Numerical simulation of bidisperse hard spheres settling in a fluid

Sangkyun Koo

Korean Journal of Chemical Engineering, Vol.28, No.2, 364-369, February, 2011

DOI10.1007/s11814-010-0416-z Export Citation

Numerical simulation of bidisperse hard spheres settling in a fluid

Sangkyun Koo^†

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

E-mail:

Average settling velocity of non-uniform hard spheres in a viscous fluid is determined by using a largescale numerical simulation that is carried out for over 103 spheres in a periodic unit cell which extends infinitely. An efficient calculation scheme is used for reducing the computation cost which steeply increases with the number of the spheres. The calculation scheme is based on a fast summation method for far-field hydrodynamic interaction among spheres. It is applied in the computation of hindered settling velocity of hard spheres with bidisperse size distribution in a viscous fluid. The simulation results are compared with the theoretical predictions by Batchelor [8] and Davis and Gecol [9]. It is found that the prediction by Davis and Gecol reasonably agrees with the numerical results.

Keywords:Bidisperse Suspension;Hindered Settling Velocity;Fast Summation Algorithm;Stokes Flow Simulation;Multipole Expansion

[References]

Bossis G, Brady JF, J. Chem. Phys., 80, 5141 (1984)
Brady JF, Bossis G, Annu. Rev. Fluid Mech., 20, 111 (1988)
Sangani AS, Mo G, Phys. Fluids., 8, 1990 (1996)
Sieru A, Brady JF, J. Fluid Mech., 448, 115 (2001)
Banchio AJ, Brady JF, J. Chem. Phys., 118(22), 10323 (2003)
Greengard L, Rokhlin V, J. Compu. Phys., 73, 325 (1987)
Greengard L, Science, 265(5174), 909 (1994)
Batchelor GK, Wen CS, J. Fluid Mech., 124, 495 (1982)
Davis RH, Gecol H, AIChE J., 40(3), 570 (1994)
Cheung MK, Powell RL, Mccarthy MJ, AIChE J., 42(1), 271 (1996)
Koo S, Sangani AS, Phys. Fluids., 14, 3522 (2002)
Abbas M, Climent E, Simonin O, Maxey MR, Phys. Fluids., 18, 121504 (2006)
Koo S, J. Ind. Eng. Chem., 14, 679 (2009)
Dorell R, Hogg AJ, Int. J. Multiphase Flow., 36, 481 (2010)
Mo G, Sangani AS, Phys. Fluids., 6, 1637 (1994)
Lamb H, Hydrodynamics., Dover, New York (1945)
Kim S, Karrila SJ, Microhydrodynamics., Butterworth-Heinemann,Boston (1991)
Hobson EW, The theory of spherical and ellipsoidal harmonics., Cambridge University Press, Cambridge (1931)
Batchelor GK, J. Fluid Mech., 52, 245 (1972)
Richadson JF, Zaki WN, Trans. Inst. Chem. Eng., 32, 35 (1954)
Ladd AC, J. Chem. Phys., 93, 3484 (1990)

[Referenced By]

[1] Bossis G, Brady JF, J. Chem. Phys., 80, 5141 (1984)

[2] Brady JF, Bossis G, Annu. Rev. Fluid Mech., 20, 111 (1988)

[3] Sangani AS, Mo G, Phys. Fluids., 8, 1990 (1996)

[4] Sieru A, Brady JF, J. Fluid Mech., 448, 115 (2001)

[5] Banchio AJ, Brady JF, J. Chem. Phys., 118(22), 10323 (2003)

[6] Greengard L, Rokhlin V, J. Compu. Phys., 73, 325 (1987)

[7] Greengard L, Science, 265(5174), 909 (1994)

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

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

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

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

[12] Abbas M, Climent E, Simonin O, Maxey MR, Phys. Fluids., 18, 121504 (2006)

[13] Koo S, J. Ind. Eng. Chem., 14, 679 (2009)

[14] Dorell R, Hogg AJ, Int. J. Multiphase Flow., 36, 481 (2010)

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

[16] Lamb H, Hydrodynamics., Dover, New York (1945)

[17] Kim S, Karrila SJ, Microhydrodynamics., Butterworth-Heinemann,Boston (1991)

[18] Hobson EW, The theory of spherical and ellipsoidal harmonics., Cambridge University Press, Cambridge (1931)

[19] Batchelor GK, J. Fluid Mech., 52, 245 (1972)

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

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