Micromixing defined

In order to visualize physically what is meant by molecular-level or micromixing, consider a point volume element of fluid within the reactor that is just large enough to possess the average value of an intensive property such as concentration at the particular location considered [P.V. Danckwerts, Chem. Eng. Sci., 8, 93 (1958)]. All molecules within a point-volume element have zero age when entering the reactor, and all have zero time to remain within the reactor (life expectancy) when the element exits. The degree of micromixing defines what happens to the individual molecules within a point-volume element in the time between its entrance and exit from the reactor. 

The sum of k i and ki2 is so high relative to the rate of micromixing that A and B will not coexist. Thus the number of ordinary mass balance differential equations requiring integration can be reduced from five to four by defining the following composite variables ... 

Thus, given the weights and abscissas, the micromixing term for the moments is closed. Applying DQMOM, the micromixing source terms (which are added to the right-hand sides of Eqs. (133)—(135)) can be shown to obey for each n — 1,..., N the linear system defined by... 

An important aspect of the micromixing models is that they define the maximum and minimum conversion possible for a given reaction and RTD. Zwietering (1959) showed that, for the reaction A - products, with power-law kinetics, ( -rA) = kAcA,... 

The micromixing time has an exact definition in terms of the rate of decay of concentration fluctuations. The mixture fraction is defined in Chapter 5. 

One of the principal difficulties faced when employing Lagrangian micromixing models is the determination of tm based on properties of the turbulent flow fields. Researchers have thus attempted to use the universal nature of high-Reynolds-number isotropic turbulence to link tm to the turbulence time scales. For example, in the E-model (Baldyga and Bourne 1989) the engulfment rate essentially controls the rate of micromixing and is defined by... 

The results from (B.43) can be combined with the multi-environment presumed PDF models to define a new class of micromixing models that agree with the DQMOM result for inhomogeneous flows. Formally, (B.43) can be written as... 

For a reactive process, the reactants must be brought into contact by mixing before a reaction can occur. In a motionless mixer in turbulent flow, the pressure drop defines the turbulent energy dissipation rate, which then determines the macro-, meso-, and micromixing rates. 

In addition to defining maximum mixedness discussed above, Zwietering also generalized a measure of micromixing proposed by Dankwerts and defined the degree of segregation, J, as... 

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