Minimum mixedness

Figure 1.6. Four micromixing models that have appeared in the literature. From top to bottom maximum-mixedness model minimum-mixedness model coalescence-redispersion model three-environment model.

Minimum Mixedness The segregation model has mixing at the latest possible point... 

Figure 3.10 From top to bottom maximum mixedness, segregated flow (minimum mixedness), coaiescence-redispersion, and three-environment modeis. (From Fox, R.O. Computational Models for Turbulent Reacting Flows, Cambridge, UK, 2003.)...

Mixing earliness may be experimentally determined by injecting two tracers A and B which can react with each other. Close to Minimum Mixedness, the best discrimination is obtained by injecting two sharp pulses of A and B separated by a short interval. Close to Maximum Mixedness, the recommended injection is a square pulse containing both A and B. The reaction extent at the reactor outlet is then strongly dependent on micromixing. The determination is simple if the reaction products are coloured (e.g., hydrolysis of p-nitrophenyl acetate) [22 [23. ... 

As already mentioned above, the usual assumption is that the reactor comprises two Environments. The Entering (or Initial) Environment, which consist of a macrofluid, and the Leaving (or Final) Environment where the fluid behaves as a microfluid. The segregation function" presented above (Sec. 3-1) describes the transfer between these Environments. The first limiting case is that of Minimum Mixedness where the Entering Environment spreads out into the whole reactor. The tubes of the BPT-model remain insulated and (4-1) is still valid. The conversion for a single reaction is written... 

Under these conditions, the uncertainty regarding the component of the element that is selected is considered. In fact, the following discussion is the same as that in the definition of the multi-component mixedness. Only the practical conditions corresponding to the maximum and minimum values of the mutual entropy are different from the case of the definition of the multi-component mixedness. According to Section 1.7, the mutual entropy 1(0, R) has the following minimum and maximum values ... 

The difference between this separation efficiency and that from the multi-component mixedness is that the correspondence of the conditions for the maximum and minimum values of the mutual entropy is reversed. Therefore, it is natural that this separation efficiency has the following clear relationship with the multi-component mixedness ... 

Figure 6. Mixing in a flow reactor with two unmixed feedstreams (60). Left, Maximum age, maximum species mixedness middle, minimum age, maximum species mixedness (mixing in this case can also he assumed to occur by molecular diffusion between two tubes having the same and (T9.)) and right, mixing between particles of the same life expectancy by a random-coalescence process (77).

The conversion is a maximum in segregated flow and a minimum under maximum mixedness conditions, for a given RTD and reaction orders >1. A few comparisons are made in Fig. 19-11. In some ranges of the parameters n or rc, the differences in reactor volume for a given conversion, when segregated or maximum mixedness flow is assumed,... 

Cautions The segregation model and the maximum mixedness model will not give the proper boimds on the conversion for certain rate laws and for nonisothermal operation. These situations arise, for example, if the rate of reaction goes through both a maximum and a minimum when plotted as a function of conversion and the initial rate is higher than the maximum (Figure 13-18). 

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