Danckwerts theory model approach

In Chapter 7 we discussed the basics of the theory concerned with the influence of diffusion on gas-liquid reactions via the Hatta theory for flrst-order irreversible reactions, the case for rapid second-order reactions, and the generalization of the second-order theory by Van Krevelen and Hofitjzer. Those results were presented in terms of classical two-film theory, employing an enhancement factor to account for reaction effects on diffusion via a simple multiple of the mass-transfer coefficient in the absence of reaction. By and large this approach will be continued here however, alternative and more descriptive mass transfer theories such as the penetration model of Higbie and the surface-renewal theory of Danckwerts merit some attention as was done in Chapter 7. 

In surface renewal models the liquid surface is assumed to consist of a mosaic of elements with different age at the surface. The rate of absorption at the surface is then an average of the rates of absorption in each element, weighted with respect to a distribution function (t)—see Eq. 6.2-5. Under this heading of surface renewal theory we will also occasionally mention results of Higbie s [23] so-called penetration-theory, which can be considered as a special case in which every element is exposed to the gas for the same length of time before being replaced. The main emphasis of this section is on the Danckwerts [24] approach using the distribution function for completely random replacement of surface elements ... 

Another possibility is to use a pseudo-first-order reaction, rather slow so that little A reacts in the film, yet sufficiently fast to make Cm zero. This approach has been used by Danckwerts et al. [36] who interpreted their results in terms of the surface renewal theory. The system they investigated was CO2 absorption in C03 /HC03"-buffers of different compositions. This is a pseudo-first-order reaction for which, the surface renewal model leads to the following rate of absorption, Eq. 6.4.b-5 N A = A,y/D (k -1- s)Cm- Danckwerts et al. plotted (Nji A versus the different values of k corresponding to the different com-... 

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