Inertial migration and multiple equilibrium positions of a neutrally buoyant spherical particle in Poiseuille flow

Choeng Ryul Choi; Chang Nyung Kim

Korean Journal of Chemical Engineering, Vol.27, No.4, 1076-1086, July, 2010

DOI10.1007/s11814-010-0214-7 Export Citation

Inertial migration and multiple equilibrium positions of a neutrally buoyant spherical particle in Poiseuille flow

Choeng Ryul Choi¹, and Chang Nyung Kim^{2, 3, †}

¹Department of Mechanical Engineering, College of Engineering, Kyung Hee University, Yongin 446-701, Korea
²College of Engineering, Kyung Hee University, Yongin 446-701, Korea
³Industrial Liaison Research Institute, Kyung Hee University, Yongin 446-701, Korea

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The radial migration of a single neutrally buoyant particle in Poiseuille flow is numerically investigated by direct numerical simulations. The simulation results show that the Segre and Silberberg equilibrium position moves towards the wall as the Reynolds number increases and as the particle size decreases. At high Reynolds numbers, inner equilibrium positions are found at positions closer to the centerline and move towards the centerline as the Reynolds number increases. At higher Reynolds numbers, the Segre and Silberberg equilibrium position disappears and only the inner equilibrium position exists. We prove that the inner annuluses in the measurements of Matas, Morris & Guazzelli (J. Fluid Mech. 515, 171-195, 2004) are not transient radial positions, but are real equilibrium positions. The results on the inner equilibrium positions and unstable equilibrium positions are new and convince us of the existence of multiple equilibrium radial positions for neutrally buoyant particles.

Keywords:Segre and Silberberg Effect;Particle Migration;Suspensions;Multiple Equilibrium Positions;Fluid-particle Interaction

[References]

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Bretherton FP, J. Fluid Mech., 14, 284 (1962)
Segre G, Silberberg A, Nature., 189, 209 (1961)
Oliver R, Nature., 194, 1269 (1962)
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Tachibana M, Rheol. Acta., 12, 58 (1973)
Aoki H, Kurosaki Y, Anzai H, Bull. JSME., 22, 206 (1979)
Han M, Kim C, Kim M, Lee S, J. Rheol., 43(5), 1157 (1999)
Rubinow SI, Keller JB, J. Fluid Mech., 11, 447 (1961)
Saffman PG, J. Fluid Mech., 22, 385 (1965)
Schonberg JA, Hinch EJ, J. Fluid Mech., 203, 517 (1989)
Asmolov ES, J. Fluid Mech., 381, 63 (1999)
Hu HH, Joseph DD, Crochet MJ, Theor. Comput. Fluid Dyn., 3, 285 (1992)
Feng J, Hu HH, Joseph DD, J. Fluid Mech., 277, 271 (1994)
Patankar NA, Huang PY, Ko T, Joseph DD, J. Fluid Mech., 438, 67 (2001)
Joseph DD, Ocando D, J. Fluid Mech., 454, 263 (2002)
Wang J, Joseph DD, Phys. Fluids., 15, 2267 (2003)
Yang BH, Wang J, Joseph DD, Hu HH, Pan TW, Glowinski R, J. Fluid Mech., 540, 109 (2005)
Matas JP, Morris JF, Guazzelli E, J. Fluid Mech., 515, 171 (2004)
Matas JP, Morris JF, Guazzelli E, Oil Gas Sci. Technol., 59, 59 (2004)
Ko T, Patankar NA , Joseph DD, Computers & Fluids., 35, 121 (2006)
Hu HH, Int. J. Multiph. Flow, 22(2), 335 (1996)
Hu HH, Patankar NA, Zhu MY, J. Comput. Phys., 169, 427 (2001)

[1] Segre G, Silberberg A, J. Fluid Mech., 14, 136 (1962)

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

[3] Bretherton FP, J. Fluid Mech., 14, 284 (1962)

[4] Segre G, Silberberg A, Nature., 189, 209 (1961)

[5] Oliver R, Nature., 194, 1269 (1962)

[6] Goldsmith HL, Mason SG, J. Colloid Sci., 17, 448 (1962)

[7] Eichhorn R, Small S, J. Fluid Mech., 20, 513 (1964)

[8] Repetti RV, Leonard EF, Nature., 203, 1346 (1964)

[9] Jeffrey RC, Pearson JRA, J. Fluid Mech., 22, 721 (1965)

[10] Brenner H, Adv. Chem. Eng., 6, 287438 (1966)

[11] Karnis A, Goldsmith HL , Mason SG, Can. J. Chem. Eng., 44, 181 (1966)

[12] Goldsmith HL, Mason SG, The microrheology of dispersions, in Rheology, Theory and Applications 4, Academic Press, New York (1967)

[13] Halow JS, Wills GB, AIChE J., 16, 281 (1970)

[14] Tachibana M, Rheol. Acta., 12, 58 (1973)

[15] Aoki H, Kurosaki Y, Anzai H, Bull. JSME., 22, 206 (1979)

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

[17] Rubinow SI, Keller JB, J. Fluid Mech., 11, 447 (1961)

[18] Saffman PG, J. Fluid Mech., 22, 385 (1965)

[19] Schonberg JA, Hinch EJ, J. Fluid Mech., 203, 517 (1989)

[20] Asmolov ES, J. Fluid Mech., 381, 63 (1999)

[21] Hu HH, Joseph DD, Crochet MJ, Theor. Comput. Fluid Dyn., 3, 285 (1992)

[22] Feng J, Hu HH, Joseph DD, J. Fluid Mech., 277, 271 (1994)

[23] Patankar NA, Huang PY, Ko T, Joseph DD, J. Fluid Mech., 438, 67 (2001)

[24] Joseph DD, Ocando D, J. Fluid Mech., 454, 263 (2002)

[25] Wang J, Joseph DD, Phys. Fluids., 15, 2267 (2003)

[26] Yang BH, Wang J, Joseph DD, Hu HH, Pan TW, Glowinski R, J. Fluid Mech., 540, 109 (2005)

[27] Matas JP, Morris JF, Guazzelli E, J. Fluid Mech., 515, 171 (2004)

[28] Matas JP, Morris JF, Guazzelli E, Oil Gas Sci. Technol., 59, 59 (2004)

[29] Ko T, Patankar NA , Joseph DD, Computers & Fluids., 35, 121 (2006)

[30] Hu HH, Int. J. Multiph. Flow, 22(2), 335 (1996)

[31] Hu HH, Patankar NA, Zhu MY, J. Comput. Phys., 169, 427 (2001)