Prediction of Hindered Settling Velocity of Bidisperse Suspensions

이중 입도 분포를 가진 현탁액의 침강 속도 예측

  • Koo, Sangkyun (Department of Industrial Chemistry, Sangmyung University)
  • 구상균 (상명대학교 공업화학과)
  • Received : 2008.07.14
  • Accepted : 2008.10.28
  • Published : 2008.12.10

Abstract

The present study is concerned with a simple numerical method for estimating the hindered settling velocity of noncolloidal suspensions with bidisperse size distribution of particles. The method is based on an effective-medium theory which uses the conditional ensemble averages for describing the velocity fields or other physical quantities of interest in the suspension system with the particles randomly placed. The effective-medium theory originally developed by Acrivos and Chang[1] for monodisperse suspensions is modified for the bidisperse case. Using the radial distribution functions and stream functions the hindered settling velocity of the suspended particles is calculated numerically. The predictions by the present method are compared with the previous experimental results by Davis and Birdsell[2] and Cheung et al.[3]. It is shown that the estimations by the effective-medium model of the present study reasonably agree with the experimental results.

Keywords

effective-medium model;hindered settling velocity;bidisperse suspensions;radial distribution function;conditional ensemble average

References

  1. G. K. Batchelor and C. S. Wen, J. Fluid Mech, 124, 495 (1982). https://doi.org/10.1017/S0022112082002602
  2. S. Mirza and J. F. Richardson, Chem. Eng. Sci., 34, 447 (1979). https://doi.org/10.1016/0009-2509(79)85088-5
  3. J. F. Richardson and W. N. Zaki, Trans. Inst. Chem. Eng, 32, 35 (1954).
  4. J. L. Lebowitz, Phys. Rev., 133, A895 (1964). https://doi.org/10.1103/PhysRev.133.A895
  5. L. G. Leal, Laminar flow and convective transport processes: Scaling principles and asymptotic analysis, Butterworth-Heinemann, Boston (1992).
  6. G. Mo and A. S. Sangani, Phys. Fluids, 6, 1637 (1994). https://doi.org/10.1063/1.868227
  7. R. G. Cox, Int. J. Multiphase Flow, 16, 617 (1990). https://doi.org/10.1016/0301-9322(90)90020-J
  8. S. P. Lin, Chem. Eng. Comm., 29, 201 (1984). https://doi.org/10.1080/00986448408940158
  9. M. S. Selim, A. C. Kothari, and R. M. Turian, AIChE J., 29, 1029 (1983). https://doi.org/10.1002/aic.690290623
  10. K. H. Song and S. Koo, J. Ind. Eng. Chem., 12, 368(2006).
  11. E. Barnea and J. Mizrahi, Chem. Eng. J., 5, 171 (1973). https://doi.org/10.1016/0300-9467(73)80008-5
  12. M. Hoyos, J. C. Bacri, J. Martin, and D. Salin, Phys. Fluids, 6, 3809 (1994). https://doi.org/10.1063/1.868372
  13. J. K. Percus and G. Y. Yevick, Phys. Rev., 110, 1 (1958). https://doi.org/10.1103/PhysRev.110.1
  14. C. J. Throop and R. J. Bearman, J. Chem. Phys. 42, 2838 (1965). https://doi.org/10.1063/1.1703249
  15. R. H. Davis and K. H. Birdsell, AIChE J., 40, 570 (1994). https://doi.org/10.1002/aic.690400317
  16. A. Acrivos and E. Y. Chang, Phys. Fluids 29, 3 (1986). https://doi.org/10.1063/1.866018
  17. P. J. Leonard, J. D. Henderson, and J. A. Barker, Mol. Phys. 21, 107 (1973). https://doi.org/10.1080/00268977100101221
  18. A. C. Ladd, J. Chem. Phys., 93, 3484 (1990). https://doi.org/10.1063/1.458830
  19. M. K. Cheung, R. L. Powell, and M. J. MaCarthy, AIChE J., 42, 271 (1996). https://doi.org/10.1002/aic.690420125
  20. E. M. Tory and R. A. Ford, Int. J. Miner. Process., 73, 119 (2004). https://doi.org/10.1016/S0301-7516(03)00068-1
  21. H.-Q. Nguyen and A. J. C. Ladd, J. Fluid Mech., 525, 73 (2005). https://doi.org/10.1017/S0022112004002563
  22. R. Davies, Powder Tech, 2, 43 (1968). https://doi.org/10.1016/0032-5910(68)80032-4
  23. S. Koo and A. S. Sangani, Phys. Fluids, 14, 3522 (2002). https://doi.org/10.1063/1.1503352