Diffusional effects

Laminar flame instabilities are dominated by diffusional effects that can only be of importance in flows with a low turbulence intensity, where molecular transport is of the same order of magnitude as turbulent transport (28). Flame instabilities do not appear to be capable of generating turbulence. They result in the growth of certain disturbances, leading to orderly three-dimensional stmctures which, though complex, are steady (1,2,8,9). 

Volt mmetiy. Diffusional effects, as embodied in equation 1, can be avoided by simply stirring the solution or rotating the electrode, eg, using the rotating disk electrode (RDE) at high rpm (3,7). The resultant concentration profiles then appear as shown in Figure 5. A time-independent Nernst diffusion layer having a thickness dictated by the laws of hydrodynamics is estabUshed. For the RDE,... 

An immobilized enzyme-carrier complex is a special case that can employ the methodology developed for evaluation of a heterogeneous cat ytic system. The enzyme complex also has external diffusional effects, pore diffusional effects, and an effectiveness factor. When carried out in aqueous solutions, heat transfer is usually good, and it is safe to assume that isothermal conditions prevail for an immobihzed enzyme complex. 

The treatment of the two-phase SECM problem applicable to immiscible liquid-liquid systems, requires a consideration of mass transfer in both liquid phases, unless conditions are selected so that the phase that does not contain the tip (denoted as phase 2 throughout this chapter) can be assumed to be maintained at a constant composition. Many SECM experiments on liquid-liquid interfaces have therefore employed much higher concentrations of the reactant of interest in phase 2 compared to the phase containing the tip (phase 1), so that depletion and diffusional effects in phase 2 can be eliminated [18,47,48]. This has the advantage that simpler theoretical treatments can be used, but places obvious limitations on the range of conditions under which reactions can be studied. In this section we review SECM theory appropriate to liquid-liquid interfaces at the full level where there are no restrictions on either the concentrations or diffusion coefficients of the reactants in the two phases. Specific attention is given to SECM feedback [49] and SECMIT [9], which represent the most widely used modes of operation. The extension of the models described to other techniques, such as DPSC, is relatively straightforward. 

Typical results, shown in Fig. 21(a), demonstrate that the rate constant for the reaction between TCNQ and aqueous Fe(CN)g increases with increasing driving force, promoted by decreasing [CIO4 as evidenced by the steeper Fe(CN)g concentration profiles. Moreover, the Tafel plot obtained for ET between Fe(CN)g and TCNQ is linear with an apparent measured a value of 0.31 0.02. In these studies, the concentration of reactant in the droplet phase was always at least 10 times the concentration of the reactant in the receptor phase, to ensure that depletion (and diffusional) effects within the droplet were negligible. 

The first factor k. 1 = 35, is expected to be temperature dependent via an Arrhenius fjfpe relationship the second factor defines functionality dependence on molecular size the third factor indicates that smaller molecules are more likely to react than larger species, perhaps due to steric hindrance potentials and molecular mobility. The last term expresses a bulk diffusional effect on the inherent reactivity of all polymeric species. The specific constants were obtained by reducing a least squares objective function for the cure at 60°C. Representative data are presented by Figure 5. The fit was good. 

In eq. 8 are shown the results of a kinetic analysis of the series of reactions in Scheme 1. The analysis is based on the quenching rate constant k, corrected for diffusional effects, which would be measured for the quenching of Ru(bpy>3 + by PQ +. 

A -4 B — C). Determine the outlet concentrations of A, B, and C, and the selectivity to the desired product B. Compare your results to those in which diffusional effects are ignored. 

Since diffusional effects are most important, we wish to emphasize these processes in the gas phase. For the control volume selected in Figure 9.7, the bold assumption is made that transport processes across the lateral faces in the x direction do not change - or change very slowly. Thus we only consider changes in the y direction. This approximation is known as the stagnant layer model since the direct effect of the main flow velocity (it) is not expressed. A differential control volume Ay x Ax x unity is selected. 

Microbes tend to form flocks as they grow, into which nutrients and dissolved oxygen must diffuse. The rate of growth thus depends on the diffusional effectiveness. This topic is developed by Atkinson (1974). Similarly enzymes immobilized in gel beads, for instance, have a reduced catalytic effectiveness analogous to that of porous granular catalysts that are studied in Chapter 7. For the M-M equation this topic is touched on in problems P8.04.15 and P8.04.16. 

Figure 8.11 Evidence of cross-diffusional effects. The homogeneous distribution of species 2 (dashed line, top) is perturbed by a coexisting gradient of species 1 (bottom).

Fig. 10.4 Impedance diagrams for a non-blocking interface when (a) bulk effects are neglected (b) bulk effects are taken into account. The impedance diagrams are different if diffusional effects are significant.

Isotope (H (deuterium), discovered by Urey et al. (1932), is usually denoted by symbol D. The large relative mass difference between H and D induces significant fractionation ascribable to equilibrium, kinetic, and diffusional effects. The main difference in the calculation of equilibrium isotopic fractionation effects in hydrogen molecules with respect to oxygen arises from the fact that the rotational partition function of hydrogen is nonclassical. Rotational contributions to the isotopic fractionation do not cancel out at high T, as in the classical approximation, and must be accounted for in the estimates of the partition function ratio /. 

Convection describes the movement of groups of particles from one place to another within the mixer volume because of the direct action of an impeller or a moving device within the mixer body. As in convection within fluids, this is likely to be a more significant effect than diffusion but diffusional effects will still be present. 

For more on the whole subject of the shift in product distribution caused by diffusional effects, see Wheeler (1951). 

Since reactant and product molecules are similar in structure, deactivation is caused by both A and R. With diffusional effects absent, the rate of deactivation is found to be... 

Activity Measurements. To test catalytic properties of various samples partial oxidation of methanol to formaldehyde was studied in a flow micro-reactor operating under normal atmospheric pressure (10). For each run about 0.2 g of catalyst sample was used and the activities were measured at 173 C in the absence of any diffusional effects. The feed gas consisted of 72, 2 and by volume of nitrogen, oxygen and methanol vapor respectively. Reaction products were analysed with a 10% Carbowax 20 M column (2m long) maintained at 60 C oven temperature. 

When the mass transfer (diffusional) effects are significant, the design equations for immobilized biocatalyst reactors can be modified, by introducing the concept of the... 

Introduction of a suppression device between the column and the detector can be expected to cause some degree of peak broadening due to diffusional effects. The shape of the analyte band will also be influenced by hydrophobic adsorption effects, especially when the adsorption and desorption processes are slow. Examination of peak shapes and analyte losses can therefore provide important insight into the use of suppressors with organic analytes which are weakly acidic or weakly basic. It can be expected that peak area recovery rates after suppression are governed by a combination of hydrophobic interactions with the suppressor and permeation through the membranes with the balance between these mechanisms being determined by eluent composition, suppression conditions and analyte properties. 

Spacer chain catalysts 3, 4, and 19 have been investigated under carefully controlled conditions in which mass transfer is unimportant (Table 5)80). Activity increased as chain length increased. Fig. 7 shows that catalysts 3 and 4 were more active with 17-19% RS than with 7-9% RS for cyanide reaction with 1-bromooctane (Eq. (3)) but not for the slower cyanide reaction with 1-chlorooctane (Eq. (1)). The unusual behavior in the 1-bromooctane reactions must have been due to intraparticle diffusional effects, not to intrinsic reactivity effects. The aliphatic spacer chains made the catalyst more lipophilic, and caused ion transport to become a limiting factor in the case of the 7-9 % RS catalysts. At > 30 % RS organic reactant transport was a rate limiting factor in the 1-bromooctane reations80), In contrast, the rate constants for the 1 -chlorooctane reactions were so small that they were likely limited only by intrinsic reactivity. (The rate constants were even smaller than those for the analogous reactions of 1-bromooctane and of benzyl chloride catalyzed by polystyrene-bound benzyl-... 

Diffusional effects were combined into apparent kinetic rate constants by using commercial-sized catalysts in kinetic experiments. The experiments were designed so that no significant external transport and axial dispersion effects occurred. 

In addition, Wei (4) has shown that if intraparticle diffusional effects are significant and if the diffusivities of the reacting species are equal, the A matrix becomes... 

Quantitative Interpretation of Intracrystalline Diffusional Effects. Since a qualitative effect of crystallite size upon selectivity was observed, the next step was to extract some quantitative values for the intracrystalline diffusional parameters. To do this, we must either know the intrinsic or diffusion-free kinetics or be able to make a simplifying assumption so that the diffusional parameters can be extracted from the available data. 

Temperature Dependence of the Activity and Selectivity of Xylene Isomerization over AP Catalyst. Based upon our analysis of the intracrystalline diffusional resistance in AP catalyst, we would expect that when the reaction temperature is increased, the selectivity would shift toward p-xylene since the diffusional effects are increased as the activity increases. A shift in selectivity toward p-xylene as the reaction temperature was increased was observed and is shown in Figure 6. The role of diffusion in changing the selectivity can be seen in the Arrhenius plot of Figure 7. The reaction rate constant for the o-xylene - p-xylene path, fc+3i, goes from an almost negligible value at 300°F to a substantial value at 600°F. Furthermore, the diffusional effects are also demonstrated by the changing... 

In view of the complicated reaction kinetics of multicomponent systems, it was not clear whether or not the diffusional effects would also affect the relative rate of conversion of feed molecules in a mixture. To answer this question we studied the hydrocracking of three multicomponent systems. The first was a C5-C8 mixture, a C5 360° C boiling range midcontinent reformate which contained 12.5 wt % n-paraffins including 4.2% n-pentane, 4.3% n-hexane, 2.9% n-heptane, l.l%n-octane, and <1% C9+ n-paraffins, with the remainder isoparaffins and aromatics. The reaction was carried out at 400 psig, 2 H2/HC, 2 LHSV, and 800°F. Secondly, a Cg-Cie mixture... 

This equation states that eddy diffusional effects on zone spreading increase with the square root of zone displacement and particle size. 

Contributions to fcobs from diffusional effects are only numerically significant for reactions which approach within a factor of 10 of the diffusion-controlled limit. From the data in Table 1, only a few self-exchange cases, e.g. Ru(bipy)33+/2+ and some of the organic couples, approach this limit although it is a common feature for net reactions where AG is highly favorable and X small. 

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