Why Theories Fail

As in the penetration theory, doubling the diffusion coefficient increases the mass transfer coefficient by s/l. 

At this point, some conclude that the surface-renewal theory is much ado about nothing. It predicts the same variation with diffusion as the penetration theory, and the new residence time x is as unknown as the film thickness / introduced in the film theory. This new theory may at first seem of small value. 

The value of the surface-renewal theory is that the simple math basic to the penetration theory is extended to a more realistic physical situation. Although the result is less exact than we might wish, the surface-renewal theory does suggest reasonable ways to think about mass transfer in complex situations. Such thoughts can lead to more effective correlations and to better models. 

Example 9.2-1 Finding the adjustable parameters of the penetration and surface-renewal theories What are the contact time /./v ax and the surface residence time x for the carbon dioxide scrubber described in Example 9.1-1  

Solution In this earlier example, we were given that D was 1.9 10 cm fsec, and we calculated that k was 2.5 10 cm/sec. Thus, from Eq. 9.2-5, 

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