Enhancement coefficient

Thus the mass transfer coefficient, enhanced by chemical reaction, h D is given by ... 

D Mass transfer coefficient enhanced by chemical reaction m/s LT 1... 

Meyyappan, N. and Gandhi, N.N. Solubility and mass transfer coefficient enhancement of benzyl acetate in water through hydrotropy, 7 Chem. Eng. Data, 49(5) 1290-1294, 2004. 

This equation can be written Nco,s k[CCor where k[ = VA, Deo, and may be regarded as a liquid-film mass transfer coefficient enhanced oy the fast chemical reaction. This is very convenient because it allows us to use the expression in Volume 2, Chapter 12 for combining liquid-film and gas-film coefficients to give an overall gas-film coefficient ... 

The reactivity of (20) is more typicai of anthraquinones in genera) whiie the formation of Dewar structures (21) and (22) is the first observation of this type of reaction for the anthraquinone system. The authors note that (18) and (19) show large perturbations in their U.V. absorption spectra compared with anthraquinone (20). These perturbations include bathochromic shifts and extinction coefficient enhancements of the longest wavelength, presumably n->7r , bands which may reflect steric interactions between one of the anthraquinone carbonyls and the adjacent ferr-butyl group. Anomalous reactivity has also been found for 9-ferf-butyl-lO-cyanoanthracene (23) which upon irradiation at -20 C gave the dibenzobicyclo(2.2. llheptane (24). This is in constrast to the photochemistry of 9-ferf-butylanthracene (25) which forms the Dewar isomer (26). The latter reaction and its reversal have been examined for their... 

Mass transfer coefficient Enhancement factor E Inlet mol fraction of CO2, yo Henry s constant, MPa 1/mol ... 

A feature of the chromophores in the above compounds is that they can detect and distinguish between hydrogen bonds and ion-pairs. Hydrogen-bond formation is accompanied (as in the infra-red method) by a small (10-30 nm) bathochromic shift of the main absorption peak, with little change in extinction coefficient. However, for strong acids and bases, ion-pairs will be formed, indicated by bathochromic shifts of 100-150 nm, coupled with an extinction coefficient enhancement by a factor of two. Typical examples of systems that have been studied are (i) phenol and dioxan in isooctane [10] and (ii) 2,4-DNP and pyridine in toluene [11]. 

The pronounced effect of the partial pressure of CO2 on Kca is the result of the ehemical reaction in the liquid phase and illustrates the difficulty of using Koa to correlate absorption when the primary resistance is in the liquid phase. The oceurrence of a reaction causes an increase in the liquid film coefficient over that which would be observed with physical absorption alone. Hie degree of liquid film coefficient enhancement is a complex function of concentrations, reaction rates and diffiisivities in the liquid phase. Discussions of enhancement factors for various generalized types of chemical reactions are given in several texts (Sherwood and Pigford, 1952B Astarita, 1967 Danckwerts, 1970 Astaritaet al., 1983). 

Figure 14.9 compares the measured size-dependent suppression and diffusion-coefficient enhancement of silica-encapsulated gold particles [78] in comparison with BOLS prediction. The trend similarity shows the correlation between the diffusivity and activity in terms of activation energy. 

The computed CWT leads to complex coefficients. Therefore total information provided by the transform needs a double representation (modulus and phase). However, as the representation in the time-frequency plane of the phase of the CWT is generally quite difficult to interpret, we shall focus on the modulus of the CWT. Furthermore, it is known that the square modulus of the transform, CWT(s(t)) I corresponds to a distribution of the energy of s(t) in the time frequency plane [4], This property enhances the interpretability of the analysis. Indeed, each pattern formed in the representation can be understood as a part of the signal s total energy. This representation is called "scalogram". 

Equation (2.106) gives rise to an implicit scheme except for 0 = 0. The application of implicit schemes for transient problems yields a set of simultaneous equations for the field unknown at the new time level n + 1. As can be seen from Equation (2.111) some of the terms in the coefficient matrix should also be evaluated at the new time level. Therefore application of the described scheme requires the use of iterative algorithms. Various techniques for enhancing the speed of convergence in these algorithms can be found in the literature (Pittman, 1989). 

Calculations usirig this value afford a partition coefficient for 5.2 of 96 and a micellar second-order rate constant of 0.21 M" s" . This partition coefficient is higher than the corresponding values for SDS micelles and CTAB micelles given in Table 5.2. This trend is in agreement with literature data, that indicate that Cu(DS)2 micelles are able to solubilize 1.5 times as much benzene as SDS micelles . Most likely this enhanced solubilisation is a result of the higher counterion binding of Cu(DS)2... 

In contrast to SDS, CTAB and C12E7, CufDSjz micelles catalyse the Diels-Alder reaction between 1 and 2 with enzyme-like efficiency, leading to rate enhancements up to 1.8-10 compared to the reaction in acetonitrile. This results primarily from the essentially complete complexation off to the copper ions at the micellar surface. Comparison of the partition coefficients of 2 over the water phase and the micellar pseudophase, as derived from kinetic analysis using the pseudophase model, reveals a higher affinity of 2 for Cu(DS)2 than for SDS and CTAB. The inhibitory effect resulting from spatial separation of la-g and 2 is likely to be at least less pronoimced for Cu(DS)2 than for the other surfactants. 

The enhanced rate expressions for regimes 3 and 4 have been presented (48) and can be appHed (49,50) when one phase consists of a pure reactant, for example in the saponification of an ester. However, it should be noted that in the more general case where component C in equation 19 is transferred from one inert solvent (A) to another (B), an enhancement of the mass-transfer coefficient in the B-rich phase has the effect of moving the controlling mass-transfer resistance to the A-rich phase, in accordance with equation 17. Resistance in both Hquid phases is taken into account in a detailed model (51) which is apphcable to the reversible reactions involved in metal extraction. This model, which can accommodate the case of interfacial reaction, has been successfully compared with rate data from the Hterature (51). 

Only slightly less accurate ( 0.3—0.5%) and more versatile in scale are other titration techniques. Plutonium maybe oxidized in aqueous solution to PuO " 2 using AgO, and then reduced to Pu" " by a known excess of Fe", which is back-titrated with Ce" ". Pu" " may be titrated complexometricaHy with EDTA and a colorimetric indicator such as Arsenazo(I), even in the presence of a large excess of UO " 2- Solution spectrophotometry (Figs. 4 and 5) can be utilized if the plutonium oxidation state is known or controlled. The spectrophotometric method is very sensitive if a colored complex such as Arsenazo(III) is used. Analytically usehil absorption maxima and molar absorption coefficients ( s) are given in Table 10. Laser photoacoustic spectroscopy has been developed for both elemental analysis and speciation (oxidation state) at concentrations of lO " — 10 M (118). Chemical extraction can also be used to enhance this technique. 

The fugacity coefficient of thesolid solute dissolved in the fluid phase (0 ) has been obtained using cubic equations of state (52) and statistical mechanical perturbation theory (53). The enhancement factor, E, shown as the quantity ia brackets ia equation 2, is defined as the real solubiUty divided by the solubihty ia an ideal gas. The solubiUty ia an ideal gas is simply the vapor pressure of the sohd over the pressure. Enhancement factors of 10 are common for supercritical systems. Notable exceptions such as the squalane—carbon dioxide system may have enhancement factors greater than 10. Solubihty data can be reduced to a simple form by plotting the logarithm of the enhancement factor vs density, resulting ia a fairly linear relationship (52). 

The presence of 0.004—0.0062% Te in a welding rod or wke produces a positive surface tension coefficient which enhances the heat transfer to the... 

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