With external diffusion

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... 

Does the rate depend on linear velocity With external diffusion, the rate at constant space velocity increases with linear velocity, at about 1/2 order. Velocity independence is a good indication of the absence of external diffusion effects. 

The effect of longitudinal dispersion in a column, as a factor which reduces the sharpness of breakthrough curves, has been considered by Barrow and co-workers (B3), Ledoux (L4), and others. Wicke (W5) has discussed the combined effect of longitudinal dispersion with internal diffusion, while Lapidus and Amundson (L3) have reviewed the combined effect with external diffusion. Van Deemter et al. (V2) have recently studied this problem with respect to gas chromatography. 

The tin alloy elements must be distributed sufficiently to allow diffusion throughout the matrix. Experience with externally diffused composites dictates that the tin-rich elements must be very close to their nearest neighbors. 

Lenhoff, J. Chromatogr., 384, 285 (1987)] or by direct numerical solution of the conservation and rate equations. For the special case of no-axial dispersion with external mass transfer and pore diffusion, an explicit time-domain solution, useful for the case of time-periodic injections, is also available [Carta, Chem. Eng. Sci, 43, 2877 (1988)]. In most cases, however, when N > 50, use of Eq. (16-161), or (16-172) and (16-174) with N 2Np calculated from Eq. (16-181) provides an approximation sufficiently accurate for most practical purposes. 

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. 

Here, as in Section 8.5.4, we treat the isothermal case for ijo, and relate tj0 to 17. may then be interpreted as the ratio of the (observed) rate of reaction with pore diffusion and external mass transfer resistance to the rate with neither of these present. 

P7.03.19. REVERSIBLE REACTION WITH EXTERNAL AND INTERNAL DIFFUSION. 

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... 

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. 

Zeolite crystal size can be a critical performance parameter in case of reactions with intracrystalline diffusion limitations. Minimizing diffusion limitations is possible through use of nano-zeolites. However, it should be noted that, due to the high ratio of external to internal surface area nano-zeolites may enhance reactions that are catalyzed in the pore mouths relative to reactions for which the transition states are within the zeolite channels. A 1.0 (xm spherical zeolite crystal has an external surface area of approximately 3 m /g, no more than about 1% of the BET surface area typically measured for zeolites. However, if the crystal diameter were to be reduced to 0.1 (xm, then the external surface area becomes closer to about 10% of the BET surface area [41]. For example, the increased 1,2-DMCP 1,3-DMCP ratio observed with decreased crystallite size over bifunctional SAPO-11 catalyst during methylcyclohexane ring contraction was attributed to the increased role of the external surface in promoting non-shape selective reactions [65]. 

Both T[f] and R[f] consist of three terms associated with the diffusion and convection induced by the external field and the macroscopic flow field. 

The wide spectrum of external conditions which can influence the conformational state of charged gels (the variation of these conditions can induce collapse or decollapse transition), makes these gels possible materials for data control devices of different types, absorbers, reactors and catalysts with regulated diffusion characteristics, carriers of immobilized enzymes, etc. The networks synthesized at high dilution are also new mechano-chemical systems which show very high sensitivity to external actions. 

A particle diffusing in a three-dimensional, inhomogeneous anisotropic medium with external force with potential U(r) obeys a generalization of (3.2),... 

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... 

Communications on the theory on diffusion and reaction-I V Combined effects of internal and external diffusion in the non-isothermal case (with B. Hatfield). Chem. Eng. ScL 24, 1213-1222 (1969). 

The situation is different in the case of ammonia oxidation. Both on platinum (156) and nonplatinum (157) catalysts under the conditions of a commercial process, the reaction occurs in the external diffusion region. Diffusion of ammonia rather than of oxygen is determining the rate since the reaction is conducted with oxygen in excess with respect to stoichiometry, as given by (397). Concentration of ammonia at the surface of the catalyst is so small as compared to its concentration in the gas flow that the difference of concentrations that determines the rate of diffusion virtually coincides with the ammonia content in the flow. 

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