Diffusion coefficients Wilke-Chang equation

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. 

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... 

There is no equation comparable to the Knudsen equation for diffusion of liquids in small pores, but the pore walls do limit the movement of molecules and cause a decrease in the diffusivity. Diffusion coefficients can be predicted from the bulk diffusivity and a hindrance factor that depends on the pore size and the solute size. For moderate-molecular-weight solutes, the empirical Wilke-Chang equation is used for the bulk diffusivity [13] ... 

For the calculations of reduced velocities or the prediction of an HETP we need to know the diffusion coefficient of an analyte in the mobile phase. However, this information is seldom available. We therefore have to estimate the diffusion coefficient. There are several different approaches available, but the one most frequently used in the HPLC literature is the Wilke-Chang equation. It is claimed to be accurate for small to medium-sized molecules within 10%, which is sufficient for most purposes (9) ... 

This relationship between the permeability values of several compounds (P) and the partition coefficient of these compounds between the IL phase immobilized in the membrane and the feed/receive phase (K) has been observed by several authors [34,71], finding that the increase in the K values for the compounds was reflected in an increase in the P values. A mathematical correlation between these parameters has been established by de los Rfos et al. [35], being the diffusion coefficient into the IL phase calculated by the empirical Wilke-Chang equation, with the bulk diffusion coefficient defined as... 

Wilke-Chang equation depicts that the diffusion coefficient of the forward transported M L complex shonld be much lower as compared to the backward transported bare ligand molecules due to smaller molar volume of the latter. This fact implies that the concentration of ligand at the aqueous feed-membrane interface will always be in excess because... 

The diffusion coefficient of MMA in water has been estimated using the Wilke-Chang equation [50] ... 

Equation 2.10, which is a simplified form of the Wilke-Chang equation [11], shows the relationship between temperature and diffusion. In this equation. S is a constant that depends bothonthe solvent and the analyte molecule. For those who are interested in the quantitative relationship, the diffusion coefficient is inversely proportional the molar volume to the power ofO.6, so approximately to the square route of molecular mass (depending on detailed molecular structure, in particular for macromolecules). In this example, neither the solvent nor analyte is altered, and thus it can be directly concluded how the temperature influences the diffusion 2.10. It shows the linear increase of with increasing temperature, but at the same time we have to consider the decrease in viscosity, which is also a function of temperature, thus increasing the diffusion coefficient even more. 

Predict the diffusion coefficient of acetonefCHjCOCHj) in water at 25° and 50°C using the Wilke-Chang equation. The experimental value is 1.28 x 10- mVsat25°C(298 K). 

The diffusion coefficient in liquids (solute A in solvent B) can be calculated for dilute solutions with errors of usually less than 20% by the Wilke-Chang equation (WUke and Chang, 1955) ... 

For comparison, the diffusion coefficient of menthol in the reaction mixture can also be calculated by the Wilke—Chang equation for diffusion in liquids ... 

Figure 6.17.10 Experimentally determined diffusion coefficients (Etzold, 2007 Etzold and Jess, 2008) and estimations by Eq. (6.17.20) and by Wilke-Chang equation [Eq. (3.1.90)] in combination with Eq. (6.17.21).

In all forms of liquid membrane configurations, the transport efficiency can be changed based on the nature of the organic extractant, feed and receiver phase compositions and the viscosity of the membrane phase. Also, the nature of the diffusing species is important as the diffusion coefficient is dependent on the molar volume of the diffusing species, as per the Wilke-Chang equation (Wilke et al, 1955) ... 

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]. 

The diffusion coefficients can be estimated from the Wilke-Chang equation... 

Use the Wilke-Chang equation (Equation 3.3) to estimate the diffusion coefficient of DDT in water at 25°C. The viscosity of water at this temperature... 

Wilke—Change equation Used to calculate the diffusion coefficient of a solute A in solvent B, Dab (hi cp) ... 

Sassiat, P.R., Mourier, P., Caude, M.H. and Rosset, R.H. (1987) Measurement of diffusion coefficients in supercritical carbon dioxide and correlation with the equation of Wilke and Chang. Analytical Chemistry, 59 (8), 1164-1170. 

The gas A must transfer from the gas phase to the liquid phase. Equation (1) describes the specific (per m2) molar flow (JA) of A through the gas-liquid interface. Considering only limitations in the liquid phase, this molar flow notably depends on the liquid molecular diffusion coefficient DAL (m2 s ). Based on the liquid state theories, DA L can be calculated using the Stokes-Einstein expression, and many correlations have been developed in order to estimate the liquid diffusion coefficients. The best-known example is the Wilke and Chang (W-C) relationship, but many others have been established and compared (Table 45.4) [28-33]. 

A number of approaches have been suggested for the determination of the molecular diffusion coefficient, D, of a component in water (Othmer and Thakar, 1953 Scheibel, 1954 Wilke and Chang, 1955 Hayduk andLaudie, 1974 Thibodeaux, 1996). Based on these five references, the diffusion coefficient ratio />/Jl2s / Dlq2 was found to vary within the interval 0.78-0.86 with an arithmetic mean value equal to 0.84. This value can be inserted in Equation (4.22) as a first estimate to determine Km. Equation (4.22) and the empirical expressions for KLC>2 outlined in Table 4.7 are the basis for the determination of the mass transfer coefficient for H2S, KL i S, and thereby, the emission of H2S from the wastewater into the sewer atmosphere. Further details relevant in this respect are dealt with in Section 4.4. 

The molecular diffusion coefficients in liquid phase were estimated from the correlations Wilke and Chang (9) for organic solutions and Hayduk and Minhas (10) for aqueous solutions, respectively. The solvent viscosities needed in the correlations were obtained from the empirical equation based on the experimental data,... 

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