Mathematical Model of Migration of Spherical Particles in Tube Flow Under the Influence of Inertia and Particle-particle Interaction

Chongyoup Kim

Korean Journal of Chemical Engineering, Vol.21, No.1, 27-33, January, 2004

Chongyoup Kim^†

Department of Chemical Engineering and Applied Rheology Center, Korea University, 1, Anam-dong 5 Ga, Seongbuk-goo, Seoul 136-701, Korea

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In this paper, a mathematical model is considered of the migration of non-colloidal, spherical particles suspended in Newtonian fluid under Poiseuille flows by combining the inertial migration theory by Ho and Leal (JFM, 1974) and particle migration model in concentrated suspension by Phillips et al. (Phys. Fluids, 1992). The numerical solutions of the model equations reveal that the model set up here explains the experimental observation reported in the literature when Rep<1, at least qualitatively. It was concluded that both the inertia and particle-particle interaction should be taken into account properly to understand the particle migration in tube flow of suspension regardless of particle loading.

Keywords:Shear-induced Migration;Inertial Migration;Particle-particle Interaction;Suspension;Velocity Blunting;Segre-Silberberg Effect

[References]

Abbot JR, Tetlow N, Graham AL, Altobelli SA, Fukushima E, Mondy LA, Stevens TS, J. Rheol., 35, 773 (1991)
Altobelli SA, Givler RC, Fukushima E, J. Rheol., 35, 721 (1991)
Cha W, Beissinger RL, Korean J. Chem. Eng., 18(4), 479 (2001)
Chow AW, Sinton SW, Iwamiya JH, J. Rheol., 37, 1 (1993)
Chow AW, Sinton SW, Iwamiya JH, Stephens TS, Phys. Fluids, 6, 2561 (1994)
Chin BD, Park OO, Korean J. Chem. Eng., 18(1), 54 (2001)
Eastman JA, Choi SUS, Li S, Yu W, Thompson LJ, Appl. Phys. Lett., 78, 718 (2001)
Graham AL, Altobelli SA, Fukushima E, Mondy LA, Stevens TS, J. Rheol., 35, 191 (1991)
Hampton RE, Mammoli AA, Graham AL, Tetlow N, Altobelli SA, J. Rheol., 41(3), 621 (1997)
Han M, Kim C, Kim M, Lee S, J. Rheol., 43(5), 1157 (1999)
Happel J, Brenner H, "Low Reynolds Number Hydrodynamics," Martinus Nijhoff (1983)
Ho BP, Leal LG, J. Fluid Mech., 65, 365 (1974)
Koh CJ, Hookam P, Leal LG, J. Fluid Mech., 266, 1 (1994)
Krieger IM, Dougherty TJ, Trans. Soc. Rheol., 3, 137 (1959)
Leighton D, Acrivos A, J. Fluid Mech., 181, 415 (1987)
Lim JS, Kim JH, Kim C, Kim SW, Korea-Aust. Rheol. J., 14(1), 11 (2002)
Mondy LA, Brenner H, Altobelli SA, Abbott JR, Graham AL, J. Rheol., 38(2), 444 (1994)
Nott PB, Brady J, J. Fluid Mech., 275, 157 (1994)
Okada K, Mitsunaga T, Nagase Y, Korea-Aust. Rheol. J., 15(1), 43 (2003)
Phillips RJ, Armstrong RC, Brown RA, Graham AL, Abott JR, Phys. Fluids A, 4, 30 (1992)
Segre G, Silberberg A, J. Fluid Mech., 14, 115 (1962)

[Referenced By]

[Related Articles]

[1] Abbot JR, Tetlow N, Graham AL, Altobelli SA, Fukushima E, Mondy LA, Stevens TS, J. Rheol., 35, 773 (1991)

[2] Altobelli SA, Givler RC, Fukushima E, J. Rheol., 35, 721 (1991)

[3] Cha W, Beissinger RL, Korean J. Chem. Eng., 18(4), 479 (2001)

[4] Chow AW, Sinton SW, Iwamiya JH, J. Rheol., 37, 1 (1993)

[5] Chow AW, Sinton SW, Iwamiya JH, Stephens TS, Phys. Fluids, 6, 2561 (1994)

[6] Chin BD, Park OO, Korean J. Chem. Eng., 18(1), 54 (2001)

[7] Eastman JA, Choi SUS, Li S, Yu W, Thompson LJ, Appl. Phys. Lett., 78, 718 (2001)

[8] Graham AL, Altobelli SA, Fukushima E, Mondy LA, Stevens TS, J. Rheol., 35, 191 (1991)

[9] Hampton RE, Mammoli AA, Graham AL, Tetlow N, Altobelli SA, J. Rheol., 41(3), 621 (1997)

[10] Han M, Kim C, Kim M, Lee S, J. Rheol., 43(5), 1157 (1999)

[11] Happel J, Brenner H, "Low Reynolds Number Hydrodynamics," Martinus Nijhoff (1983)

[12] Ho BP, Leal LG, J. Fluid Mech., 65, 365 (1974)

[13] Koh CJ, Hookam P, Leal LG, J. Fluid Mech., 266, 1 (1994)

[14] Krieger IM, Dougherty TJ, Trans. Soc. Rheol., 3, 137 (1959)

[15] Leighton D, Acrivos A, J. Fluid Mech., 181, 415 (1987)

[16] Lim JS, Kim JH, Kim C, Kim SW, Korea-Aust. Rheol. J., 14(1), 11 (2002)

[17] Mondy LA, Brenner H, Altobelli SA, Abbott JR, Graham AL, J. Rheol., 38(2), 444 (1994)

[18] Nott PB, Brady J, J. Fluid Mech., 275, 157 (1994)

[19] Okada K, Mitsunaga T, Nagase Y, Korea-Aust. Rheol. J., 15(1), 43 (2003)

[20] Phillips RJ, Armstrong RC, Brown RA, Graham AL, Abott JR, Phys. Fluids A, 4, 30 (1992)

[21] Segre G, Silberberg A, J. Fluid Mech., 14, 115 (1962)