NJS  ¼ Sn0:1d0:2

0:45

0:13

—0:85

p   ðgDr=rLÞ X D

(15)

pumping hydrofoils in a fully baffled STR are the most

effective and achieve drawdown without ingesting air [47].

S is a dimensionless parameter, independent of scale, but related to the system geometry. For a distribution of particle sizes, the mass mean should be used [39]. Recently, an extension of earlier NJS correlations, each based on Kolmo- gorov’s theory has been produced especially for down pumping hydrofoil impellers [41]:

In addition, the rate of solids addition must be controlled.

A new and important area of application involving solid- liquid systems is the dispersion of nano-particles. After they have been manufactured, nanoparticles generally agglomer- ate and need to be re-dispersed for the desirable properties associated with their very small size to be exhibited. Most impellers are only able to produce a small reduction in size

because  of  the  strong  forces  holding  the    agglomerates

together. The use of rotor-stator mixers [48] and saw-tooth impellers [26] in an STR are relatively effective, in each case

The accuracy of the two correlations is similar, but the

advantage of the more recent one is that it only needs the power number Po, which, though it changes with relative impeller size and clearance, it does so much less than S and is more readily available. The other difference that arises

from the two equations is that with the latter, ¯eT;JS is constant on scale-up whilst with the former it falls. Where particles of different size and density are present, NJS behaves in a com- plex manner and cannot at present be predicted [42].

At high solids concentration at NJS, a clear liquid layer may form at the top. This happens even at AR = ~1, be- cause it is difficult to convey the solids up the tank, appear- ing as a cloud often limited to only 0.5H to 0.6H at NJS [43]. It is generally more energy efficient to use a second impeller to lift the cloud height compared to increasing the stirrer speed, especially at AR > 1. The clear layer above the cloud is a region of very low specific energy dissipation and as such is very poorly micro- and macromixed so that in semi- batch processes a reactant added to it would produce enhanced levels of unwanted by-products [44]. Very re- cently, an empirical equation for predicting cloud height has been proposed [45].

A second upper impeller is also an effective way of achieving a more constant vertical distribution of solids in the STR. An even distribution and an approximation to iso- kinetic withdrawal is important when solids are being with- drawn from a batch vessel to feed to a centrifuge, e.g., in order to keep a steady flow of constant concentration between the two. It is also important in continuous process- ing where, if the concentration leaving the STR is less than that within it, build-up of solids in the STR occurs, which may lead to impeller erosion or even filling the tank with solids [39]. Using a down-pointing cone as the base of   the

rotating at very high speeds to give extremely large eT;max. In general, higher energy intensive devices than STRs are required for deagglomeration [49].

4.3 Gas-Liquid and Boiling Systems

The first impeller specifically recommended (1950s) for gas dispersion in STRs was the disc turbine with 6 flat blades, now generally called the Rushton turbine [12]. However, when gas is sparged beneath the disc (Fig. 4), the power drawn by that impeller typically falls by about 50 to 60 %, a fall about 5 times greater than that associated with the decrease in density of the dispersion based on Eq. (3). The reason for this fall, the formation of large gas-filled cavities behind the flat blades, was only established in 1974 [50] when it was also shown to be much less if the blades were made concave with an included angle of 120°. A further increase in included angle to 180° is even more effective and led to the development of the Chemineer CD6 impeller (Fig. 4b) in the late 1980s [51]. Many similar impellers are now available [26, 51, 52], the change in relative power draw arising because large cavity formation is suppressed [53].