approach is valid under the condition that liquid saturation within the gas... 

As shown in Figure 23, the fully humidified case shows a maximum liquid saturation around 10% near the inlet and decreases in the flow direction due to decreasing reaction rate in the cathode catalyst layer. The 10% level of liquid saturation results from using a realistic GDL permeability on the order of 10 m2 67 Higher liquid saturation values reported in the literature were obtained only by using unrealistically small permeability, i.e., 95% maximum liquid saturation with GDL permeability of 7.3 x 10 m. °... 

Figure 23. Liquid saturation profiles at cathode GDL— catalyst layer interface along the channel direction for different humidification levels at Keii = 0.65 V. Anode and cathode stoichiometries are 1.4 at 1.0 A/cm. ...

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