Micromixing relationship

On the relationship between Lagrangian micromixing models and computational fluid dynamics. Chemical Engineering and Processing 37, 521-535. 

Ottino, J. M. (1980). Lamellar mixing models for structured chemical reactions and their relationship to statistical models macro- and micromixing and the problem of averages. 

The data determined for the micromixing time, rM, from various curves are illustrated in Fig. 10.13, which meet approximately the relationship below ... 

Similar to the case of the investigation on micromixing, the impinging velocity cannot be adjusted and controlled directly, but is done by changing the rotary speed of the propellers, N. Prior to all the measurements the curve describing the relationship between (> and N was calibrated with the same method as that used in Ref. [110], and the results are shown in Fig. 11.2, in which the curve is, in turn, used for conversion between the rotary speed and the impinging velocity in the data treatment. The curve in Fig. 11.2 is essentially the same as that shown in Fig. 10.9 but with some differences in specific data. The existence of such differences is natural, because the shape of the propeller paddle and particularly the width of the gap between the paddle of the propeller and the drawing tube have a fundamental influence on the flow rate drawn by the propeller, while errors in mechanical manufacture are also unavoidable.. 

The pressure fluctuation must affect the condition of the micromixing in the device and thus promote process kinetics. The results to be introduced in the next chapter will provide the experimental evidence for this topic. Unfortunately, a quantitative description for such influences cannot as yet be made because of the complexity of the problems involved, and further investigations are certainly needed in order to make the relationships clear, particularly the influence of pressure fluctuation on micromixing. 

Depending on the reactions, results can be very different, and it is almost impossible to predict quantitatively the effect of improved mixing by rules of thumb. Few studies have addressed the relationship between the micromixer geometry and the product composition of multiple reactions and, in that sense, the work carried out by Aoki et al. [68] is pioneering and interesting, because it shows all the complexity of this topic. Even if it is undeniable that micromixers have brought considerable improvements in reactions control, one should encourage the user to be careful in the interpretation and the use of the experimental results of product selectivity. 

This equivalence also holds for predicting chemical conversion as can be seen in Fig. 12 where reaction extent was calculated for a second order reaction with unmixed feedstreams. The agreement is excellent. More generally, equivalence relationships can be established between all one-parameter micromixing models. For instance, the various models cited above yield approximately the same results under the equivalence conditions ... 

Example 2-4b Scale-up with Exact Geometric Similarity. In this example we consider the relationship between the spectrum of velocity fluctuations and the micromixing scales. At the lab scale, a T = 0.25 m vessel is used to formulate a homogeneous reaction in an aqueous phase. The fully baffled vessel is equipped with a Rushton turbine impeller of D = T/2 at C = T/3 with Np = 5.0. The... 

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