Chemical reaction controlled regime

According to Equation (5.7) the increase in processing temperature and preform thickness leads to larger values of Valid poor density uniformity. As stated previously, CVI processes preferably operate in a chemical-reaction-controlled regime where the ratio of k/D is small. For Fick diffusion, discussed in Section2.3.1, the diffusivity D is inversely proportional to the pressure and thus operates at lower pressures. Furthermore, coarser pore structures correspond to more uniform deposition. Figure 5.5 shows the microstructures of C/SiC composites prepared at different 9 numbers. 

Accoring to the processing conditions of a CVD process, supersaturation can be divided into two categories, bulk supersaturation and local supersaturation [13], If a CVD process occurs in the chemical reaction control regime discussed in Section 4.3.4, it is reasonable to assume that the compositions of a gas on the substrate surface equal that in the bulk gas. Accordingly, the expression of supersaturation in Equation (6.2) is used for calculation. However, if a CVD process occurs in the... 

In a temperature scanning experiment, where both temperature and concentrations vary in each run, one must be sure that the range of conditions that will be covered does not include a transition from a chemical-reaction-controlled regime to one controlled by an intervening process, say diffusion. Validation of temperature scanning data therefore requires careful examination of the conditions present at the site of reaction. 

In a first case we will model the chemical reaction controlled regime and discuss the effects of temperature, pressure, catalyst loading and presence of adsorbable additives on the selectivity. 

Figure 6, Combustion rates various coals near chemical reaction controlling regime (2, 22,23,24,25 ...

An empirical equation in the chemical reaction controlling regime developed by Wen ( ) based on the volume reaction model has the form ... 

Over 25 years ago the coking factor of the radiant coil was empirically correlated to operating conditions (48). It has been assumed that the mass transfer of coke precursors from the bulk of the gas to the walls was controlling the rate of deposition (39). Kinetic models (24,49,50) were developed based on the chemical reaction at the wall as a controlling step. Bench-scale data (51—53) appear to indicate that a chemical reaction controls. However, flow regimes of bench-scale reactors are so different from the commercial furnaces that scale-up of bench-scale results caimot be confidently appHed to commercial furnaces. For example. Figure 3 shows the coke deposited on a controlled cylindrical specimen in a continuous stirred tank reactor (CSTR) and the rate of coke deposition. The deposition rate decreases with time and attains a pseudo steady value. Though this is achieved in a matter of rninutes in bench-scale reactors, it takes a few days in a commercial furnace. 

Particles of constant size Gas film diffusion controls, Eq. 11 Chemical reaction controls, Eq. 23 Ash layer diffusion controls, Eq. 18 Shrinking particles Stokes regime, Eq. 30 Large, turbulent regime, Eq. 31 Reaction controls, Eq. 23... 

In the reaction controlled regime the overall rate of layer formation is only limited by the rate of chemical transformations (chemical reaction as such). Therefore, the ApBq layer grows at the highest rate possible under given conditions ... 

If the layer of the ApBq chemical compound grows in the reaction controlled regime with regard to component A, then... 

In the reaction controlled regime the layer of each of two chemical compounds ApBq and ArBs grows at the expense of two partial chemical reactions taking place at its interfaces with adjacent phases. 

The error becomes largest when the relative importance of chemical reaction and diffusion are of the same magnitude = 1). As the asymptotic regime of either chemical reaction control (ctJ <0.1) or diffusion control ((Tg > 10) is approached, the error becomes small. 

A further important feature of the grain model is that it allows one to define quantitatively the asymptotic regimes of chemical reaction control and duffusion control and thus enables the rational planning of experimental programs. A full discussion of this problem is presented in Chapter 6. 

As it has appeared in recent years that many hmdamental aspects of elementary chemical reactions in solution can be understood on the basis of the dependence of reaction rate coefficients on solvent density [2, 3, 4 and 5], increasing attention is paid to reaction kinetics in the gas-to-liquid transition range and supercritical fluids under varying pressure. In this way, the essential differences between the regime of binary collisions in the low-pressure gas phase and tliat of a dense enviromnent with typical many-body interactions become apparent. An extremely useful approach in this respect is the investigation of rate coefficients, reaction yields and concentration-time profiles of some typical model reactions over as wide a pressure range as possible, which pemiits the continuous and well controlled variation of the physical properties of the solvent. Among these the most important are density, polarity and viscosity in a contimiiim description or collision frequency. 

When considering the macrokinetics of PAR described by equations (Eq. 17), it is reasonable to focus on two limiting regimes. The first of these, the kinetically-controlled regime, takes place provided the rate of diffusion of molecules Z appreciably exceeds that of the chemical reaction. In this case, a uniform concentration Z = Ze should be established all over the globule after time interval t R2/D. Subsequently, during the interval t 1 /kZe, which is considerably larger than f[Pg.152]

At low temperatures (T<1320 °C) and small particles, combustion regime (I) prevails [11,74,75]. Regime (I) is controlled by chemical kinetics intraparticle (reaction control), see Figure 55. The oxygen content is constant at any radius inside the particle since the rate of diffusion is fast compared to the rate of heterogeneous reaction. The particle then burns with reducing density and a constant diameter, see Figure 55. 

In the case of constant interfacial-area-stirred cells, although zone A is certainly an indication that the process is controlled by diffusional processes, the opposite is not true for zone B. In fact, in spite of the increased stirring rate, it may happen that the thickness of the diffusion films never decreases below a sufficiently low value to make diffusion so fast that it can be completely neglected relative to the rate of the chemical reactions. This effect, sometimes called slip effect, depends on the specific hydrodynamic conditions of the apparatus in which the extraction takes place and simulates a kinetic regime. 

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