time very close to the feed point that is decisive-micromix- ing. The micromixing time is dependent on the local eT val- ue which is ¯eT close to the impeller and  ¯eT  near  the surface. Thus, the feed point is very important if excessive unwanted  by-products  are  to  be  avoided  (Fig. 8). Model

reactions have been developed to help address micromixing issues for competitive reactions [35], listed as outstanding book in [11]. These reactions show that there are a wide range of feed times where the amount of byproduct pro- duced does not change. However, on scale-up, since the vol- ume of reactants increases with cube of the length scale and the area of feed pipes with the square, the feed velocity into the semi-batch reactor may be so fast that the reactions are not completed close to the feed point. The same thing hap- pens at any scale if the feed time is too short. This phenom- enon is called mesomixing and leads to increasing byprod- uct formation with increasing flow rate (Fig. 8). It is a major scale-up problem often requiring longer semi-batch  times to prevent it [35]. There is insufficient room for detail here, but Bourne, who pioneered such studies starting in the late 1970s, has described excellent experimental protocols for handling such issues [36].

Figure 8. Generic indication of by-product formation  with competi- tive fast chemical reactions.

Generally feeding into the region of eT;max very close to the impeller improves mixing performance, whether for mi- cromixing [35 – 37], mesomixing [35, 36] or macromixing [33]. It is also recommended to control non-linear quasi- chemical reactions, such as pH and primary heterogeneous nucleation (the latter for crystallization and precipitation processes). At the other end of the feeding timescale, if the feed velocity is too slow (usually associated with a large feed

pipe) and unfortunately, especially if the feed is in a region of eT;max where local turbulence and velocities are high, the reactant in the vessel may enter the feed pipe so that the re- actions actually occur at very low eT. Again, high by-prod- uct formation can occur. Little work has been done on this, but some guidelines are available [38].

4.2 Solid-Liquid Systems

Solid particles are often found in STRs either to aid, or as products of different processes. Typical examples are crys- tallization, catalytic reactions, cell culture on microcarriers, etc. and the rate of mass transfer between the phases is criti- cal because any reaction involved cannot proceed faster than that [39]. For the whole surface area to be available for mass transfer, the agitation speed must give full suspension

NJS, and further increases in speed produce only a small increase in overall rate at best. Indeed, if the overall rate is reaction-controlled, it is zero. However, ¯eT;JS is very depen- dent on agitator choice and as was shown by Zwietering in 1958 [40], another classic paper according to [11], down pumping impellers are best, especially axial flow hydrofoils (e.g., Fig. 5a) of D/T = ~0.4 at a clearance, C/T = ~0.2. Op- erating the STR just above NJS  is generally    recommended

for batch and semi-batch processes and for many stirrers, it can be calculated from [40]:

tank makes removal easy but suspension during processing difficult. A better solution is to use a second small stirrer, called a tickler, such as the Lightnin’ KT-3 (D/T = 0.2) close to a dished base (C/T = 0.03 to 0.016) and contoured to be parallel to it [46].

Much less work has been undertaken on the ingestion of floating solids, which requires higher ¯eT, especially in semi- batch processing with the addition of fine, difficult to wet solids when air can be trapped in the interstices of the par- ticles. It may happen even when the actual particles are denser  than  water.  It  has  recently  been  shown  that  up-