Diffusion effects determination

Hence, from equation (10.48), the effective diffusion coefficient determined by "chromatographic" testing is given by... 

Example 10.6 A commercial process for the dehydrogenation of ethylbenzene uses 3-mm spherical catalyst particles. The rate constant is 15s , and the diffusivity of ethylbenzene in steam is 4x 10 m /s under reaction conditions. Assume that the pore diameter is large enough that this bulk diffusivity applies. Determine a likely lower bound for the isothermal effectiveness factor. 

Kinetics of chemical reactions at liquid interfaces has often proven difficult to study because they include processes that occur on a variety of time scales [1]. The reactions depend on diffusion of reactants to the interface prior to reaction and diffusion of products away from the interface after the reaction. As a result, relatively little information about the interface dependent kinetic step can be gleaned because this step is usually faster than diffusion. This often leads to diffusion controlled interfacial rates. While often not the rate-determining step in interfacial chemical reactions, the dynamics at the interface still play an important and interesting role in interfacial chemical processes. Chemists interested in interfacial kinetics have devised a variety of complex reaction vessels to eliminate diffusion effects systematically and access the interfacial kinetics. However, deconvolution of two slow bulk diffusion processes to access the desired the fast interfacial kinetics, especially ultrafast processes, is generally not an effective way to measure the fast interfacial dynamics. Thus, methodology to probe the interface specifically has been developed. 

A spectral model similar to (3.82) can be derived from (3.75) for the joint scalar dissipation rate eap defined by (3.139), p. 90. We will use these models in Section 3.4 to understand the importance of spectral transport in determining differential-diffusion effects. As we shall see in the next section, the spectral interpretation of scalar energy transport has important ramifications on the transport equations for one-point scalar statistics for inhomogeneous turbulent mixing. 

At the same time as the basic work was being done on the kinetics and difFusivity effects in coke burning, the kinetics of the processes that determined the CO/CO2 ratio from slow coke was investigated by Weisz (1966). Studies were made of the cumulative CO2/CO ratios for individual, whole, spherical catalyst beads. The results, shown in Fig. 28, scattered very badly. 

Selected entries from Methods in Enzymology [vol, page(s)] Analysis of GTP-binding/GTPase cycle of G protein, 237, 411-412 applications, 240, 216-217, 247 246, 301-302 [diffusion rates, 246, 303 distance of closest approach, 246, 303 DNA (Holliday junctions, 246, 325-326 hybridization, 246, 324 structure, 246, 322-324) dye development, 246, 303, 328 reaction kinetics, 246, 18, 302-303, 322] computer programs for testing, 240, 243-247 conformational distribution determination, 240, 247-253 decay evaluation [donor fluorescence decay, 240, 230-234, 249-250, 252 exponential approximation of exact theoretical decay, 240, 222-229 linked systems, 240, 234-237, 249-253 randomly distributed fluorophores, 240, 237-243] diffusion coefficient determination, 240, 248, 250-251 diffusion-enhanced FRET, 246, 326-328 distance measurement [accuracy, 246, 330 effect of dye orientation, 246, 305, 312-313 limitations, 246,... 

When the steps become bigger, or p-xylene concentration is lower, the corner in the steps forms a groove. In this tage, the diffusion effect is increasing in rate determining factors instead of the surface Integration. 

The first-order decomposition of A is run in an experimental mixed flow reactor. Find the role played by pore diffusion in these runs in effect determine whether the runs were made under diffusion-free, strong resistance, or intermediate conditions. 

Giddings (5) also determined theoretically that for a well packed column (y) should be about 0.6 so again the longitudinal diffusion effect confirms that the column was reasonably well packed. 

Frontal analysis brings with it the requirement of the system to have convex isotherms (see Section 1.2.6). This results in the peaks having sharp fronts and well-formed steps. An inspection of Figure 1.3 reflects the problem of analytical frontal analysis— it is difficult to calculate initial concentrations in the sample. One can, however, determine the number of components present in the sample. If the isotherms are linear, the zones may be diffuse. This may be caused by three important processes inhomogeneity of the packing, large diffusion effects, and nonattainment of sorption equilibrium. 

Diffusion in liquids is four to five orders of magnitude less than that found in gases. For this reason we may neglect longitudinal diffusion effects in the liquid phase in zone broadening. However, longitudinal diffusion must be considered in equilibrium effects because it may determine the rate of mass transfer. 

When intraparticle diffusion occurs, the kinetic behaviour of the system is different from that which prevails when chemical reaction is rate determining. For conditions of diffusion control 0 will be large, and then the effectiveness factor tj( 1/ tanh 0, from equation 3.15) becomes. From equation 3.19, it is seen therefore that rj is proportional to k Ul. The chemical reaction rate on the other hand is directly proportional to k so that, from equation 3.8 at the beginning of this section, the overall reaction rate is proportional to k,n. Since the specific rate constant is directly proportional to e"E/RT, where E is the activation energy for the chemical reaction in the absence of diffusion effects, we are led to the important result that for a diffusion limited reaction the rate is proportional to e E/2RT. Hence the apparent activation energy ED, measured when reaction occurs in the diffusion controlled region, is only half the true value ... 

An extensive review with many examples125 shows that the reactivity-selectivity principle cannot be used to predict the selectivity of a reaction except in unique systems where one reaction is close to or diffusion controlled. The relative importance of the Hammond effect and the frontier-orbital effects determines the reactivity-selectivity relationship that will be found in a particular system. The review also concludes that the Hammond-Leffler a-value cannot be used as an indicator of transition-state structure. 

This process is a relatively fast one and the diffusion coefficient determined from the correlation time of the fluctuations in the scattering can be too large202) giving too small radii, tm- To avoid this effect, Mazer et al.33) made measurements on sodium dodecyl sulphate in high salt concentration to contract the counterion charge cloud. 

---