Wilke-Chang method

The liquid diffusion coefficient of component i in the mixture (D ) can be estimated using a Wilke-Change method variation ... 

Diffusion coefficients in liquid phases depend on concentration and are valid for dilute solutions, that is, solute concentrations no greater than 10%. Also, the lower the solute concentration, the more accurate the calculated coefficients. For a binary mixture of solute A in solvent B, the diffusion coefficient can be represented as D gfor concentrations of A up to 5 or 10 mole percent [20]. A number of correlations have been proposed for predicting D°gin dilute liquid solutions [21,22,23]. Here, the Wilke-Chang method is employed for estimating D°g. This can be expressed as ... 

THE PROGRAM USES THE WILKE-CHANG METHOD TO CALCULATE THE DIFFUSION COEFFICIENT OF A BINARY MIXTURE OF SOLUTE A IN SOLVENT B. 

Both methods give values in reasonable agreement with experiment althoogh the Wilke-Chang method does have the adjustable parameter 0. The Gainer-Metzner correlation is to be preferred as the viscosity of a solution liquid increases. 

Estimation of Liquid Diffusivity. It is desired to predict the diffusion coefficient of dilute acetic acid (CH3COOH) in water at 282.9 K and at 298 K using the Wilke-Chang method. Compare the predicted values with the experimental values in Table 6.3-1. 

In order to solve the mathematical model for the emulsion hquid membrane, the model parameters, i. e., external mass transfer coefficient (Km), effective diffu-sivity (D ff), and rate constant of the forward reaction (kj) can be estimated by well known procedures reported in the Hterature [72 - 74]. The external phase mass transfer coefficient can be calculated by the correlation of Calderback and Moo-Young [72] with reasonable accuracy. The value of the solute diffusivity (Da) required in the correlation can be calculated by the well-known Wilke-Chang correlation [73]. The value of the diffusivity of the complex involved in the procedure can also be estimated by Wilke-Chang correlation [73] and the internal phase mass transfer co-efficient (surfactant resistance) by the method developed by Gu et al. [75]. 

If no diffusivity data is available at any concentration, estimation can still be used. First, the infinite dilution diffusivity is estimated using one of several methods available (Reid et al. 1987) such as the Wilke-Chang (Wilke and Chang 1955) method... 

Solution Although the liquids are somewhat viscous, first estimate the infinite-dilution diffiisivities using the Wilke-Chang correlation, Eq. (2.3-17). The molar volumes at the boiling point are estimated by Shroeder s method as... 

Estimation of the corresponding parameters for liquid-phase systems is more uncertain. Equation 5.284 is valid for liquid-filled catalyst pores. The molecular liquid-phase diffusion coefficients can be estimated from, that is, the Wilke-Chang equation [20]. Different estimation methods are discussed further in the book The Properties of Gases and Liquids [20]. Eor the liquid phase, the film coefficient, ki, is always used. Different empirical correlations for the liquid film coefficient are presented and compared, for example, in Ref [23]. Methods for estimating liquid-phase diffusion coefficients and liquid film coefficients are described in Appendices 6 and 7. 

The diffusion coefficients in gas and liquid phases play an important role in the correlation equations, because the film thickness, film coefficient, and diffusion coefficient are related to each other. Gas-phase diffusion coefficients can be estimated using the Fuller-Schettler-Giddings equation [9] and the Wilke approximation [9] (Appendix 4). Liquid-phase diffusion coefficients are more difficult to estimate. A frequently used correlation equation for the liquid-phase diffusion coefficient is the Wilke-Chang equation [4,9], which is reliable for poorly soluble gases, in clean liquids and liquid mixtures (Appendix 6). There are also several other methods presented in the literature. The estimation methods are discussed in detail in the book The Properties of Gases and Liquids [9]. 

Four empirical methods are given by Reid et al. (1987) to estimate D in liquid mixtures. These are the methods of Wilke Chang (1955) and lyn Calus (1975),... 

Estimate molecular diffusivities (cm s ) for naphthalene in water using the following methods described in Chapter 5 (a) Stokes-Einstein, (b) Wilke-Chang, (c) Hayduk-Laudie, (d) Scheibel, and (e) the molecular weight correlation (Figure 5.4). Compare the results to the measured value, D,42 = 7.64 X10 cm s (Gustafson and Dickhut, 1994a). 

The value of coefficient depends on the composition. As the mole fraction of component A approaches 0, approaches ZJ g the diffusion coefficient of component A in the solvent B at infinite dilution. The coefficient Z g can be estimated by the Wilke and Chang (1955) method ... 

For prediction of the diffiisivity of a dilute dissolved gas (hydi ocarbon or nonhydi ocaibon) in a liquid, the standard method is that of Wilke and Chang shown by Eq. (2-155). 

For predic ting diffiisivities in binary polar or associating liquid systems at liign solute dilution, the method of Wilke and Chang " defined in Eq. (2-156) can be utilized. The Tyn and Cains equation (2-152) can be used to determine the molar volume of the solute at the normal boihng point. Errors average 20 percent, with occasional errors of 35 percent. The method is not considered to be accurate above a solute concentration of 5 mole percent. 

Because the theory of the liquid state is not nearly so well developed as the kinetic theory of gases, estimation methods for liquid diffusion coefficients are not as reliable as those used for gases. For dilute solutions of non-electrolytes, one widely used correlation is that due to Wilke and Chang[48]... 

Diffusion coefficients are required to interpret all the data, but measured values are not available in most cases. The method of Wilke and Chang [33] represents the widely accepted standard for prediction of diffusion coefficients ... 

Rates of mass transfer to the catalyst surface and pore diffusion can be calculated by the methods of Section 2.2.2 if the diffusion coefficients are known. However, the molecular theory of diffusion in liquids is relatively undeveloped and it is not yet possible to treat diffusion in liquids with the same rigour as diffusion in gases. The complicating factors are that the diffusion coefficient varies with concentration and that the mass density is usually more constant than the molar density of the solution. An empirical equation, due to Wilke and Chang, which applies in dilute solution, gives... 

Correlation of Xa2 with Pore Blocking for Benzene-Water Data. The blocking of the pores on the membrane surface by the preferentially sorbed solute, which was discussed qualitatively in the preceding section, is now treated more quantitatively. Equation 4 was used to estimate the appropriate k value for each cell. The diffuslvlty of the solute in water was estimated by the method of Wilke and Chang (27), and the diffusivity of sodium... 

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