U L

The authors call attention for the fact that a high load of particles may cause an increase in Dax (up to twofold figures).

Increasing the rotation rates of the inner cylinder will eventually overcome film resistance and turn the inherent (or the apparent, when pore diffusion is significant) enzymatic reaction velocity into the rate-controlling step. For a typical enzymatic reaction, this will be possible within a reasonable range of rotation rates of the inner cylinder. Figure 4 is a practical example of this situation.

6. Stirring Power

One important advantage of VFRs is low-shear stress, when compared with conventional impellers. Essentially, for moderate to high Taylor numbers, t a Tam, with m between 1.5 and 1.57 (using the definition for Ta shown in the Notations table).

Two of the published correlations for stirring power were selected here to illustrate this point. For low rotational Reynolds numbers, Dubrulle and Hersant (26)

Immobilisation Definition Reaction

0 250 500 750 1000

Reaction time (s)

Fig. 4. Testing the presence of external resistance to mass transfer. VFR Batch assays. Bioparticle: agarose gel (55 x 10-6 m) with multipoint-attached alcalase. Substrate: cheese whey concentrate, 58 kg/m3 (pH 9.5) and 50oC. For ff > 21 s-1 external mass transfer resistances became negligible (17).

0 250 500 750 1000

Reaction time (s)

Fig. 4. Testing the presence of external resistance to mass transfer. VFR Batch assays. Bioparticle: agarose gel (55 x 10-6 m) with multipoint-attached alcalase. Substrate: cheese whey concentrate, 58 kg/m3 (pH 9.5) and 50oC. For ff > 21 s-1 external mass transfer resistances became negligible (17).

use an analogy with turbulent convection to calculate the torque on the inner cylinder, resulting in the following equation for the agitation power, P:

P = 1.46apv2L 11 (ReJ3/2, for 400 <Ree < 104 (5)

22 n Ree

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