For micromixing

In the SFM the reactor is divided into three zones two feed zones fj and (2 and the bulk b (Figure 8.1). The feed zones exchange mass with each other and with the bulk as depicted with the flow rates mi 2, i,3 and 2,3 respectively, according to the time constants characteristic for micromixing and mesomix-ing. As imperfect mixing leads to gradients of the concentrations in the reactor, different supersaturation levels in different compartments govern the precipitation rates, especially the rapid nucleation process. 

Micromixing Models. Hydrodynamic models have intrinsic levels of micromixing. Examples include laminar flow with or without diffusion and the axial dispersion model. Predictions from such models are used directly without explicit concern for micromixing. The residence time distribution corresponding to the models could be associated with a range of micromixing, but this would be inconsistent with the physical model. 

Characteristic time constant for micromixing calculated and measured... 

We develop the CFD equations using the DQMOM model for micromixing. Nevertheless, care must also be taken when using other micromixing models, including transported PDF methods. 

For higher-order reactions, the fluid-element concentrations no longer obey (1.9). Additional terms must be added to (1.9) in order to account for micromixing (i.e., local fluid-element interactions due to molecular diffusion). For the poorly micromixed PFR and the poorly micromixed CSTR, extensions of (1.9) can be employed with (1.14) to predict the outlet concentrations in the framework of RTD theory. For non-ideal reactors, extensions of RTD theory to model micromixing have been proposed in the CRE literature. (We will review some of these micromixing models below.) However, due to the non-uniqueness between a fluid element s concentrations and its age, micromixing models based on RTD theory are generally ad hoc and difficult to validate experimentally. 

Figure 5.15. Two examples of age-based micromixing models. In the top example, it is assumed that fluid particles remain segregated until the latest possible age. In the bottom example, the fluid particles mix at the earliest possible age. Numerous intermediate mixing schemes are possible, which would result in different predictions for micromixing-sensitive reactions. 

Owing to the sensitivity of the chemical source term to the shape of the composition PDF, the application of the second approach to model molecular mixing models in Section 6.6, a successful model for desirable properties. In addition, the Lagrangian correlation functions for each pair of scalars (( (fO fe) ) should agree with available DNS data.130 Some of these requirements (e.g., desirable property (ii)) require models that control the shape of /, and for these reasons the development of stochastic differential equations for micromixing is particularly difficult. 

The BMC/GIEM model for micromixing in non-premixed turbulent reacting flows. 

The status of micromixing is described by the parameter characteristic time constant for micromixing , fM, which can be simply called micromixing time. It represents the time needed to achieve completely uniform micromixing, and is correlated to the microscale A by... 

A number of experimental methods and mathematical models for micromixing have been proposed to date,... 

Bourne et al. LI61-163] presented a chemical method for micromixing measurement which has been widely accepted and applied. The core of the method is the use of the following parallel-competition reactions as the detection system ... 

Comparison between measured and theoretically predicted results for micromixing time... 

Figure 2.19 Manufactured structures by sandblasting for micromixers (a) Cavity for the setting up of a bar mixer.

Table 5.1 Glossiness of the imprinted color (GU = glossiness units) for micromixer-based and conventional Yellow 12 pigment manufacture.

In calculations of this kind, two different equations of mixing according to Dankwerts131 are usually used one for micromixing and one for complete segregation of flows. The imperfect reactor operation can be taken into account by means of the curve of residence time distribution and various empirical combinations of elementary reactor volumes based on it. 

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