An understanding of the performance of extraction equipment is furthered by an understanding of what may be going on inside individual drops. With the assumption of transfer of a solute A from a dispersed feed phase into a continuous solvent, as shown in Fig. 13, a concentration profile across the interface would appear to have a discontinuity (Fig. 14). The discontinuity is a consequence of the distribution coefficient, and reflects the general practice of choosing a solvent which has a greater preference for the solute than the feed phase has. If activities instead of concentrations were used, there would be no discontinuity at the interface.
Transfer of solute across the interface can be assumed to be controlled by what happens through the immobilized films on both sides ofthe interface. Handles and Baron[5J have presented generalized correlations for the calculation of the individual inside and outside coefficients for mass transfer across these films.
Figure 13. Drop mechanics.
Figure 14. Solute concentration at the interface.
Small drops lead to more transfer area and better extraction, but to slower settling and less capacity. Thus, selection of extraction equipment frequently involves a compromise choice balancing efficiency against capacity.
The terminal velocity of liquid drops is the same as solid spheres when the diameter is small. The drag coefficient versus Reynold's number can be recalculated to provide a diameter-free ordinate versus a velocity-free abscissa to facilitate direct solution, as shown in Fig. 15. With drops, a maximum velocity is attained, and this maximum has been correlated with a parameter based on physical properties of the system.
The practical sequence of this phenomenon in column extraction is illustrated in Fig. 16. Drops larger than d* won't travel any faster, so there is no capacity gain, and they have less specific area, so there will be an efficiency loss. Drops smaller than d* will result in more extraction by providing more transfer area and a longer contact time, but at the potential expense of lower capacity.
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