Dear Sirs,
In his recent article [l], Chu presents a model of micromixing in chemical reactors from which he draws the (as he admits) surprising conclusion that the conversion for intermediate degrees of micromixing can exceed the conversions at the complete segregation and maximum mixedness limits. Even more surprising is the assertion that this situation can exist for the case of a first order reaction.
It has long been accepted that, for a first order reaction, the conversion depends only on the residence time distribution, and not on the degree of micromixing. This is easily seen to be true, because for first order reaction the probability of any molecule reacting while in the reactor depends only on its time of residence and not on its environment. One is thus led to suspect that there is a fault in Chu's argument.
This fault is evident in the analysis of the example given in the Appendix of the paper. The example of intermediate mixing considered, which gives a greater conversion than at the mixing limits, involves the mixing of fluid volumes of unequal life expectation. Such mixing cannot occur. Volumes-of unequa life expection leave the reactor at different times. Therefore, if they are mixed, they must subsequently unmix before leaving the react&. Ai had been pointed out before (e.g. [2]), this conflicts with the Second Law of Thermodynamics. Only volumes of equal life expectation can mix, and the degree of micromixing depends on the earliness or lateness of this mixing.