Mixing mesomixing

Several mesomixing and mieromixing models have been proposed to deseribe the influenee of mixing on ehemieal reaetions on the meso- and moleeular seale. Most of them fall into one of the three eategories diseussed below (Villermaux and Falk, 1994). 

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. 

Torbaeke and Rasmuson (2001) report the empirieal influenee of different seales of mixing in reaetion erystallization of benzole aeid in a loop reaetor. The authors infer that the proeess is mainly governed by mesomixing in terms of liquid eireulation rate but find anomalous behaviour in respeet of feed pipe diameter. 

For liquid-liquid crystal precipitation systems where the particle formation processes are fast, mixing becomes an important determiner of performance with a subtle interplay of micro- and mesomixing, which changes as scale of... 

The composition PDF thus evolves by convective transport in real space due to the mean velocity (macromixing), by convective transport in real space due to the scalar-conditioned velocity fluctuations (mesomixing), and by transport in composition space due to molecular mixing (micromixing) and chemical reactions. Note that any of the molecular mixing models to be discussed in Section 6.6 can be used to close the micromixing term. The chemical source term is closed thus, only the mesomixing term requires a new model. 

The mesomixing time t , is the time for "significant mixing of an incoming jet of feed liquid with the surrounding fluid. A formula for estimating f , is the time for turbulent diffusion to transport liquid over a distance equal to the feed pipe diameter d0. 

The importance of feed rate on yield for a mixing-sensitive reaction was demonstrated in Ref. ". The addition time in a semibatch reaction is often increased on scale-up because of heat transfer limitations. In the case of a mixing-sensitive reaction, the time of addition is increased on scale-up to compensate for the increase in blend time and to maintain the expected molar ratio at the feed point. The minimum feed time to achieve the expected yield is, therefore, scale dependent. Feed times that are too short will result in mesomixing conditions and reduced yield. 

Mesomixing effects occur in stirred vessels when the reagent(s) feed rate is faster than the local mixing rate, resulting in a plume of reagent concentration that is not yet mixed to... 

The characteristic time of mesomixing (the mixing carried out via the exchange between large and small (internal) vortexes is calculated in the formula) ... 

Figure 2.10 Characteristic times of turbulent mixing Tfufi, (I) micromixing T icro (3-6) and mesomixing (2) dependence on a reaction mixture flow rate V. Dynamic viscosity values 0.001 (3), 1 (4), 10 (5), and 50 (6) Pa-s. = 0.025 m,...

Characteristic time of mesomixing The amount of reacted monomer in the / zone Characteristic time of micromixing Reactants mixing duration... 

---