Gas phase diffusion limitations

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. ... 

Gas Phase Diffusion. The gas phase diffusion limitation arises when the diffusional flux of molecules to the surface of the droplet is less than the maximum possible flux of gas across the surface as given by Equation 2. Under these circumstances the gas density near the surface of the droplet (n ) is smaller than average volume density (n). The situation can be simply analyzed by writing the rate equation for the total number of molecules N in the neighborhood of the droplet ... 

This criterion for gas-phase diffusion limitation is illustrated in Figure 12.7 for a series of droplet diameters and an arbitrarily chosen sg = 0.1. In Figure 12.7 the inequality (12.85) corresponds to the area below and to the left of the lines. For a given situation if the point (k, H K) is to the left of the corresponding line in Figure 12.7, then gas-phase mass transport limitation does not exceed 10%. Similar plots, introduced by Schwartz (1984), provide an easy way to ascertain whether there is a mass transport limitation for a given condition of interest. 

For the 500 pm thick membrane, the thickest membrane employed, data falls fairly well on the Sieverts Law line, which is interpreted as implying that bulk diffusion of dissociated hydrogen is the rate limiting step. Experimentally measured permeability for the 500 pm membrane was 3.2 x 10 mol m" s" Pa" . As the higher feed pressures were approached (13.1 bar partial pressure hydrogen, 34 bar total pressure with heUum), some deviations from Sieverts Law were observed. These are attributed to gas phase diffusion limitations, as discussed below. 

It can be shown that the intrinsic growth or evaporation rate associated with a given organic volatility is given by vdC where the characteristic velocity is 226 nm h V(pg m ) [75]. This is modified by three important terms - the mass accommodation coefficient, a, the surface-energy (Kelvin) term for particles smaller than 50 nm or so, and the Fuchs term for gas-phase diffusion limitations in the boundary layer around a particle for particles larger than 50 nm or so (with Knudsen... 

Gas-Phase Diffusion Limitation The diffusion of reactant in the gas phase is limited to some value. In principle, we can imagine that there is a maximum rate that perfume can diffuse from the front of a room to the back of the room. Now consider the perfume is being consumed at the back of the room. The consumption rate would be limited to the maximum perfume diffusion rate, as the reaction rate is limited by reactant availability. At the double layer, a greater polarization will be required to attract the required adsorbed species for reaction in a limiting condition. 

Using purely gas-phase diffusion, an expression for the gas-phase diffusion limiting current density was derived ... 

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. 

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. 

Diffusion into the bulk. This is determined by the diffusion coefficient in the liquid (D,). Diffusion within the bulk aqueous phase is much slower than gas-phase diffusion and can be rate-limiting under conditions of high reactant concentrations where the rate of the chemical reaction is high. This appears to have been a problem in some experimental studies of some aqueous-phase reactions relevant to the atmosphere where either bulk solutions or large droplets and reactant concentrations higher than atmospheric were used (Freiberg and Schwartz, 1981). 

Use the data of Hu et al. (1995) in Fig. 5.19 to derive the second-order rate constant for the O, + I" reaction in the liquid phase assuming that solubility and gas-phase diffusion are not limiting factors. Also derive a value for the mass accommodation coefficient for O-, based on these data. The Henry s law constant for O-, can be taken to be 0.02 M atm-1, the temperature is 277 K, and the diffusion coefficient in the liquid phase 1.3 X 10-5 cm2 s-1. 

Equation 13 reduces to the Rayeigh equation (3) when the ratio of the gas-phase diffusivities, , is unity. Since gas-phase diffusivity is inversely proportional to the square root of the reduced mass, in the case of fission product-sodium systems where sodium has the smallest molecular weight, the above diffusivity ratio is less than unity. Therefore, the Rayleigh equation, which was derived on the basis of equilibrium vaporization, in fact represents an upper limit for the fractional fission-... 

Here ng is the density of the gas molecules, c is the average thermal velocity and 7 is the mass accommodation coefficient This is the maximum flux of gas into a liquid. In many circumstances, however, the actual gas uptake is smaller. It may be limited tty several processes, the most important of which are gas phase diffusion and Henry s Law saturation. The treatment of Henry s Law saturation in turn involves liquid phase diffusion and, in some cases, liquid phase chemical reactions. 

The large S02 mass accommodation coefficient (7 - 0.11) indicates that interfacial mass transport will not limit the rate of S02 uptake into clean aqueous cloud and fog droplets. Either gas phase diffusion, Henry s law solubility, or aqueous reactivity will control the overall rate of aqueous S(IV) chemistry. This conclusion is demonstrated by modeling studies of S02 oxidation in clouds by Chamedies (3) showing that the conversion time of S(FV) to S(IV) is independent of the mass accommodation coefficient for 1 7 > 10 2 Schwartz (1 ) has also shown that, with 7 as large as our measured value, the interfacial mass transport is unlikely to inhibit the oxidation of SC by or Ho02 in cloud droplets for gas concentrations typical of non-urban industrialized regions. 

Conde-Gallardo, A., Guerrero, M., Fragoso, R. and Castillo, N. (2006). Gas-phase diffusion and surface reaction as limiting mechanisms in the aerosol-assisted chemical vapor deposition of Ti02 films from titanium diisopropoxide. J. Mater. Res. 21(12), 3205-3209. 

Reaction of dissolved gases in clouds occurs by the sequence gas-phase diffusion, interfacial mass transport, and concurrent aqueous-phase diffusion and reaction. Information required for evaluation of rates of such reactions includes fundamental data such as equilibrium constants, gas solubilities, kinetic rate laws, including dependence on pH and catalysts or inhibitors, diffusion coefficients, and mass-accommodation coefficients, and situational data such as pH and concentrations of reagents and other species influencing reaction rates, liquid-water content, drop size distribution, insolation, temperature, etc. Rate evaluations indicate that aqueous-phase oxidation of S(IV) by H2O2 and O3 can be important for representative conditions. No important aqueous-phase reactions of nitrogen species have been identified. Examination of microscale mass-transport rates indicates that mass transport only rarely limits the rate of in-cloud reaction for representative conditions. Field measurements and studies of reaction kinetics in authentic precipitation samples are consistent with rate evaluations. 

Solution of the coupled mass-transport and reaction problem for arbitrary chemical kinetic rate laws is possible only by numerical methods. The problem is greatly simplified by decoupling the time dependence of mass-transport from that of chemical kinetics the mass-transport solutions rapidly relax to a pseudo steady state in view of the small dimensions of the system (19). The gas-phase diffusion problem may be solved parametrically in terms of the net flux into the drop. In the case of first-order or pseudo-first-order chemical kinetics an analytical solution to the problem of coupled aqueous-phase diffusion and reaction is available (19). These solutions, together with the interfacial boundary condition, specify the concentration profile of the reagent gas. In turn the extent of departure of the reaction rate from that corresponding to saturation may be determined. Finally criteria have been developed (17,19) by which it may be ascertained whether or not there is appreciable (e.g., 10%) limitation to the rate of reaction as a consequence of the finite rate of mass transport. These criteria are listed in Table 1. 

Using these simplified models, process variables can be varied so that the deposition process is either limited by gas-phase diffusion to the substrate surface or by reaction at the substrate. Such control of the process is valuable because, for example, geometric surface irregularities in the substrate (grooves and corners) are coated uniformly in a kinetically controlled process, but in a process controlled by diffusion a protrusion receives a thicker coating while a depression is thinly coated. 

During ultrasonic irradiation of aqueous solutions, OH radicals are produced from dissociation of water vapor upon collapse of cavitation bubbles. A fraction of these radicals that are initially formed in the gas phase diffuse into solution. Cavitation is a dynamic phenomenon, and the number and location of bursting bubbles at any time cannot be predicted a priori. Nevertheless, the time scale for bubble collapse and rebound is orders of magnitude smaller than the time scale for the macroscopic effects of sonication on chemicals (2) (i.e., nanoseconds to microseconds versus minutes to hours). Therefore, a simplified approach for modeling the liquid-phase chemistry resulting from sonication of a well-mixed solution is to view the OH input into the aqueous phase as continuous and uniform. The implicit assumption in this approach is that the kinetics of the aqueous-phase chemistry are not controlled by diffusion limitations of the substrates reacting with OH. 

The extent to which surface transport affects global rates of reaction has not been established. For it to be important, adsorption must occur, but this is also a requirement for catalytic activity. Indirect evidence suggests that in some cases the effect is considerable. For example. Miller and Kirk found higher rates of dehydration of alcohols on silica-alumina than could be explained with only pore-volume diffusion to account for intraparticle resistances. They attributed the discrepancy to surface diffusion. Masamune and Smith found that surface transport of ethanol on silica gel at temperatures as high as 175°C predominated over gas-phase diffusion in the pore. In view of the data available, it seems wise at least to consider the possibility of surface migration in any evaluation of intraparticle effects. This can be done by adding a surface-diffusion contribution to the effective diffusivity considered in the previous section. The method of doing this is presented below, but its usefulness is still limited because of inadequate experimental and theoretical aspects of surface transport. 

When one of the components in a mixture is a condensable vapor and the pores are small enough, the condensate can block gas-phase diffusion through the pores. This is the limiting case of surface diffusion where the adsorbed layer fills the pore. This condensate will evaporate on the low partial pressure side of the membrane. The Kelvin equation predicts that condensation can occur in small pores even through the partial pressure of that component is below its vapor pressure. The Kelvin equation represents thermodynamic equilibrium between the gas phase and fluid in the pore ... 

Some catalytic processes are limited by gas phase diffusion, usually those with very high surface area catalysts which in turn means very small diameter, restricted pores within the material. After the gas has diffused to the active... 

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