Micromixing

There is another way to solve the problem of disguised chemical selectivity of extremely fast competitive reactions, which does not need to slow the reactions, i.e. micromixing, based on microstructures that makes the diffusion path very short. 

With the advancement of microfabrication technology to make various kinds of microstructures, microdevices for chemical reactions have been developed. Micro-fabricated devices for chemical reactions are generally called microreactors and they are expected to produce a revolutionary change in chemical synthesis. 

The principle and structures of micromixers will be discussed in Chapter 7. In the following sections, we focus on an example of the effectiveness of micromixing for conducting extremely fast reactions with a high level of control of product selectivity, with the emphasis on its principle. 

7 Friedel-Crafts Alkylation Using an N-Acyliminium Ion Pool 

In a previous section (Section 6.1.3), we discussed the problem of disguised chemical selectivity for extremely fast competitive consecutive reactions. This problem could be solved using micromixers, in which the mixing takes place in a very short period by virtue of a small diffusion path caused by the microstructure. Friedel-Crafts alkylation using N-acyliminium ion pools provides a nice example of the effectiveness of micromixing. 

The experimental set-up for the measurement and a typical result are shown in Fig. 3.8. A measuring device is installed in a reactor. The device is sensitive to a change of some property conductivity, pH, color, optical density, Schlieren methods, O2, T, radio pill, fluorimetry, radioactivity (Beyeler et al., 1981,1983 Bryant and Sadeghzadeh, 1979 Einsele, 1976b Kappel, 1976 Kipke, 1984 Middleton, 1979 Moser, 1987 Schneider et al. 1986 Zlokarnik, 1967). The response function of such a measurement often has the typical appearance shown in Fig. 3.8. 

The so-called degree of mixing, m, is sufficient to determine the mixing time, necessary to reach a particular value of m. Representing the asymptotic value of the concentration by c, the degree of mixing m can be defined with Equ. 3.17 

The mixing time, which was primarily intended as a measurement for discontinuous stirred reactors, can also be applied in the case of loop reactors. As shown in Fig. 3.8b the deviation from can be taken as a direct measure in the definition of an inhomogeneity, / (Lehnert, 1972). 

It should be noted that the RTD character of a whole recycle reactor system, quantified with BOt j, depends not only on the recycle ratio r, but also on BOint, the internal RTD characteristic of the reactor (Moser, 1985a). 

In practice, situations are even more complicated due to the simultaneous effect of r on Botot and BOi j, so that computer simulations fail to describe experiments as they operate with constant Boj j. Experimental evaluation of BOint from RTD functions shows that the value goes through a maximum at about r — 10, when using a tubular reactor with recycling (Moser and Steiner, 1975a,b). 

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Macromixing vs Micromixing. Mixing in an agitated tank is considered to occur at two levels, macromixing and micromixing. 

Macromixing is estabflshed by the mean convective flow pattern. The flow is divided into different circulation loops or zones created by the mean flow field. The material is exchanged between zones, increasing homogeneity. Micromixing, on the other hand, occurs by turbulent diffusion. Each circulation zone is further divided into a series of back-mixed or plug flow cells between which complete intermingling of molecules takes place. 

Micromixing Mixing among molecules of different ages (i.e., mixing between macrofluid clumps). Mixing on a scale smaller tlian tlie minimum eddy size or minimum striation diickness by molecular diffusion. 

Guichardon etal. (1994) studied the energy dissipation in liquid-solid suspensions and did not observe any effect of the particles on micromixing for solids concentrations up to 5 per cent. Precipitation experiments in research are often carried out at solids concentrations in the range from 0.1 to 5 per cent. Therefore, the stirred tank can then be modelled as a single-phase isothermal system, i.e. only the hydrodynamics of the reactor are simulated. At higher slurry densities, however, the interaction of the solids with the flow must be taken into account. 

As the flow of a reacting fluid through a reactor is a very complex process, idealized chemical engineering models are useful in simplifying the interaction of the flow pattern with the chemical reaction. These interactions take place on different scales, ranging from the macroscopic scale (macromixing) to the microscopic scale (micromixing). 

In what follows, both macromixing and micromixing models will be introduced and a compartmental mixing model, the segregated feed model (SFM), will be discussed in detail. It will be used in Chapter 8 to model the influence of the hydrodynamics on a meso- and microscale on continuous and semibatch precipitation where using CFD, diffusive and convective mixing parameters in the reactor are determined. 

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. 

Using the SFM, the influence of micromixing and mesomixing on the precipitation process and properties of the precipitate can be investigated. Mass and population balances can be applied to the individual compartments and to the overall reactor accounting for different levels of supersaturation in different zones of the reactor. 

The failure of conventional criteria may be due to the fact that it is not only one mixing process which can be limiting, rather for example an interplay of micromixing and mesomixing can influence the kinetic rates. Thus, by scaling up with constant micromixing times on different scales, the mesomixing times cannot be kept constant but will differ, and consequently the precipitation rates (e.g. nucleation rates) will tend to deviate with scale-up. 

The conventional scale-up criteria scale-up with constant stirrer speed , scale-up with constant tip speed and scale-up with constant specific energy input are all based on the assumption that only one mixing process is limiting. If, for example, the specific energy input is kept constant with scale-up, the same micromixing behaviour could be expected on different scales. The mesomixing time, however, will change with scale-up as a result, the kinetic rates and particle properties will be different and scale-up will fail. 

In order to account for both micromixing and mesomixing effects, a mixing model for precipitation based on the SFM has been developed and applied to continuous and semibatch precipitation. Establishing a network of ideally macromixed reactors if macromixing plays a dominant role can extend the model. The methodology of how to scale up a precipitation process is depicted in Figure 8.8. 

Each stage of particle formation is controlled variously by the type of reactor, i.e. gas-liquid contacting apparatus. Gas-liquid mass transfer phenomena determine the level of solute supersaturation and its spatial distribution in the liquid phase the counterpart role in liquid-liquid reaction systems may be played by micromixing phenomena. The agglomeration and subsequent ageing processes are likely to be affected by the flow dynamics such as motion of the suspension of solids and the fluid shear stress distribution. Thus, the choice of reactor is of substantial importance for the tailoring of product quality as well as for production efficiency. 

The reactor has been successfully used in the case of forced precipitation of copper and calcium oxalates (Jongen etal., 1996 Vacassy etal., 1998 Donnet etal., 1999), calcium carbonate (Vacassy etal., 1998) and mixed yttrium-barium oxalates (Jongen etal., 1999). This process is also well adapted for studying the effects of the mixing conditions on the chemical selectivity in precipitation (Donnet etal., 2000). When using forced precipitation, the mixing step is of key importance (Schenk etal., 2001), since it affects the initial supersaturation level and hence the nucleation kinetics. A typical micromixer is shown in Figure 8.35. 

Baldyga, J. and Bourne, J.R., 1984b. A fluid mechanical approach to turbulent mixing and chemical reaction. Part II Micromixing in the light of turbulence theory. Chemical Engineering Communications, 28, 243-258. 

Baldyga, J. and Poherecki, R., 1995. Turbulent micromixing in chemical reactors - a review. Chemical Engineering Journal, 58, 183-195. 

Bourne, J.R., 1985. Micromixing revisited. Institution of Chemical Engineers Symposium Series, 87(ISCRE 8), 797-813. 

Bourne, J.R. and Yu, S., 1994. Investigation of micromixing in stirred tank reactors using parallel reactions. Industrial and Engineering Chemistry Research, 33, 41-55. 

Chen, J., Zheng, C. and Chen, G., 1996. Interaction of macro- and micromixing on particle size distribution in reactive precipitation. Chemical Engineering Science, 51, 1957-1966. 

David, R. and Marcant, B., 1994. Prediction of micromixing effects in precipitation Case of double-jet precipitators. American Institution of Chemical Engineers Journal, 40, 424M32. 

Fournier, M.-C., Falk, L. and Villermaux, J., 1996. A new parallel competing reaction system for assessing micromixing efficiency - experimental approach. Chemical Engineering Science, 51, 5053-5064. 

Garside, J. and Tavare, N.S., 1985. Mixing, reaction and precipitation limits of micromixing in an MSMPR crystallizer. Chemical Engineering Science, 40, 1485-1493. 

Geisler, R., Mersmann, A. and Voit, H., 1991. Macro- and micromixing in stirred tanks. International Chemical Engineering, 31, 642-653. 

Guichardon, P., Falk, L., Fournier, M.C. and Villermaux, J., 1994. Study of micromixing in a liquid-solid suspension in a stirred reactor. American Institute of Chemical Engineers Symposium Series, 299, 123-130. 

Harada, M., Arima, K., Eguchi, W. and Nagata, S., 1962. Micromixing in a continuous flow reactor. Memoir of the Faculty of Engineering, Kyoto University, Japan, 24, 431. 

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