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These equations were validated against experimental data within the range 400 < Ree < 106. For higher values of Ree, Moore (5) adopted the correlation of Beaudoin and Jaffrin (27):

d using the definition of Tc from the Notations table.

It is interesting to compare the stirring power of a VFR with a conventional tank. With this purpose, the correlation of Rushton, Costich, and Everett, after Bailey and Ollis (28), was used to estimate P for a 1-m3 baffled stirred tank, with water at 25°C, turbulent flow and a flat blade impeller (i.e., power number P0 = 4, and Pstirred tank = P0pN3Di5, with N in rotations/s). The 1-m3 VFR has n = 0.618. Figure 5 shows the results. The stirred tank was assumed to have height equal to diameter and its impeller diameter (D) was set equal to the VFR inner cylinder diameter.

Rotation (rpm)

Fig. 5. Comparison between VFR and agitated tank stirring powers, for 1 m3 reactors: PvfR from Eq. 6.

Rotation (rpm)

Fig. 5. Comparison between VFR and agitated tank stirring powers, for 1 m3 reactors: PvfR from Eq. 6.

It should be noticed that, for the VFR dimensions and fluid properties used here, Ree > 106 already at 30 rpm. Therefore, the rotations in Fig. 5 are beyond the validation range of Ree used for Eq. 5.

Equation 5 predicts that the ratio Pstirred tank/PVFR varies linearly with ro, whereas Eq. 6 gives Pstirred tank/PVFR a ro05. Anyway, the agitation power (and, consequently, shear stress) is much lower for VFRs than for conventional stirred tanks. For tanks without baffles, in turbulent regime, the ratio Pstirred tank/PVFR would be smaller, but the VFR would still have lower energy consumption.

7. Reactor Scale-Up

The fluidynamics of TCP flow, in the absence of end effects (i.e., for an infinite-length apparatus) is characterized by three dimensionless parameters: the rotational (Ree) and the axial (Reax) Reynolds numbers, and the radius ratio (n = R/Re) of the apparatus (for an in-depth discussion of linear models of TCP flow, see ref. 3). The role of end effects is linked to a fourth parameter, the device aspect ratio (r = L/d). Nevertheless, VFRs usually are not sensitive to entrance/exit disturbances. Hence, the characteristic numbers Re0, Reax, and n should be the basis for reactor scale-up.

A rough estimate of capital costs, following Peters and Timmerhaus (29), shows that the fixed cost of a VFR (with n ~ 0.65) would be approx 18% higher than that of a CSTR with the same working volume (because of the "dead volume" of the inner cylinder). The lower power demands of the VFR, however, implies lower variable costs.

8. Notes

1. The VFR design must minimize damage of shear-sensitive particles (e.g., gel supports) in long-run experiments. One of the important causes of particle destruction is the friction between moving and stationary parts of the equipment (seals and bearings).

2. To avoid crushing of biocatalyst, the reactor should be assembled in the vertical position, and the bottom bearing of the inner cylinder should be eliminated, keeping it in balance. The outlet (for a continuous VFR) should be positioned at the cylinder wall, below the top of the apparatus (i.e., there should be a heading space, filled with air or nitrogen). In this way, fluid and particles have no contact with moving seals. The extreme vortices within the VFR always impel the particles towards the seals. If the end walls of the device are stationary, the adjacent vortex layer moves towards the inner cylinder, dragging the particles to the friction zone (the seal between the inner cylinder and the stationary wall). A drawback of this design is that the absence of the bottom bearing increases the internal cylinder wobbling, and thus an accurately balanced cylinder must be used when rotation rates should be high.

3. In continuous operation, it may be interesting to recycle the catalyst instead of entrapping it within the VFR with a sieve that might clog. When pumping a suspension of particles, clogging is common. This problem can be avoided by alternating the suspension flow with air bubbles.

4. Minimal rotations to ensure uniform fluidization in a closed device may be lower than for a continuous reactor, because entrance effects disturb the first vortex and the axial flow will be small. Accumulation of particles at the bottom of the device, close to the inlet, must be avoided; one alternative may be feeding the particles in the center of the vortex.

References

1. Koschmieder, E. L. (1993) Benard Cells and Taylor Vortices, Cambridge Univ. Press, New York, NY.

2. Taylor, G. I . (1923) Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. R. Soc. A, 223, 289-343.

3. Chandrasekhar S. (1961) Hydrodynamic andHydromagnetic Stability, Clarendon Press, Oxford, UK.

4. Tagg, R. (1992) A guide to literature related to the Taylor-Couette problem. In: Ordered and Turbulent Patterns in Taylor-Couette Flow (Andereck, C. D. and Hayot, F., eds.) Plenum Press, New York, NY, pp. 303.

5. Janes, D. A. Thomas, N. H., and Callow, J. A. (1987). Demonstration of a bubble-free annular-vortex membrane bioreactor for batch culture of red beet cells. Biotechnol. Techn. 1, 257-262.

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11. Ameer, G. A., Raghavan, S., Sasisekharan, R., Harmon, W., Cooney, C. L., and Langer, R. (1999). Regional heparinization via simultaneous separation and reaction in a novel Taylor-Couette flow device. Biotechnol. Bioeng. 63, 618-624.

12. Grovender, E. A., Cooney, C. L., Langer, R. S., and Ameer, G. A. (2001). Modeling the mixing behavior of a novel fluidized extracorporeal immunoadsorber Chem. Eng. Sci. 56, 5437-5441.

13. Giordano, R. L. C., Giordano, R. C., Cooney, C. L. (2000). Performance of a continuous Taylor-Couette-Poiseuille vortex flow enzymic reactor with suspended particles. Process Biochem. 35, 1093-1101.

14. Giordano, R. L. C., Giordano, R. C., Cooney, C. L. (2000). Analysis of a Taylor-Poiseuille vortex flow reactor-II: Reactor modeling and performance assessment using glucose-fructose isomerization as test reaction. Chem. Eng. Sci. 55, 3611-3626.

15. Jin, Z., Shukunobe, Y., Miura, M., and Taneya, S. (1997). Continuous enzymatic hydrolysis of milk casein in an automatic vortex flow filtration system. J. Jap. Soc. Food Sci. Tech. 44, 653-658.

16. Giordano, R. C., Giordano, R. L. C., Prazeres, D. M. F., and Cooney, C. L. (1998). Analysis of a Taylor-Poiseuille vortex flow reactor-I: flow patterns and mass transfer characteristics. Chem. Eng. Sci. 53, 3635-3652.

17. Souza, Jr., R., Rezende, M. M., Giordano, R. L. C., and Giordano, R. C. (2003) Hybrid model for an enzymatic reactor: hydrolysis of cheese whey proteins by alcalase immobilized in agarose gel particles. Appl. Biochem. Biotech. 105-108, 413-422.

18. Resende, M. M., Sousa, Jr. R., Tardioli, P. W., Giordano, R. L. C., and Giordano, R. C.(2005) Enzymatic tailor-made proteolysis of whey in a vortex flow reactor. A.I.Ch.E. J. 51, 314-322.

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20. Resende, M. M. (2002). Enzymatic proteolysis of cheese whey in a Taylor-Couette-Poiseuille reactor (Port.). PhD Thesis, Universidade Federal de Säo Carlos, Brazil.

21. Tardioli, P. W., Pedroche, J., Giordano, R. L. C., Fernandez-Lafuente, R,. and Guisan, J. M. (2003). Hydrolysis of proteins by immobilized-stabilized alcalase glyoxyl-agarose. Biotechnol. Progress 19, 352-360.

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29. Peters, M. S. and Timmerhaus, K. D. (1991). Plant Design and Economics for Chemical Engineers, McGraw Hill, New York, NY.

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