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Figure 10. A self-induc- ing agitator for a dead- end gas-liquid STR. The ar- row indicates a hole in
the hollow shaft in the head space through which gas is sucked to be discharged into the liquid (from [12] with permis- sion).
Very recently, an understanding of other gas-liquid sys- tems, boiling [61] and sparged hot systems [62] has emerged from the work of Smith, Gao et al., but the details are beyond the scope of this article.
4.4 Liquid-Liquid Systems
In liquid-liquid systems, the industrial processes which re- late to them, such as solvent extraction or the production of emulsions, are very dependent on drop size. Thus, much of
the research related to them has concentrated on drop size prediction which is complex because it depends on both drop break-up and on coalescence, the latter being particu- larly important at higher dispersed phase fractions. The outstanding work [11] that established the analysis of invis- cid drop break-up in turbulent systems was by Hinze [63] in 1955. It was based on Kolmogorov isotropic turbulence concepts [15] and in the inertial sub-range leads, after some manipulation, to the equation
is the best. In general, an equation which can be developed from Eq. (19), has been modified to give
d32=D ¼ Adð1 þ BdFÞWe—0:6 (21)
where F is the volume fraction of the dispersed phase and We, the Weber number. Ad depends on the impeller type, and Bd on the coalescence tendency of the drops which in surfactant free systems has been reported to range from ~3 to ~20 [69]. In general, for any given liquid-liquid system,
the outcome is that in STRs, so-called high shea’ Rushton
where dp;max is the maximum stable drop size and s is the interfacial tension. The drop size distribution is self-similar [64] when normalized by the Sauter mean size d32. Eq. (19) was used by Davies [65] to show that if eT;max was known, then the drop size in coalescence-repressed systems from a wide variety of equipment could all be correlated by it, indi- cating, e.g., that normally rotor-stator mixers would give smaller drops than other impellers. The applicability of the theory to rotor-stator mixers in batch STRs has also been demonstrated [66]. A similar early paper for viscous drops [67] showed
turbines actually give larger drops than other impellers, even so-called low shear impellers such as the Chemineer HE3 (Fig. 5) [70].
One of the reasons that the analysis of second order coa- lescing systems is so difficult is because there are also aniso- tropic macro-scale flow phenomena impacting on it as well as isotropic turbulence [69]. The second is because aqueous
(A) in organic (O) systems (A/O) behave differently from O/A. At concentrations greater than approximately 0.2 vol- ume fraction, O is incorporated into A drops (drops-in- drops) to give O/A/O dispersions but the opposite does not occur (Fig. 11). The reason for this difference is not clear,
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but as a result, at the same volume fraction, A drops are big- ger than O. At higher volume fractions, coalescence domi-
where md is the drop viscosity. Though both Eq. (19) and
(20) neglect coalescence, in many high concentration emul-
sions, surfactants are added to prevent it (as well as to lower s). Hence, they provide useful guidelines for practitioners making such products.
The first papers addressing the second order process of coalescence were by Tavlarides and co-workers [68] who used Kolmogorov’s theory and population balance concepts to predict drop sizes under such conditions. Since then, many papers have extended their theory. However, it has proven very difficult to establish which of the many theories