Factor homogeneity

To increase the sorption component of the separation factor, homogeneously distributed tetracyanoethylene, a strong electron acceptor having high affinity for electron donors, was added to the polyimide matrix [77]. It can be seen from data presented in Table 9.12 that this is accompanied by an increase in the sorption component /3s (benzene/cyclohexane) by a factor of 1.5 probably as a result of selective sorption of aromatic compounds by tetracyanoethylene with a simultaneous increase in the diffusion component /3d. The prepared membranes showed good pervaporation properties with respect to benzene/cyclohexane, toluene/isooctane mixtures. For example, for a two-component 50/50 wt% benzene/cyclohexane mixture at 343 K, the flux was 2 = 0.44 kg p,m/m h, and /3p (benzene/cyclohexane) = 48 and for a two-component toluene/isooctane mixture, 45/55 wt%, at 343 K the flux was 2 = 1-1 kg p-m/m h, and /3p (toluene/wo-octane) = 330. 

As noted earlier in section A2.5.6.2. the assumption of homogeneity and tlie resnlting principle of two-scale-factor universality requires the amplitude coefficients to be related. In particnlar the following relations can be derived ... 

The central quantity of interest in homogeneous nucleation is the nucleation rate J, which gives the number of droplets nucleated per unit volume per unit time for a given supersaturation. The free energy barrier is the dommant factor in detenuining J J depends on it exponentially. Thus, a small difference in the different model predictions for the barrier can lead to orders of magnitude differences in J. Similarly, experimental measurements of J are sensitive to the purity of the sample and to experimental conditions such as temperature. In modem field theories, J has a general fonu... 

The equation does not take into account such pertubation factors as steric effects, solvent effects, and ion-pair formation. These factors, however, may be neglected when experiments are carried out in the same solvent at the same temperature and concentration for an homogeneous set of substrates. So, for a given ambident nucleophile the rate ratio kj/kj will depend on A and B, which vary with (a) the attacked electrophilic center, (b) the solvent, and (c) the counterpart cationic species of the anion. The important point in this kind of study is to change only one parameter at a time. This simple rule has not always been followed, and little systematic work has been done in this field (12) stiH widely open after the discovery of the role played by single electron transfer mechanism in ambident reactivity (1689). 

Several factors affect the bandshapes observed ia drifts of bulk materials, and hence the magnitude of the diffuse reflectance response. Particle size is extremely important, siace as particle size decreases, spectral bandwidths generally decrease. Therefore, it is desirable to uniformly grind the samples to particle sizes of <50 fim. Sample homogeneity is also important as is the need for dilute concentrations ia the aoaabsorbiag matrix. 

The mechanism and rate of hydrogen peroxide decomposition depend on many factors, including temperature, pH, presence or absence of a catalyst (7—10), such as metal ions, oxides, and hydroxides etc. Some common metal ions that actively support homogeneous catalysis of the decomposition include ferrous, ferric, cuprous, cupric, chromate, dichromate, molybdate, tungstate, and vanadate. For combinations, such as iron and... 

Digester Control For control purposes at constant sulfidity and alkah charge, the deligniftcation rate is treated as a homogeneous reaction, which is first order with respect to the lignin, % remaining in the wood, —dL jdt = kL. The influence of time, t, and temperature, T (Kelvin), has been incorporated into one term, called the JT-factor (33). 

Early ia the development of chemical reaction engineering, reactants and products were treated as existing ia single homogeneous phases or several discrete phases. The technology has evolved iato viewing reactants and products as residing ia interdependent environments, a most important factor for multiphase reactors which are the most common types encountered. 

Direct Chlorination of Ethylene. Direct chlorination of ethylene is generally conducted in Hquid EDC in a bubble column reactor. Ethylene and chlorine dissolve in the Hquid phase and combine in a homogeneous catalytic reaction to form EDC. Under typical process conditions, the reaction rate is controlled by mass transfer, with absorption of ethylene as the limiting factor (77). Ferric chloride is a highly selective and efficient catalyst for this reaction, and is widely used commercially (78). Ferric chloride and sodium chloride [7647-14-5] mixtures have also been utilized for the catalyst (79), as have tetrachloroferrate compounds, eg, ammonium tetrachloroferrate [24411-12-9] NH FeCl (80). The reaction most likely proceeds through an electrophilic addition mechanism, in which the catalyst first polarizes chlorine, as shown in equation 5. The polarized chlorine molecule then acts as an electrophilic reagent to attack the double bond of ethylene, thereby faciHtating chlorine addition (eq. 6) ... 

Both homogeneous and heterogeneous mechanisms requite relatively high supersaturation, and they exhibit a high order dependence on supersaturation. These factors often lead to production of excessive fines ia systems where primary aucleatioa mechanisms are important. The classical theoretical treatment of primary nucleation results ia the expressioa (5) ... 

This relation also holds for the average droplet size and a doubling of Z with other factors retained causes a reduction in average droplet size by 25%. Z is the energy density per time and this feature is to the advantage of emulsification using a homogenizer as compared to the process with a stirrer (Fig. 3). 

Few mechanisms of liquid/liquid reactions have been established, although some related work such as on droplet sizes and power input has been done. Small contents of surface-ac tive and other impurities in reactants of commercial quality can distort a reac tor s predicted performance. Diffusivities in liquids are comparatively low, a factor of 10 less than in gases, so it is probable in most industrial examples that they are diffusion controllech One consequence is that L/L reactions may not be as temperature sensitive as ordinary chemical reactions, although the effec t of temperature rise on viscosity and droplet size can result in substantial rate increases. L/L reac tions will exhibit behavior of homogeneous reactions only when they are very slow, nonionic reactions being the most likely ones. On the whole, in the present state of the art, the design of L/L reactors must depend on scale-up from laboratoiy or pilot plant work. 

For many laboratoiy studies, a suitable reactor is a cell with independent agitation of each phase and an undisturbed interface of known area, like the item shown in Fig. 23-29d, Whether a rate process is controlled by a mass-transfer rate or a chemical reaction rate sometimes can be identified by simple parameters. When agitation is sufficient to produce a homogeneous dispersion and the rate varies with further increases of agitation, mass-transfer rates are likely to be significant. The effect of change in temperature is a major criterion-, a rise of 10°C (18°F) normally raises the rate of a chemical reaction by a factor of 2 to 3, but the mass-transfer rate by much less. There may be instances, however, where the combined effect on chemical equilibrium, diffusivity, viscosity, and surface tension also may give a comparable enhancement. 

The momentum balance for homogeneous flow can be factored to a form which enables integration as ... 

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