Binary diffiisivities

This mixing rule is used to determine the diffiisivity of any component in a / -I-1 component mixture and requires binary diffiisivities of component i with all other components. It has been estimated that errors are about 5 percent greater than the greatest error in the binary diffiisivities. Fairbanks and Wilke, using the same Eq. (2-154), made the same recommendation with essentially the... 

Do and D o are dilute solution binary diffiisivities. Errors depend on the procedure used to determine the dilute solution diffiisivities. 

Where is the axial velocity in laminar flow, a function of the radial position and represented by the classical non-symmetric parabolic profile characteristic of annular spaces (Bird etal., 2002, p. 55). The use of a pseudo-binary diffiisivity is only an approximation if more accuracy is needed the Maxwell-Stefan relationships should be used. The initial ... 

The form of Eq. 3.2.C-1 is too complex for many engineering calculations, and a common approach is to define a mean effective binary diffiisivity for species j diffusing through the mixture ... 

The semi-open system of Stefan has been used to calculate the binary diffiisivity. Lee and Wilke (1954) criticised this method. However, with the exception of solvents of high volatility, the Stefan method is one of the convenient methods for calculating the binary diffiisivity. 

The matrices B and A of (n, n) dimension are function of binary diffiisivities, Knudsen diffusivities and mole fractions as follows ... 

The are the binary diffusion coefficients for an i - j mixture thus, no additional information is required for computations of multicomponent diffusion in dilate gas mixtures although one might prefer a form in which the fluxes appeared explicitly. Generalization of the Stefon-Maxwell form to derm gases and to liquids has been suggested, Iwt in ffiese cases there is no rigorous relationship to the binary diffiisivities. Furthermore, the form of Eq. (2.3-10) in which the fluxes do not appear explicitly has little to recommend it. 

ComposUhn Dependence of D b. The diffusion coefficient of a binaiy solution is a function of composition. If the true driving force for ordinary diffusion is the isothermal, isobaiic gradient of chemical potential, then the binary diffiisivity can be written in the form... 

Use the Chapman—Enskog equation for the binary diffiisivity at low density (Eqn (2.43)) ... 

For certain applications, we define an effective binary diffiisivity with the flow relative to the fixed solid and include only bulk flow in the values of Di... 

At ambient temperature and pressure, gas-phase diffusion coefficients are of the order of tO -tO ft /s (10 -10 mVs). Table 2.3-1 presents some rqiresentative values for binary gas mixtures at I atm. Marrero and Mason" have provided an extensive review of experimental values of gas phase binary diffiisivities. 

Vignes" correlated the composition dependence of binary diffiision coefficients in terms of their infinite-dilution values and this thermodynamic correction factor. 

Some representative curves from his paper are also shown in Fig. 2.34-. The corrdation appears to be quite successful unless the mixtures are strongly associating (e.g., CHjCI-aoelone). Leffler arid Cullinan have provided a derivation of Eq. (2.3-20) based on Absolute Rate Theory while Gainer has used Absolute Rate Theoiy to provide a difiiemt correlation for the composition dependence of binary diffiision coefficients. 

In metal alloys fomung solid solutions over significant composition ranges, the binary diffiisivity varies wiffi composition. Figure 2.3-6 shows some typical data lor difliision in the Fe-Ni stem at 1185 C. Vignes arid Birchenall have presented a correlation for the concentmtion dependence in binary aih s similar to Eq. (2.3-18) for liquids but they requited an additional factor involvirig the melting temperature of ttie alloy to obtain a satisfoctoiy correlation. 

For a gas mixture consisting of more than three components, the approximation ofWilke (1986) based on the binary diffiision coefficients and the molar content y is useful ... 

The Maxwell-Stefan diffusion coefficients represent binary diffiisivities for ideal and many nonideal mixtures, they are independent of the concentration of the species in the multicomponent mixtures. 

Mass and molar diffusion are important in practice, and can be derived from the Maxwell-Stefan description of diffusion. The Maxwell-Stefan multicomponent diffiisivities are obtained from the binary diffiisivities, which are easy to measure. 

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