The Effective Diffusivity—Closing Remarks

The advantage of the effective diffusivity formulation is its simplicity. The primary disadvantage is that effective diffusivities are not system properties except for the limiting cases noted above. Furthermore, they depend on the fluxes N, which are not always known in advance. More complicated variations on the effective diffusivity theme, some requiring iteration on others incorporating a variation of position or composition have 

The numerical examples in this chapter show the effective diffusivity approach in about as bad a light as possible. This was partly our intention. Strictly speaking, none of the limiting cases presented above applies to the conditions pertaining to the above examples. Nevertheless, it is common practice to use an effective diffusivity in situations where it is not warranted, so these examples provide a small indication of the errors that may be encountered using an effective diffusivity formula in situations it was not designed to handle. 

It would be unfair of us to end this chapter with the impression that these results are typical. If conditions are such that the limiting cases do indeed apply we will find that the effective diffusivity approach does much better Example 8.6.1 is a case in point. 

Once the equations have been solved to obtain the composition and temperature profiles, the diffusion fluxes can be calculated and the interfacial transfer rates determined. It is customary to determine, on the basis of the chosen hydrodynamic model, mass transfer coefficients that reflect the overall transfer facility (molecular and turbulent transport) of the phase under consideration. 

In Chapter 7 we define mass transfer coefficients for binary and multicomponent systems. In subsequent chapters we develop mass transfer models to determine these coefficients. Many different models have been proposed over the years. The oldest and simplest model is the film model this is the most useful model for describing multicomponent mass transfer (Chapter 8). Empirical methods are also considered. Following our discussions of film theory, we describe the so-called surface renewal or penetration models of mass transfer (Chapter 9) and go on to develop turbulent eddy diffusivity based models (Chapter 10). Simultaneous mass and energy transport is considered in Chapter 11. 

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