Reactant concentration distribution

II. THE EFFECT OF THE REACTANT CONCENTRATION DISTRIBUTIONS ON THE ENZYME MEMBRANE BEHAVIORS... 

Now, we noted at the beginning of this section that an important goal of determining the reactant concentration distribution within the pellet is to calculate the effectiveness factor rjcat. In terms of the reactant concentration, this can be expressed in the form... 

Figure 2.10 (A) Experiment device for measuring the reactant concentration distribution in separating the diffusion from the convection regions (B) Reactant distribution near the electrode surface. (For color version of this figure, the reader is referred to the online version of this book.)...

Unfortunately, the case presented in Figure 2.10 is ideal, not necessary to reflect the real situation. For a practical electrode, both diffusion and convection processes coexist. Even inside the diffusion layer, there is some degree of convection—that is, the solution within the diffusion layer is not static. Therefore, the diffusion layer thickness should be determined by both the diffusion and convection processes. Fortunately, using mathematical modeling, the reactant concentration distribution profile near the electrode surface has been found to be similar to tbat shown in Figure 2.9, from which the effective (or equivalent) diffusion-layer thickness can also be defined in tbe same way as Eqn (2.51). Eor a detailed expression about tbis diffusion layer thickness induced by both diffusion and convection process, we will give more discussion in Chapter 5. 

The parametric areas of five regimes are identified for two values of the diffusion ratio. Typical radial concentration profiles associated with each physical picture are also shown. In this case, the boundary for the kinetically controlled regime is given by the value of the Damkohler number so that the effectiveness factor is kept, for example, above 0.9. Since in this case conversion in the channel is negligible, the reactant concentration distribution at the interface with the coating is uniform and close to the inlet value. 

Levent, M. (2001) Water-gas shift reaction over porous catalyst temperature and reactant concentration distribution. Int.J. Hydrogen Energ., 26, 551-558. 

However, before extrapolating the arguments from the gross patterns through the reactor for homogeneous reactions to solid-catalyzed reactions, it must be recognized that in catalytic reactions the fluid in the interior of catalyst pellets may diSer from the main body of fluid. The local inhomogeneities caused by lowered reactant concentration within the catalyst pellets result in a product distribution different from that which would otherwise be observed. 

FIGURE 2-3 Concentration distribution of the oxidized and reduced forms of the redox couple at different times during a cyclic voltammetric experiment corresponding to the initial potential (a), to the formal potential of the couple during the forward and reversed scans (b, d), and to the achievement of a zero reactant surface concentration (c). 

Dynamic simulations for an isothermal, continuous, well-mixed tank reactor start-up were compared to experimental moments of the polymer distribution, reactant concentrations, population density distributions and media viscosity. The model devloped from steady-state data correlates with experimental, transient observations. Initially the reactor was void of initiator and polymer. 

Palladium metal is not produced in the new reaction and the substitution of a twenty-fold excess of lithium chloride for cupric chloride prevented reaction kinetic data revealed first-order dependences upon both Pd(II) and Cu(II). The distribution of products varied in an unpredictable way with reactant concentrations. The following mechanism was proposed by Henry (X = CP or CH3CO2 )... 

FIGURE 11.3 Distributions of reactant concentration near the electrode after different times of galvanostatic operation (a) t < (b) > t. ... 

For a solution of differential equations (18.12) and (18.15) and for a quantitative calculation of the current distribution, we must know how the current density depends on polarization at constant reactant concentrations or on reactant concentrations at constant polarization. We must also formulate the boundary conditions. Examples of such calculations are reported below. 

In the case of other parallel reactions with different reaction rate expressions, similar analyses can be used to determine the influence of various reactant concentrations on the selectivity of a proposed process. Such analyses would lead to the following generalization, which is useful in considerations of parallel reactions where the reactant concentration level influences the product distribution. 

If the two competing reactions have the same concentration dependence, then the catalyst pore structure does not influence the selectivity because at each point within the pore structure the two reactions will proceed at the same relative rate, independent of the reactant concentration. However, if the two competing reactions differ in the concentration dependence of their rate expressions, the pore structure may have a significant effect on the product distribution. For example, if V is formed by a first-order reaction and IF by a second-order reaction, the observed yield of V will increase as the catalyst effectiveness factor decreases. At low effectiveness factors there will be a significant gradient in the reactant concentration as one moves radially inward. The lower reactant concentration within the pore structure would then... 

The counterparts of dissolving particles are the processes of precipitation and crystallization the description and simulation of which involve several additional aspects however. First of all, the interest in commercial operations often relates to the average particle size and the particle size distribution at the completion of the (batch) operation. In precipitation reactors, particle sizes strongly depend on the (variations in the) local concentrations of the reactants, this dependence being quite complicated because of the nonlinear interactions of fluctuations in velocities, reactant concentrations, and temperature. 

Surfactant solutions critical micelle concentration distribution of reactants among particles surfactant aggregation numbers interface properties and polarity dynamics of surfactant solutions partition coefficients phase transitions influence of additives... 

A similar prediction can be made for the concentration distribution of reagents for a diffusion limited reaction occurring at the phase boundary. The concentration of the reactants decreases around the phase boundary, as this is the site where they are consumed. In Figure 2.14, it is assumed that the reactant A has about one tenth of the solubility in phase 2 compared to phase 1, thus in most cases some of reactant A will diffuse across the phase boundary into this phase. As in phase 1, the concentration distribution will not be equal throughout the phase, but it will be lower in proximity to the phase boundary. If the reaction is very fast, reactant A will be consumed at the phase boundary and will therefore not enter phase 2. 

For reactions in parallel, the concentration level of reactants is the key to proper control of product distribution, A high reactant concentration favors the reaction of higher order, a low concentration favors the reaction of lower order, while the concentration level has no effect on the product distribution for reactions of the same order. 

For these reactions the concentration-time curves are of little generality for they are dependent on the concentration of reactant in the feed. As with reactions in parallel, a rise in reactant concentration favors the higher-order reaction a lower concentration favors the lower-order reaction. This causes a shift in and this property can be used to improve the product distribution. 

Figure 18.4 Distribution and average value of reactant concentration within a catalyst pore as a function of the parameter mL = L Vkl ...

Since Zn2+ ion does not hydrolyze as readily as cations of higher charge, bases need to be added in order to initiate precipitation by forced hydrolysis. Particles of different morphologies, including spheroids and ellipsoids, formed in the presence of different weak bases on heating solutions of zinc salts (Figure 1.1.16) (110). Dispersions of narrow size distributions resulted under specific reactant concentrations as shown in Figure 1.1.17 (110). X-ray diffraction analysis showed all particles of different shapes to be composed of zincite, ZnO. 

Other studies by Drakesmith and Hughes [124] have used the fluorination of propene and octanoyl chloride as model compounds to investigate the effects of anode potential, current density, reactant concentration, temperature, etc. on reproducibility, product structure, distribution and yield in novel cell designs ranging in scale from 100 ml to 1001 cell capacities. 

The radial distribution of the reactant concentrations in the spherical catalyst particle is theoretically given as ... 

Figure 7.3 Concentration distribution of reactant within a sphericai cataiyst particie.

We can think of the reactant concentration and some initial spatial distribution of the intermediate concentration and temperature profiles specifying a point on Fig. 10.9. If we choose a point above the neutral stability curve, then the first response of the system will be for spatial inhomogeneity to disappear. If the value of /r lies outside the range given by (10.79), then the system adjusts to a stable spatially uniform stationary state. If ji lies between H and n, we may find uniform oscillations. 

Rather than discuss a concentration distribution of B reactants about A reactants, it is more convenient to use a distribution of B about A normalised to the initial concentration of reactant B in solution [B] o - Because [ B] o > [A], the change of average concentration of B during the course... 

It is clear that a complete treatment of the recombination kinetics requires careful incorporation of mutual particle distribution, including fluctuations in their local concentrations due to diffusion and reaction. At present the role of fluctuations in reactant concentrations in chemical kinetics is well known... 

Let us focus now our attention on (2.1.70). Assume that initial distribution of reactant concentration satisfies the thermal equilibrium (2.1.42). Then... 

---