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. 

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. 

In order to determine the mesomixing time, a least square fit of the 300 ml eontinuous ealeium oxalate (CaOx) preeipitation results for the number mean size and nueleation rate was performed. From these ealeulations, the faetor A in equation 8.15 was obtained as 17.7. Using the kinetie parameters determined from the laboratory-seale eontinuous experiments (Zauner, 1999), the large-seale experiments were simulated with the SFM and eompared with the experimental findings. 

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 characteristic time constant for mesomixing caused by turbulence is given by Baldyga and Bourne (1992) ... 

The characteristic time constant for mesomixing by the inertial-convective process (Corrsin, 1964) is given by... 

Combining the characteristic rate constant for engulfment and the characteristic time for mesomixing for the i-th species into the ratio... 

Inertial-convective mesomixing controls the process if M 1, micromixing limitations prevail if M 1, and both are of similar significance if M 1. 

Mesitylene, production from acetone, 1 164 Mesityl oxide, 14 589-590 characteristics of, 16 337 hydrogenation, 16 337-338 hydrogen peroxide treatment of, 16 338 Z-menthol from, 24 520 production of, 16 336-337 production from acetone, 1 164, 174 Mesogenic diols, 25 460 Mesogenic molecules, solids of, 15 82 Mesogens, 24 53, 54 Mesomixing, 16 683 Mesomorphic behavior, 24 53-54 Mesomorphic phase transitions, 15 102 Mesomorphism, 15 81. See also Liquid crystalline materials Mesophase pitch-based carbon fiber, 26 734-735... 

In chemical-reaction engineering, this process is sometimes referred to as mesomixing. 

The importance of including mesomixing in the definition of tm has been demonstrated using jet-mixer scale-up experiments by Baldyga et al. (1995). In these experiments, the micromixing rate was found to scale as... 

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. 

In motionless mixers, mesomixing time can be estimated from... 

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. 

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