Diffusion regime, control

The parameter t represents the reaction rate of a catalytic particle divided by the reaction rate if all of the particle surfaces (external and internal) are contacted with the reagent at the same concentration as in the surface. If t] = 1, the entire surface is accessible, i.e., there is no internal diffusion regime control. Figure 8 shows the dependence of t on three different reaction orders. Some plots are calculated for particles with a shape different from a sphere. Tb... 

On the basis of the Hatta number, the transformations carried out in biphasic systems can be described as slow (Ha < 0.3), intermediate (with a kinetic-diffusion regime 0.3 < Ha < 3.0), and fast (Ha > 3). These are diffusion limited and take place near the interface (within the diffusion layer). Slow transformations are under kinetic control and occur mostly in a bulk phase, so that the amount of substrate transformed in the boundary layer in negligible. When diffusion and reaction rate are of similar magnitude, the reaction takes place mostly in the diffusion layer, although extracted substrate is also present in the continuous phase, where it is transformed at a rate depending on its concentration [38, 50, 54]. 

As described in Section 9.2.2, grain-boundary diffusion rates in the Type-C diffusion regime can be measured by the surface-accumulation method illustrated in Fig. 9.12. Assume that the surface diffusion is much faster than the grain-boundary diffusion and that the rate at which atoms diffuse from the source surface to the accumulation surface is controlled by the diffusion rate along the transverse boundaries. If the diffusant, designated component 2, is initially present on the source surface and absent on the accumulation surface and the specimen is isothermally diffused, a quasi-steady rate of accumulation of the diffusant is observed on the accumulation surface after a short initial transient. Derive a relationship between the rate of accumulation... 

Variation of catalyst area. The catalytic rate is proportional to the total surface area, A, external and internal, for reactions controlled by surface kinetics. In the case of internal or pore diffusion control, the rate is proportional to A1,2 and is also a function of the catalyst shape and size [49, 53]. Under an external diffusion regime, the catalytic rate is proportional to the external surface area of the catalyst, Aex. 

The reaction diffusion regime was further clarified by Russell et al. [42] According to their model, the actual residual termination rate constant lie between two limiting values, a minimum, corresponding to a rigid chain, sue as polystyrene, and a maximum, corresponding to a flexible chain. It has beer found that the expression of the reaction diffusion controlled kt from Stickler e> al. [41] is the same as the minimum value proposed by Russell et al [42]. Both approaches share some common characteristics. Reaction diffusion control plays an important role in styrene homopolymerization since it is the main method of termination in later stages of the polymerization. 

These descriptions apply to diffusion processes inside a pore, but on a longer time scale (interpore regime), the diffusion of solutes will be controlled by the shape of the porous network itself (which can be treated as a Knudsen diffusion regime). The description of Knudsen diffusion is beyond the scope of this paper, but we can recollect that the tortuosity of the medium, besides the pore diameter, is an important parameter that can slow down interpore diffusion and hence diffusion-controlled reactions. ... 

Equation 5.93 reflects the fact that in the diffusion regime the surface is always assumed to be equilibrated with the subsurface. In particular, if E, = 0, then we must have Cj = 0. In contrast, Equation 5.94 stems from the presence of barrier for time intervals shorter than the characteristic time of transfer, the removal of the surfactant from the interface (Tj = 0) cannot affect the subsurface layer (because of the barrier) and then Cij(O) = c. This purely theoretical consideration implies that the effect of barrier could show up at the short times of adsorption, whereas at the long times the adsorption will occur under diffusion control." The existence of barrier-affected adsorption regime at the short adsorption times could be confirmed or rejected by means of the fastest methods for measurement of dynamic surface tension. 

Non-catalytic reactions involving two phases are common in the mineral industry. Reactions such as the roasting of ores or the oxidation of solids are carried out on a massive scale but the rates of these processes are often controlled by physical, not chemical, effects. Reactant or product diffusion is the main rate controlling factor in many cases. As a result, mechanisms of reaction become models of reaction with consideration of factors such as external diffusion film control or the shrinking core yielding the various models. Matters are further complicated by considerations regarding particle shape and external fluid flow regimes. 

Therefore, if the first reaction Ai=>Bj is the desired one and it is faster (e.g. ki>k2), the selectivity in the diffusion regime is lower than under pure kinetic control. 

This configuration gives a uniform contact time, which can be tailored to a particular reaction by choice of the membrane thickness and/or reactant flow rate. The pore size of the membrane controls the diffusion regime. Also, the membrane geometry can be used to place a catalyst in the membrane optimally, or to control the partial pressure of the reactants in the phase in contact with the catalyst. 

Non-Thermal Discharge Regime Controlled by Charged-Particle Diffusion to the Walls The Engel-Steenbeck Relation... 

Figure 4-16. Universal relation between electron temperature, pressure, and discharge tube radius in the non-equilibrium discharge regime controlled by diffusion of charged particles.

Ga(III) leads first to Ga(I), then upon further reduction the elemental Ga forms from Ga(I). On glassy carbon the electrodeposition involves instantaneous three-dimensional nucleation with diffusion-controlled growth of the nuclei. No alloying with A1 was reported if deposition of Ga was performed in the Ga(I) diffusion regime. Reproducible electrodeposition of Ga is a promising route to binary and ternary compound semiconductors. A controlled electrodeposition of GaX quantum dots (X = P, As, Sb) would be very attractive for nanotechnology. 

An inspection of the figure leads to two major conclusions (1) an increase in catalyst concentration (i.e., in v/A/lh) leads to a shift in regime from chemical to diffusion control (as expected) and (2) an increase in the diffusion parameter k raises the enhancement factor in the kinetic regime but lowers it in the diffusion regime. 

For gas-liquid reactions Ha < 1 regime 1 reaction occurs exclusively in bulk and is controlled by either chem. reaction, k (regime 1) overall temp effect positive or (regime 2) diffusion across the liquid film controls, slow reaction overall temp effect negative regime Ha << 1 or kinetic regime reaction is controlled by film diffusion, kinetics control... 

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