Mixing micromixing processes

However, Equations 2.13 and 2.14 do not consider the molecular diffusion and viscous flow effects, which occur in the turbulent flow of small amounts of substance. That is why, if micromixing processes form the limiting stage, other estimating expressions should be used. The engulfment model is often used in this case [21, 22], with the following equation to estimate the characteristic mixing time ... 

The parameters which determine the characteristic mixing time are the linear flow rate V, device diameter D, diffuser opening angle y, as well as the kinematic viscosity V for micromixing processes. Practically, a single and available way of influencing the reaction mixture homogeneity, in a diffuser-confusor reactor, is the variation of its diameter and linear flow rate of reactants. 

Very recently, EW has been employed to trigger self-excited oscillations of millimetersized sessile droplets of water-glycerol mixtures [13]. During these oscillations, contact angles of the droplets have been found to vary periodically between 130° and 80°, with a frequency between 10 and 125 s. The resultant mixing of fluids within the droplets has been found to be two orders of magnitudes faster than the conventional chaotic micromixing processes. 

To describe the mixing process and its influence on the performance of chemical reactors, different models were developed [3,4]. Herein we discuss the influence of the micromixing process using the concept of segregation as proposed by Baldyga... 

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. 

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. 

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. 

Establishing the process sensitivity with respect to the above-mentioned factors is crucial for further scale-up considerations. If the sensitivity is low, a direct volume scale-up is allowed and the use of standard batch reactor configurations is permitted. However, many reactions are characterized by a large thermal effect and many molecules are very sensitive to process conditions on molecular scale (pH, temperature, concentrations, etc.). Such processes are much more difficult to scale up. Mixing can then become a very important factor influencing reactor performance for reactions where mixing times and reaction times are comparable, micromixing also becomes important. 

If the characteristic micromixing time scale is much smaller than Atf, then care must be taken in implementing tiie intra-cell processes. For example, several smaller time steps may be required to represent mixing and chemical reactions at each iteration. 

Meticulous observation of this mixing process (the slow disappearance of the Schlieren patterns as result of the disappearance of density differences), reveals that macromixing is quickly accomplished compared to the micromixing. This time-consuming process already takes place in... 

In contrast to this, when a solution of a substance is diluted, the molecules of the solute mix on a molecular scale with fresh solvent and essentially lose their identity in the process. This is called micromixing. In the same way solutions of two different solutes can undergo micromixing. 

For a reactive process, the reactants must be brought into contact by mixing before a reaction can occur. In a motionless mixer in turbulent flow, the pressure drop defines the turbulent energy dissipation rate, which then determines the macro-, meso-, and micromixing rates. 

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