Reaction-diffusion systems generalized chemical kinetics

It is generally assumed, for reasons of mathematical simplification, that one of these processes is slower than the rest and that this is the rate determining step. Because the reaction mechanism is rarely known in sufficient detail, steps 2, 3 and 4 are usually considered together. Where the rates of adsorption/reaction/desorp-tion are slower than the rate of diffusion, the true chemical kinetics will be observed. If, however, the reverse is true, diffusion kinetics will be observed and the results will not be characteristic of the chemical reactivity of the system. 

Pollard and Newman" have also studied CVD near an infinite rotating disk, and the equations we solve are essentially the ones stated in their paper. Since predicting details of the chemical kinetic behavior is a main objective here, the system now includes a species conservation equation for each species that occurs in the gas phase. These equations account for convective and diffusive transport of species as well as their production and consumption by chemical reaction. The equations stated below are given in dimensional form since there is little generalization that can be achieved once large chemical reaction mechanisms are incorporated. 

In Fig. 1, various elements involved with the development of detailed chemical kinetic mechanisms are illustrated. Generally, the objective of this effort is to predict macroscopic phenomena, e.g., species concentration profiles and heat release in a chemical reactor, from the knowledge of fundamental chemical and physical parameters, together with a mathematical model of the process. Some of the fundamental chemical parameters of interest are the thermochemistry of species, i.e., standard state heats of formation (A//f(To)), and absolute entropies (S(Tq)), and temperature-dependent specific heats (Cp(7)), and the rate parameter constants A, n, and E, for the associated elementary reactions (see Eq. (1)). As noted above, evaluated compilations exist for the determination of these parameters. Fundamental physical parameters of interest may be the Lennard-Jones parameters (e/ic, c), dipole moments (fi), polarizabilities (a), and rotational relaxation numbers (z ,) that are necessary for the calculation of transport parameters such as the viscosity (fx) and the thermal conductivity (k) of the mixture and species diffusion coefficients (Dij). These data, together with their associated uncertainties, are then used in modeling the macroscopic behavior of the chemically reacting system. The model is then subjected to sensitivity analysis to identify its elements that are most important in influencing predictions. 

When intraparticle diffusion is rate limiting, the kinetic behaviour of a chemically reacting system is generally different from that which would prevail if chemical reaction were rate limiting. It is therefore extremely important to develop criteria to assess whether intraparticle diffusion effects may be neglected and thus define the conditions of experiment which would reveal true chemical kinetics rather than overall kinetics disguised by intraparticle diffusion effects. 

In this text, the conversion rate is used in relevant equations to avoid difficulties in applying the correct sign to the reaction rate in material balances. Note that the chemical conversion rate is not identical to the chemical reaction rate. The chemical reaction rate only reflects the chemical kinetics of the system, that is, the conversion rate measured under such conditions that it is not influenced by physical transport (diffusion and convective mass transfer) of reactants toward the reaction site or of product away from it. The reaction rate generally depends only on the composition of the reaction mixture, its temperature and pressure, and the properties of the catalyst. The conversion rate, in addition, can be influenced by the conditions of flow, mixing, and mass and heat transfer in the reaction system. For homogeneous reactions that proceed slowly with respect to potential physical transport, the conversion rate approximates the reaction rate. In contrast, for homogeneous reactions in poorly mixed fluids and for relatively rapid heterogeneous reactions, physical transport phenomena may reduce the conversion rate. In this case, the conversion rate is lower than the reaction rate. 

In the previous section we developed a generalized model for the reaction between a porous solid and a reactant gas, for systems with first-order kinetics with respect to the reactant gas. The model provided general criteria for relating structural effects to the reactivity of porous solids, and the reaction modulus defined therein allowed the assessment of the relative importance of pure diffusion and chemical kinetics. 

Mass transfer effects may also be minimized by operating the system at lower temperatures since mass transfer involves gaseous diffusion through a boundary layer, which is not an activated process, while the chemical reaction between the gas and the solid generally has a substantial activation energy, operation at progressively lower temperatures will eventually lead to control by chemical kinetics, as shown in Fig. 6.11. 

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