Lamellar mixing models for structured chemical reactions and their relationship to statistical models; Macro- and micromixing and the problem of averages

In the lamellar mixing model, statistical treatments and average values of important variables are introduced near the end of the analysis, not at the beginning. A description based on a Lagrangian point of view of fluid mechanics, diffusion, and reaction in the neighborhood of a moving material particle is compared with other mixing approaches. Rational definitions for micro and macro mixing are specified. Usefulness of the lamellar model is demonstrated by (a) solution for concentrations field with multicomponent diffusion and n-linear chemical reactions in an arbitrary local flow field, (b) indication of criteria for the relative importance of molecular diffusion chemical reaction, local flow, and associated real time in each micro-flow element, (c) effect of real time in each micro-flow element. Potential uses include (a) perturbation schemes for analysis of mixing influence on complex chemical reactions, (b) use of chemical reactions to obtain average fluid mechanical information in complex motions.