Micromixers chemical methods

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 ... 

A New Chemical Method for the Study of Local Micromixing Conditions in Industrial Stirred Tanks... 

Experimentally, many authors (see (J -6)) have tried to analyze micromixing phenomena using as an indicator the extent or yield of model reactions whose kinetics were known a priori. However to our knowledge, if one excepts the work of Bourne et al. O), the chemical method has not yet been systematically used to investigate the local state of micromixing at different points in a... 

For the first two cases Da << 1 (slow reactions) and Da >> 1 (very fast reactions) adequate closure models are available in many commercial CFD codes. For the third case, where the time scale for chemical conversion approximately equals the time scale for turbulent micromixing, moment methods are inappropriate and other methods should be used. In this situation the reactor performance may be significantly affected by mixing efficiency. Here the engineer is faced with the difficult problem of predicting the overall conversion and/or selectivity of the chemical process. In the last three decades this problem has received considerable attention in three scientific areas, namely, chemical reaction engineering, fluid mechanics and combustion, and various approaches have been followed. 

Barth OLE ).P., David R., Villermaux J, A new chemical method for the study of local micromixing conditions in industrial stirred tanks, ACS Symp. Ser. 196 (1982), p. 545-554... 

Experimental characterization of the mixing quaUty in conventional stirred tank reactors, as well as in micromixers, is an important step for the proper comprehension of the performance of chemical reactors. To identify interactions between mixing and chemical reactions and quantify them, a variety of physical and chemical methods have been developed, whose application to a given mixer may either be easy or may require appropriate adaptations to obtain valuable measurements. The next section gives a brief overview of existing methods. 

Barthole, J., R. David, and J. Villermaux (1982). A New Chemical Method for the Study of Local Micromixing Conditions in Industrial Stirred Tanks, ISCRE, Boston. 

The CFD model developed above is an example of a moment closure. Unfortunately, when applied to reacting scalars such as those considered in Section III, moment closures for the chemical source term are not usually accurate (Fox, 2003). An alternative approach that yields the same moments can be formulated in terms of a presumed PDF method (Fox, 1998). Here we will consider only the simplest version of a multi-environment micromixing model. Readers interested in further details on other versions of the model can consult Wang and Fox (2004). 

Multi-environment presumed PDF models can also be easily extended to treat cases with more than two feed streams. For example, a four-environment model for a flow with three feed streams is shown in Fig. 5.24. For this flow, the mixture-fraction vector will have two components, 2 and 22- The micromixing functions should thus be selected to agree with the variance transport equations for both components. However, in comparison with multi-variable presumed PDF methods for the mixture-fraction vector (see Section 5.3), the implementation of multi-environment presumed PDF models in CFD calculations of chemical reactors with multiple feed streams is much simpler. 

Of all of the methods reviewed thus far in this book, only DNS and the linear-eddy model require no closure for the molecular-diffusion term or the chemical source term in the scalar transport equation. However, we have seen that both methods are computationally expensive for three-dimensional inhomogeneous flows of practical interest. For all of the other methods, closures are needed for either scalar mixing or the chemical source term. For example, classical micromixing models treat chemical reactions exactly, but the fluid dynamics are overly simplified. The extension to multi-scalar presumed PDFs comes the closest to providing a flexible model for inhomogeneous turbulent reacting flows. Nevertheless, the presumed form of the joint scalar PDF in terms of a finite collection of delta functions may be inadequate for complex chemistry. The next step - computing the shape of the joint scalar PDF from its transport equation - comprises transported PDF methods and is discussed in detail in the next chapter. Some of the properties of transported PDF methods are listed here. 

Transported PDF methods combine an exact treatment of chemical reactions with a closure for the turbulence field. (Transported PDF methods can also be combined with LES.) They do so by solving a balance equation for the joint one-point, velocity, composition PDF wherein the chemical-reaction terms are in closed form. In this respect, transported PDF methods are similar to micromixing models. 

Unlike presumed PDF methods, transported PDF methods do not require a priori knowledge of the joint PDF. The effect of chemical reactions on the joint PDF is treated exactly. The key modeled term in transported PDF methods is the molecular mixing term (i.e., the micromixing term), which describes how molecular diffusion modifies the shape of the joint PDF. 

The method, which makes use of simple and cheap chemicals, is amenable to a quantitative exploitation for the determination of micromixing times. 

The material and process parameters, which govern the micro-mixing efficiency can only be determined by the selectivity of extremely fast chemical reactions, whose progress (conversion and yield) can be simply and rapidly monitored. Consequently the application of chemical reactions as probes of molecular resolution [94] represents the most sensitive investigating method for characterizing micromixing. There are a number of comprehensive reviews of this technique [13, 40, 94, 565]. 

Numerical simulations of styrene free-radical polymerization in micro-flow systems have been reported. The simulations were carried out for three model devices, namely, an interdigital multilamination micromixer, a Superfocus interdigital micromixer, and a simple T-junction. The simulation method used allows the simultaneous solving of partial differential equations resulting from the hydrodynamics, and thermal and mass transfer (convection, diffusion and chemical reaction). 

It is important to recognize the limitations of the RTD method. Residence time distribution does not discern between a reacting fluid that is mixed on the molecular level (micromixing) and one that flows in segregated blobs. Also, the same RTD is obtained when the reacting fluid is mixed near the entrance or near the exit. Both of these factors affect the chemical reactions and the performance of the reactor. 

---