이중 입도 분포를 가진 현탁액의 침강 속도 예측

구상균; Sangkyun Koo

Journal of the Korean Industrial and Engineering Chemistry, Vol.19, No.6, 609-616, December, 2008

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이중 입도 분포를 가진 현탁액의 침강 속도 예측

Prediction of Hindered Settling Velocity of Bidisperse Suspensions

구상균^†

상명대학교 공업화학과

Sangkyun Koo^†

Department of Industrial Chemistry, Sangmyung University, Seoul 110-743, Korea

E-mail:

초록

본 연구는 크기가 다른 두 종류의 입자를 가진 비(非)콜로이드성 현탁액의 평균 침강 속도를 예측하는 수치적 방법을 제공한다. 이 방법은 무수히 많은 입자들이 유체에 불규칙적으로 분포된 현탁액 시스템의 유체 속도, 온도 등의 물리량을 앙상블 평균의 개념을 사용해서 표현하는 유효 매체 이론에 기초한다. 본 연구에서는 Acrivos와 Chang[1]이 단일(單一)입도 현탁액에 대해 제안한 모델을 이중(二重) 입도 현탁액에 응용한다. 구체적으로 방사 분포 함수(radial distribution function)에 대한 계산과 stream function을 이용하여 침강 속도를 계산하고 그 결과를 Davis와 Birdsell[2]과 Cheung 등[3]의 실험 결과와 비교하였다. 그 결과 본 연구의 모델에 의한 예측이 실험 결과와 일치하는 것으로 나타났다.

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]

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Cheung MK, Powell RL, Mccarthy MJ, AIChE J., 42(1), 271 (1996)
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Mo G, Sangani AS, Phys. Fluids, 6, 1637 (1994)
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[1] Acrivos A, Chang EY, Phys. Fluids, 29, 3 (1986)

[2] Davis RH, Gecol H, AIChE J., 40(3), 570 (1994)

[3] Cheung MK, Powell RL, Mccarthy MJ, AIChE J., 42(1), 271 (1996)

[4] Batchelor GK, Wen CS, J. Fluid Mech, 124, 495 (1982)

[5] Mirza S, Richardson JF, Chem. Eng. Sci., 34, 447 (1979)

[6] Selim MS, Kothari AC, Turian RM, AIChE J., 29, 1029 (1983)

[7] Hoyos M, Bacri JC, Martin J, Salin D, Phys. Fluids, 6, 3809 (1994)

[8] Koo S, Sangani AS, Phys. Fluids, 14, 3522 (2002)

[9] Tory EM, Ford RA, Int. J. Miner. Process., 73, 119 (2004)

[10] Barnea E, Mizrahi J, Chem. Eng. J., 5, 171 (1973)

[11] Richardson JF, Zaki WN, Trans. Inst. Chem. Eng, 32, 35 (1954)

[12] Percus JK, Yevick GY, Phys. Rev., 110, 1 (1958)

[13] Lebowitz JL, Phys. Rev., 133, A895 (1964)

[14] Throop CJ, Bearman RJ, J. Chem. Phys, 42, 2838 (1965)

[15] Leonard PJ, Henderson JD, Barker JA, Mol. Phys., 21, 107 (1973)

[16] Leal LG, Laminar flow and convective transport processes: Scaling principles and asymptotic analysis, Butterworth-Heinemann, Boston (1992)

[17] Song KH, Koo S, J. Ind. Eng. Chem., 12(3), 368 (2006)

[18] Nguyen HQ, Ladd AJC, J. Fluid Mech., 525, 73 (2005)

[19] Ladd AC, J. Chem. Phys., 93, 3484 (1990)

[20] Mo G, Sangani AS, Phys. Fluids, 6, 1637 (1994)

[21] Davies R, Powder Tech, 2, 43 (1968)

[22] Cox RG, Int. J. Multiphase Flow, 16, 617 (1990)

[23] Lin SP, Chem. Eng. Comm., 29, 201 (1984)