Diffusivity gas-phase

For prediction of gas phase diffusion coefficients in multicomponent hydi ocarbon/nonKydi ocai bon gas systems, the method of Wilke shown in Eq. (2-154) is used. 

Many more correlations are available for diffusion coefficients in the liquid phase than for the gas phase. Most, however, are restiicied to binary diffusion at infinite dilution D°s of lo self-diffusivity D -. This reflects the much greater complexity of liquids on a molecular level. For example, gas-phase diffusion exhibits neghgible composition effects and deviations from thermodynamic ideahty. Conversely, liquid-phase diffusion almost always involves volumetiic and thermodynamic effects due to composition variations. For concentrations greater than a few mole percent of A and B, corrections are needed to obtain the true diffusivity. Furthermore, there are many conditions that do not fit any of the correlations presented here. Thus, careful consideration is needed to produce a reasonable estimate. Again, if diffusivity data are available at the conditions of interest, then they are strongly preferred over the predictions of any correlations. 

For gas-phase diffusion in small pores at lowpressure, the molecular mean free path may be larger than the pore diameter, giving rise to Knudsen diffusion. Satterfield (Ma.s.s Tran.sfer in Heterogeneous Catalysis, MIT, Cambridge, MA, 1970, p. 43), gives the following expression for the pore dimisivity ... 

The reaction of Si02 with SiC [1229] approximately obeyed the zero-order rate equation with E = 548—405 kJ mole 1 between 1543 and 1703 K. The proposed mechanism involved volatilized SiO and CO and the rate-limiting step was identified as product desorption from the SiC surface. The interaction of U02 + SiC above 1650 K [1230] obeyed the contracting area rate equation [eqn. (7), n = 2] with E = 525 and 350 kJ mole 1 for the evolution of CO and SiO, respectively. Kinetic control is identified as gas phase diffusion from the reaction site but E values were largely determined by equilibrium thermodynamics rather than by diffusion coefficients. 

Liquid phase diffusivities are strongly dependent on the concentration of the diffusing component which is in strong contrast to gas phase diffusivities which are substantially independent of concentration. Values of liquid phase diffusivities which are normally quoted apply to very dilute concentrations of the diffusing component, the only condition under which analytical solutions can be produced for the diffusion equations. For this reason, only dilute solutions are considered here, and in these circumstances no serious error is involved in using Fick s first and second laws expressed in molar units. 

The gas-phase diffusion coefficients are estimated from the molecular weights M of the speciesl0 ... 

Heterogeneous uptake on surfaces has also been documented for various free radicals (DeMore et al., 1994). Table 3 shows values of the gas/surface reaction probabilities (y) of the species assumed to undergo loss to aerosol surface in the model. Only the species where a reaction probability has been measured at a reasonable boundary layer temperature (i.e. >273 K) and on a suitable surface for the marine boundary layer (NaCl(s) or liquid water) have been included. Unless stated otherwise, values for uptake onto NaCl(s), the most likely aerosol surface in the MBL (Gras and Ayers, 1983), have been used. Where reaction probabilities are unavailable mass accommodation coefficients (a) have been used instead. The experimental values of the reaction probability are expected to be smaller than or equal to the mass accommodation coefficients because a is just the probability that a molecule is taken up on the particle surface, while y takes into account the uptake, the gas phase diffusion and the reaction with other species in the particle (Ravishankara, 1997). 

After passing through the boundary layer, the molecules of adsorbate diffuse into the complex structure of the adsorbent pellet, which is composed of an intricate network of fine capillaries or interstitial vacancies in a solid lattice. The problem of diffusion through a porous solid has attracted a great deal of interest over the years and there is a fairly good understanding of the mechanisms involved, at least for gas phase diffusion. Here, diffusion within a single cylindrical pore is considered and, then, the pore is related to the pellet as a whole. 

Typical cathode performance curves obtained at 650°C with an oxidant composition (12.6% 02/18.4% C02/69% N2) that is anticipated for use in MCFCs, and a common baseline composition (33% 02/67% CO2) are presented in Figure 6-3 (20,49). The baseline composition contains O2 and CO2 in the stoichiometric ratio that is needed in the electrochemical reaction at the cathode (Equation (6-2)). With this gas composition, little or no diffusion limitations occur in the cathode because the reactants are provided primarily by bulk flow. The other gas composition, which contains a substantial fraction of N2, yields a cathode performance that is limited by gas phase diffusion from dilution by an inert gas. 

This equation shows that the saturation greatly affects the effective gas-phase diffusion coefficients. Hence, flooding effects are characterized by the saturation. 

Because the Adler model is time dependent, it allows prediction of the impedance as well as the corresponding gaseous and solid-state concentration profiles within the electrode as a function of time. Under zero-bias conditions, the model predicts that the measured impedance can be expressed as a sum of electrolyte resistance (Aeiectroiyte), electrochemical kinetic impedances at the current collector and electrolyte interfaces (Zinterfaces), and a chemical impedance (Zchem) which is a convolution of contributions from chemical processes including oxygen absorption. solid-state diffusion, and gas-phase diffusion inside and outside the electrode. 

In the limit of a semi-infinite (thick) porous electrode with no gas-phase diffusion limitations, the chemical term Zhem reduces to an impedance reflecting co-limitation by oxygen absorption and transport. ... 

As we have seen in the previous sections, our understanding of SOFC cathode mechanisms often hinges on interpretation on the magnitude and time scale of electrochemical characteristics. However, these characteristics are often strongly influenced by factors that have nothing to do with the electrode reaction itself but rather the setup of the experiment. In this section we point out two commonly observed effects that can potentially lead to experimental artifacts in electrochemical measurements (1) polarization resistance caused gas-phase diffusion and (2) artifacts related to the cell geometry. As we will... 

One can roughly estimate the effects of gas-phase diffusion at steady state using a simple ID diffusion model, which has been employed (in some form) by numerous workers. 343 This approach yields the following expression for the linearized steady-state chemical resistance due to binary diffusion of O2 in a stagnant film of thickness... 

Figure 52. Effect of binary gas-phase diffusion on the impedance characteristics of porous mixed-conducting electrodes at low Por (a) zero-bias impedance of LSC on rare-earth-doped ceria at 1 atm and 750 °C as a function of Pq using concentrations and balance gases as indicated. (Reprinted with permission from ref 350. Copyright 2000 Elsevier B.V.) (b) Zero-bias impedance of SSC x= 0.5) on SDC at 800 °C and P02 — 9-91 a function of total...

The results reviewed above suggest that gas-phase diffusion can contribute significantly to polarization as O2 concentrations as high as a few percent and are not necessarily identifiable as a separate feature in the impedance. Workers studying the P02 -dependence of the electrode kinetics are therefore urged to eliminate as much external mass-transfer resistance in their experiments as possible and verify experimentally (using variations in balance gas or total pressure) that gas-phase effects are not obscuring their results. 

Along with electronic transport improvements must come attention to substrate transport in such porous structures. As discussed above, introduction of gas-phase diffusion or liquid-phase convection of reactants is a feasible approach to enabling high-current-density operation in electrodes of thicknesses exceeding 100 jxm. Such a solution is application specific, in the sense that neither gas-phase reactants nor convection can be introduced in a subclass of applications, such as devices implanted in human, animal, or plant tissue. In the context of physiologically implanted devices, the choice becomes either milliwatt to watt scale devices implanted in a blood vessel, where velocities of up to 10 cm/s can be present, or microwatt-scale devices implanted in tissue. Ex vivo applications are more flexible, partially because gas-phase oxygen from ambient air will almost always be utilized on the cathode side, but also because pumps can be used to provide convective flow of any substrate. However, power requirements for pump operation must be minimized to prevent substantial lowering of net power output. 

Fig. 6. Chemical reaction rate data for NH3 reacting with H3PO4 solution droplets, from Rubel and Gentry (1984a). The data are compared with theory for surface reaction control (S) and gas-phase diffusion control (D). Reprinted with permission from J. Aerosol Sci. 15,661-671, Rubel, G. O., and Gentry, J. W., Copyright 1984, Pergamon Press pic.

Equation (105) is the basis for the determination of gas-phase diffusion coefficients and ultra low vapor pressures using the methods proposed by Davis and Ray (1977), Ravindran et al. (1979), and Ray et al. (1979). Additional information can be gained by writing the Chapman-Enskog first approximation for the gas-phase diffusivity (Chapman and Cowling, 1970),... 

Diffusion of gases is fast relative to diffusion in the aqueous phase i.e., step 1 is fast relative to step 3. Thus diffusion coefficients for gases at 1 atm pressure are 0.1-1 cm2 s l, whereas in liquids they are 10 5 cm2 s"1 for small molecules. As discussed in detail by Schwartz and Freiberg (1981), gas-phase diffusion, in most (but not all) cases, will not be the slowest (i.e., rate-determining) step. 

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