Age Distributions and Macromixing

consider a second example, that of turbulent flow through the tube. Again there exists some sort of velocity profile, but in addition there is some level of micromixing due to eddy motion among the elements. In this case it is possible to identify a distribution of residence times for individual molecules within the system, not volume elements, and the RTD is a measure of the combined effects of macro-and micromixing. 

In the most general case, then, measurements of residence-time distribution by the methods to be discussed here cannot define micromixing. In spite of this limitation, knowledge of the residence-time distribution is most valuable because it provides us with as much information on the state of mixing as we can obtain short of detailed measurements on the microscopic level. 

In addition to the residence-time distribution, there are a number of other age distributions which are of importance and which sound just a Httle like something from a life-insurance brochure. The distribution of ages of elements or molecules within the system at a given time is called the internal-age distribution, and the distribution of ages on exit from the system is the exit-age distribution. Finally, corresponding to the internal-age distribution there is a residual Hfetime or life-expectancy distribution, which is a measure of time remaining before exit from the 

It is most convenient to define these distributions quantitatively within the context of the experimental methods normally used for the determination of the residence-time distribution. Once again we base the vocabulary and the development on the pioneering work of Danckwerts [P.V. Danckwerts, Chem. Eng. ScL, 2, 1 (1953)]. 

The fraction of materials with ages between t and t + dt on leaving the system is E t)dt. 

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