Korean Chemical Engineering Research

The Korean Institute of Chemical Engineers (한국화학공학회)
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Permeability of Viscous Flow Through Packed Bed of Bidisperse Hard Spheres

이분산 구형 입자로 구성된 충전층을 흐르는 점성 유체 흐름의 투과도

  • Sohn, Hyunjin (Department of Industrial Chemistry, Sangmyung University) ;
  • Koo, Sangkyun (Department of Industrial Chemistry, Sangmyung University)
  • 손현진 (상명대학교 공업화학과) ;
  • 구상균 (상명대학교 공업화학과)
  • Received : 2011.06.28
  • Accepted : 2011.09.02
  • Published : 2012.02.01
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Abstract

We deal with a problem to determine experimentally as well as theoretically permeability of incompressible viscous flow through packed bed of bidisperse hard spheres in size. For the size ratios of large to small spheres ${\lambda}$=1.25 and 2, we set up bidisperse packing and measured porosity and permeability at various volumetric ratios of small to large spheres ${\gamma}$. Bidisperse packing shows lower porosity and permeability than monodisperse packing does. Variation of porosity as a function of ${\gamma}$ does not match with that of permeability. A theoretical expression for predicting permeability of a viscous flow for packed bed of bidisperse packing is derived based on calculation of drag force acting on each sphere and its predictions are compared with the experimental data and those from some relations previously suggested. It is found that our theory shows better agreement with experimental results than the previous studies and is proved to be quite simple and accurate in estimating the permeability.

본 연구에서는 크기가 다른 두 종류의 단단한 구형 입자들로 충전된 이분산(二分散) 충전층을 지나는 비압축성 유체 흐름의 투과도를 실험적으로 측정하고 이론적으로 예측하는 문제를 다룬다. 작은 입자에 대한 큰 입자의 크기 비 ${\lambda}$가 1.25와 2인 두 가지 경우에 대해 여러 가지 입자 혼합 비율로 충전층을 만들고 그 공극률과 유체 흐름의 투과도를 측정하였다. 이분산 충전은 입자 크기가 일정한 단분산 충전에 비해 공극률이 감소하고 투과율이 감소하나 입자들의 크기 비 ${\lambda}$나 혼합 비율 ${\gamma}$에 따라 다르게 나타난다. 두 가지 입자의 혼합 비율에 따른 공극률의 변화와 투과율의 변화 형태는 서로 일치하지 않는다. 개별 충전 입자에 걸리는 항력 계산에 기초한 모델을 고안하여 투과도를 예측하는 간단한 이론식을 유도하였고 이 식을 이용한 예측값을 실험 결과 및 선행 연구 결과들과 비교한 결과, 이 이론식에 의한 투과도 예측값이나 입자 혼합 비율에 따른 투과도 변화 경향이 실험값에 가장 근사하였다. 이 이론식을 이용해 이분산 충전층을 지나는 유체 흐름의 투과도를 간단하고 정확하게 예측할 수 있음을 보였다.

Keywords

Acknowledgement

Supported by : 상명대학교 자연과학연구소

References

  1. Carman, P. C., "Fluid Flow Through Granular Beds," Trans. Inst. Chem. Eng., 15, 150-166(1937).
  2. Zick, A. A. and Homsy, G. M., "Stokes Flow Through Periodic Arrays of Spheres," J. Fluid Mech., 115, 13-26(1982). https://doi.org/10.1017/S0022112082000627
  3. Sangani, A. S. and Acrivos, A., "Slow Flow Through a Periodic Array of Spheres," Int. J. Multiphase Flow, 8, 343-360(1982). https://doi.org/10.1016/0301-9322(82)90047-7
  4. Brady, J. F. and Bossis, G., "Stokesian Dynamics," G. Annu. Rev. Fluid Mech., 20, 111-157(1988). https://doi.org/10.1146/annurev.fl.20.010188.000551
  5. Ladd, A. J. C., "Hydrodynamics Transport Coefficients of Random Dispersions of Hard Spheres," J. Chem. Phys., 93, 3484-3494(1990).
  6. Mo, G. and Sangani, A. S., "A Method for Computing Stokes Flow Interactions Among Spherical Objects and Its Application to Suspensions of Drops and Porous Particles," Phys.Fluids, 6, 1637-1652(1994). https://doi.org/10.1063/1.868227
  7. Thies-Weesie, D. M. E. and Philpse, A. P., "Liquid Permeation of Bidisperse Colloidal Hard Spheres Packings and the Kozeny-Carman Scaling Relation," J. Colloid Interface Sci., 162, 470-480 (1994). https://doi.org/10.1006/jcis.1994.1062
  8. Mota, M., Teixeira, J. A., Bowen, W. R. and Yelshin, A., "Binary Spherical Particle Mixed Beds: Porosity and Permeability Relationship Measurement," Trans.Filt. Soc., 1(4), 101-106(2001).
  9. Koo, S. and Sangani, A. S., "Effective-Medium Theories for Prediction Hydrodynamic Transport Properties of Bidisperse Suspensions," Phys. Fluids, 14, 3522-3533(2002). https://doi.org/10.1063/1.1503352
  10. Leitzelement, M., Cho, S. L. and Dodds, J., "Porosity and Permeability of Ternary Mixtures of Particles," Powder technol., 41, 159-164(1985). https://doi.org/10.1016/0032-5910(85)87034-0
  11. Yu, A. B. and Standish, N., "Porosity Calculations of Multi-component Mixtures of Spherical Particles," Powder technol., 52, 233-241(1987). https://doi.org/10.1016/0032-5910(87)80110-9
  12. Rassouly, S. M. K., "The Packing Density of 'perfect' Binary Mixtures," Powder technol., 103, 145-150(1999). https://doi.org/10.1016/S0032-5910(98)00223-X
  13. Dias, R. P., Teixeira, J. A., Mota, M. G. and Yelshin, A., "Particulate Binary Mixtures: Dependence of Packing Porosity on Particle Size Ratio," Ind. Eng. Chem. Res., 43, 7912-7919(2004). https://doi.org/10.1021/ie040048b
  14. Kristiansen, K. D. L., Wouterse, A. and Philipse, A., "Simulation of Random Packing of Binary Sphere Mixtures by Mechanical Contraction," Physica A, 358, 249-262(2005). https://doi.org/10.1016/j.physa.2005.03.057
  15. Koo, S., "Estimation of Drag Force Acting on Spheres by Slow Flow and Its Application to a Micro Fluidic Device," Korean J. Chem. Eng., 23(2), 176-181(2006). https://doi.org/10.1007/BF02705712
  16. Song, K. H. and Koo, S., "Numerical Computation of Pressure Drop by Slow Flow Through Micro Packed Bed Reactors," J. Ind. Eng. Chem., 12(3), 368-372(2006).