Also in the 1970s, the different two-phase flow patterns for Rushton turbines were codified [54], the most important being the transition from flooded  to  loaded  conditions (Fig. 9). The speed required to produce this transition NF can be determined from

FlG;F ¼ 30ðD=TÞ3:5FrF (17)

where FlG,F = QG/NFD3 (gas flow number) and FrF = NFD2/g

based on the swept diameter. It has been found that Eq. (17)

Figure  9.   The flooding

(a) to loading (b) transi- tion in a gas-sparged re- actor with a radial flow stirrer (from [12] with per- mission).

essentially predicts NF for other concave blade, radial flow impellers, all of which have a lower power number based on the swept impeller diameter than the Rushton  turbine. Thus, for simple retrofitting at equal speed, specific power and torque, concave impellers need to be of larger D/T ratio. Thus, from Eq. (17), they can disperse more gas before flooding.

Such considerations are very important, because in 1979 van’t Riet [55] showed that within the accuracy with which it can be determined, the gas-liquid mass transfer coefficient kLa is independent of impeller type, and can be determined from

up-flowing air. It was later shown that the improved blend- ing was also achieved with similar multiple impellers pump- ing upwards, but without instabilities because under these conditions the stirring direction and the gas flow combine to enhance the liquid flow. In addition, there is only a small loss of power on aeration and a high gas handling capacity (both similar to that found with concave radial flow impel- lers). Such multiple up-pumping impellers [57, 58] (often with a concave blade impeller as the lower one [46, 51]) is often the system of choice.

Up-pumping, high solidity ratio impellers also suspend solids very efficiently in 3-phase (g-s-l) systems, [59] such as bio-leaching and catalytic hydrogenation. The latter ex- ample is also often undertaken in so-called dead-end reac- tors. In these cases, the stirrers are often of the self-inducing type where a hollow shaft is used with vent holes above the liquid and with gas being sucked down through a hollow impeller by the low pressure behind the blades (Fig. 11). Above a certain scale, such impellers do not work because the low pressure behind the blades is not sufficient to over- come the static head [60].

where ¯eT;g is the mean specific energy dissipation rate from agitation under sparged conditions and vS is the superficial gas velocity (= 4QG/pT2). There is some debate as to whether ¯eT from the sparging itself should be included  and a range of values have been published for a and b (typically

~0.5 ± 0.1).   With   increasing    viscosity,    kLa    falls (kLa / m~0:5) though the exponent on viscosity is less-well established [12]. The value of A (which is dimensional), is more variable and is very sensitive to the composition of the liquid phase, antifoam reducing it and solutes and alco- hols generally increasing it as the latter repress coalescence, thereby reducing bubble size and enhancing their specific surface area a. Most importantly, Eq. (18) explains why con- cave blade impellers are now the radial impellers of choice for gas-liquid systems, especially with STRs of AR » 1.

However, in stirred commercial scale aerobic bioreactors, generally AR is > 1, typically ~2. Therefore, multiple impel- lers (typically 2 or 3) are used and as discussed earlier, the problem with such configurations on the large scale is the greatly enhanced mixing time. Thus, in the 1980s, wide- blade, down-pumping hydrofoil impellers of high solidity ratio (= plan area of stirrer blades/plan area swept out by the agitator) of the type shown in Fig. 5b were introduced [46] and shown to improve bioperformance [56]. Unfortu- nately, this improvement in mixing time was associated with mechanical instability issues associated with the oppo- sition in flows from the down-pumping impellers and    the