Diffusion external

The diffusion rate ud at border-layer, based on Pick s diffusion first law, is as follows  

The chemical reaction rate v is proportional to reactant concentration Cg for simple first order reaction  

Comparing with the case without external diffusion effect, the difference in rates is Tf fold. Tf is called as external diffusion factor if rate is only limited by external diffusion. Smaller rj means that the reaction is majorly dominated by diffusion. Otherwise, smface reaction is overwhelming, r] approaches 1 when 1 i.e., ks indicating that the diffusion effect can be neglected. In order to eliminate the effect of external-fihn diffusion, it is necessary to reduce values of kg and L, or to increase value of D. 

The second way is to measure the change of reaction rate with temperature under the same experimental conditions, as the dependence of kg (reaction rate 

D oc If the change of reaction rate observed is not so obvious, and activation energy is also less than 20kJ-mol, it is possible that the catalytic reaction carries out at the region of external diffusion. In order to reach rj close 1, i.e., fcg D/L or reaction rate is not limited by external diffusion, the reaction temperature should be further decreased and thus rate constant can decrease faster. 

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It ought to be verified, however, in all cases, that the experimental Q-9 curve truly represents the distribution of surface sites with respect to a given adsorbate under specified conditions. The definition of differential heats of adsorption [Eq. (39) 3 includes, in particular, the condition that the surface area of the adsorbent A remain unchanged during the experiment. The whole expanse of the catalyst surface must therefore be accessible to the gas molecules during the adsorption of all successive doses. The adsorption of the gas should not be limited by diffusion, either within the adsorbent layer (external diffusion) or in the pores (internal diffusion). Diffusion, in either case, restricts the accessibility to the adsorbent surface. 

The rate of a gas phase reaction, 2A =s> B, is believed controlled by external diffusion and second order surface reaction with only substance A adsorbed to a substantial extent. The rate of diffusion is rd - 0.9(pg-ps), mol/(h)(kg catalyst)... 

The rate of solid catalyzed reaction is controlled by external diffusion and surface reaction, with equation... 

Under adiabatic conditions with external diffusion, temperature and concentration differences will develop between the bulk of the fluid and the surface of the catalyst. The rate of reaction is the rate of diffusion, r = kga(Cg-Cs) and the heat balance is... 

External diffusion of reactants. This step depends on the fluid dynamic characteristics of the system. Reactants must first diffuse from the bulk gaseous phase to the outer surface of the carrier through a stagnant thin film of gas. Molecular diffusion rates in the bulk have the activation energy E1 = 2 to 4 kcal/mol and they vary with Tm. 

External diffusion of products. The last step is the diffusion of product(s) through the stagnant film into the bulk gas under conditions similar to those in step 1. 

There is a thermally activated structural rearrangement of the protein such that channels appear and the quencher molecules are able to penetrate the protein—the penetration model.(67) This model distinguishes between external diffusion, kd(ext), and diffusion within the protein as follows ... 

The reaction conditions were as follows temperature, 490-530°C hydrogen partial pressure 0.27-0.91 atm DPM partial pressure (Pp), 0.05-0.20 atm and W/F, 8.8 g catal hr mole (here, W is the weight of the catalyst used and F is the moles of DPM per hour). Reaction rates under these conditions were not affected by the mass transfer of internal and external diffusion of the reactants. The observed values are shown in Table III. 

Some simulation results for trilobic particles (citral hydrogenation) are provided by Fig. 2. As the figure reveals, the process is heavily diffusion-limited, not only by hydrogen diffusion but also that of the organic educts and products. The effectiviness factor is typically within the range 0.03-1. In case of lower stirrer rates, the role of external diffusion limitation becomes more profound. Furthermore, the quasi-stationary concentration fronts move inside the catalyst pellet, as the catalyst deactivation proceeds. 

Meshko et al. (2001) used a homogeneous solid model taking into account both internal and external diffusion. They found that the adsorption of the dye had not been significantly affected by the agitation speed, which indicated that the process was solid diffusion-controlled. Furthermore, for the specified conditions, they found that kf = 6.66 X 10 s m/s and /), =10 12 m2/s. 

Hatfield, B. and Aris, R. (1969). Communications on the theory of diffusion and reaction, part (iv), combined effects of internal and external diffusion in the non-isothermal case. Chem. Eng. Sci., 24, 1213-22. 

Figure 2. Breakthrough curves for adsorption of nitrogen—external diffusion...

A common method of assessing the relative importance of internal diffusion and point adsorption resistances is to measure, as a function of time, the uptake of adsorbent from a solution containing solid particles. Batch data of this type taken at different temperatures and particle sizes can usually be analyzed so as to establish the importance of internal resistances. However, some types of diffusion have relatively high activation energies so that the separation is complex. Also, in such methods care must be taken to ensure rapid motion of the fluid with respect to the particles, for example by stirring, in order to eliminate external diffusion... 

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