Micromixers mixing efficiency

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. 

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]. 

It is important to note that mixing efficiency strongly depends on flow rate and that each micromixer has its characteristic flow rate range for efficient mixing. Therefore, we have to choose an appropriate flow rate to achieve fast mixing. If the flow rate is fixed, we have to choose a suitable micromixer at that flow rate. 

Therefore, the observed selectivity is the disguised chemical selectivity caused by an extremely fast reaction. The reaction using a microflow system, however, gives rise to a dramatic increase in the product selectivity. The monoalkylation product was obtained in excellent selectivity and the amount of dialkylation product was very small. In this case, a solution of the N-acyliminium ion and that of trimethoxy-benzene are introduced to a multilamination-type micromixer at —78°C and the product solution leaving the device was immediately quenched with triethylamine in order to avoid the consecutive reactions. Extremely fast 1 1 mixing using the micromixer and efficient heat transfer in the microflow system seem to be responsible for the dramatic increase in the product selectivity. 

The caterpillar micromixer consists of a number of serial oriented unit cells that repeat and complete the same type of mixing process. Eight such cells are serially combined in the standard version that is commercially available. Dependent on the mixing problem, however, more or less units may be appropriate, which, especially for production, needs to be optimized to reduce the pressure drop to the limit really needed and for efficient power dissipation. For this reason, caterpillar devices (600 pm width and depth) with 0, 2, 4, 6, and 8 mixing cells have been manufactured to test mixing efficiency by a standardized protocol (Fig. 6.3) ]27]. 

Evidently, mixing efficiency improves strongly with miniaturization of the mixing elements for the caterpillar micromixer [27]. For all three mixers tested, mixing efficiency improves with increasing flow rate, which is due to more intense recirculation patterns and thus interfacial stretching. The slope is steeper for the smaller caterpillar micromixers, i.e., the 800-pm device shows a more pronounced increase of mixing efficiency with flow rate. 

The effect of the flow rate on molecular weight distribution (Table 1, runs 4-6) indicates the importance of mixing, because it is known that mixing efficiency decreases with a decrease in the flow rate in the micromixer [65]. Reaction temperature is also important for controlling molecular weight distribution, as demonstrated by an increase in with an increase in temperature (runs 4... 

An array of nanochannels has been used in the microfluidic micromixers to enhance the mixing process [14]. Figure 8 illustrates the optical image of the proposed micromixer by Yu and colleagues. The nonequilibrium electrokinetic effects at the connections of the microchannels and the nanochannels (ion emichment-depletion) cause circulating flow in the system. These circulations boost the mixing efficiency of the system. 

The present chapter aims to be complementary to the studies and reviews already published to present theoretical basis elements for the understanding of mixing principles in laminar flows, mainly developed in micromixers. Among different characterization techniques of mixing efficiency, this chapter more specifically focuses on the chemical test method, called the Villermaux-Dushman reaction, that we have developed over many years and which is named in memory of Professor Jacques Villermaux. It will be shown how to obtain the mixing time and how to relate it to operating parameters such as the Reynolds number of the flow and the specific power dissipation per unit mass of fluid. A non-exhaustive comparison of several micromixers will be presented. 

This expression shows that the mixing time is in practice almost inversely proportional to the mixing efficiency. For predetermined channel size and fluid velocity, the design of the internal structure of a micromixer is then primordial to maximize the mixing efficiency, i.e. to rniriimize the mixing time. 

Many authors have adapted their own concentration protocol of the Villermaux-Dushman method so that it is almost impossible to compare the performances of the studied micromixers simply by the confrontation of the segregation indices. The best way to propose a comparative study is to consider mixing times which are independent of the chemical conditions. Below we present a detailed comparison of the mixing times in different mixers. The theoretical developments presented previously are used to propose an interpretation of experimental data versus the Reynolds number and the power dissipation. From the confrontation with theoretical values, the energetic mixing efficiency in micromixers can be estimated. 

Figure 6.9 Evolution of the mixing time in different micromixers versus specific power dissipation. Influence of the energetic mixing efficiency.

It has been shown in this chapter how to characterize mixing efficiency in micromixers and particularly how to relate mixing time to relevant operating parameters such as the Peclet number and the specific power dissipation. In spite of a low mixing energetic efficiency, micromixers can mix in a few milliseconds, much faster than conventional mixers. 

There are mainly three characteristic features of micromixers that might be effective for the enhancement of chemical selectivity fast mixing, efficient heat exchange (which has not been considered here) and precise residence time control, although it is difficult to separate completely the effects of these three factors on the outcome of chemical reactions. 

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