Wilke — Chang equation

Umesi-Danner They developed an equation for nonaqueous solvents with nonpolar and polar solutes. In all, 258 points were involved in the regression. Rj is the radius of gyration in A of the component molecule, which has been tabulated by Passut and Danner for 250 compounds. The average absolute deviation was 16 percent, compared with 26 percent for the Wilke-Chang equation. 

Siddiqi-Lucas In an impressive empirical study, these authors examined 1275 organic liquid mixtures. Their equation yielded an average absolute deviation of 13.1 percent, which was less than that for the Wilke-Chang equation (17.8 percent). Note that this correlation does not encompass aqueous solutions those were examined and a separate correlation was proposed, which is discussed later. 

Hayduk-Laudie They presented a simple correlation for the infinite dilution diffusion coefficients of nonelectrolytes in water. It has about the same accuracy as the Wilke-Chang equation (about 5.9 percent). There is no explicit temperature dependence, but the 1.14 exponent on I compensates for the absence of T in the numerator. That exponent was misprinted (as 1.4) in the original article and has been reproduced elsewhere erroneously. 

Siddiqi-Lucas These authors examined 658 aqueous liqiiid mixtures in an empirical study. They found an average absolute deviation of 19.7 percent. In contrast, the Wilke-Chang equation gave 35.0 percent and the Hayduk-Laudie correlation gave 30.4 percent. 

The Wilke-Chang equation gives satisfactory predictions for the diffusivity of organic compounds in water but not for water in organic solvents. 

Diffusion coefficients may be estimated using the Wilke-Chang equation (Danckwerts, 1970), the Sutherland-Einstein equation (Gobas et al., 1986), or the Hayduk-Laudie equation (Tucker and Nelken, 1982), which state that Dw values decrease with the molar volume (Vm) to the power 0.3 to 0.6. Alternatively, the semi-empirical Worch relation may be used (Worch, 1993), which predicts diffusion coefficients to decrease with increasing molar mass to the power of 0.53. These four equations yield very similar D estimates (factor of 1.2 difference). Using the estimates from the most commonly used Hayduk-Laudie equation... 

Table 3.5 Examples of the association parameter in the Wilke-Chang equation for diffusion in liquids (Wilke and Chang, 1955)...

Some compound class-specific outliers are described, and an explanation of why they are predicted incorrectly is given. The interpretation of the results shows that there are serious inadequacies in the development of prior models such as the Wilke-Chang equation. 

A comparison with the Wilke-Chang equation will be made in the Discussion. 

There are several similarities to the results of this work. In log form, the Wilke-Chang equation is... 

This relationship is clearly related to equation (15.18) in particular. The term in log is of note. In the original reference [3] very limited justification for its inclusion was made. Furthermore, the values of quoted in Reference [3] were obtained from then unpublished work, and effectively have the nature of an empirical correction, which in itself is not a major problem in the utility of the model. However, when the work was published the values of the parameter were quite different [12], yet this error in the Wilke-Chang equation has not been corrected in the literature, to the authors knowledge. 

The Wilke-Chang equation may be modified for a mixed solvent case... 

Assume that the mixture is a dilute solution. Use the Wilke-Chang equation ... 

The association parameter for solvent water is f = 2.6. Using the Wilke-Chang equation, we find... 

Silva and Macedo [Ind. Eng. Chem. Res. 37,1490 (1998)] measured diffusivities of ethers in C02 under supercritical conditions and compared them to the Wilke-Chang [Eq. (5-218)], Tyn-Calus [Eq. (5-219)], Catchpole-King [Eq. (5-210)], and their own equations. They found that the Wilke-Chang equation provided the best fit. 

Although the B and C terms exhibit opposite relationships with analyte diffusion, the C-term relationship is mainly of interest because resistance to mass transfer is the dominant form of band-spreading at the faster velocities that are desired. Equations (17-9) and (17-10) imply that speeding up diffusion will increase mass transfer and help decrease plate height. The Wilke-Chang equation [9] shows that diffusivity is directly proportional to temperature and inversely proportional to viscosity ... 

Di = 4.64 X 10 m /s (estimated using Wilke-Chang equation. Chapter 8)... 

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