Korean Journal of Chemical Engineering

, Volume 21, Issue 1, pp 27–33 | Cite as

Mathematical model of migration of spherical particles in tube flow under the influence of inertia and particle-particle interaction

  • Chongyoup Kim


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.

Key words

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


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  1. Abbot, J. R., Tetlow, N., Graham, A. L., Altobelli, S. A., Fukushima, E., Mondy, L. A. and Stevens, T. S., “Experimental Observations of Particle Migration in Concentrated Suspensions: Couette Flow,”J. Rheol.,35, 773 (1991).CrossRefGoogle Scholar
  2. Altobelli, S.A., Givler, R. C. and Fukushima, E., “Velocity and Concentration Measurements of Suspensions by Nuclear Magnetic Resonance Imaging,”J. Rheol.,35, 721 (1991).CrossRefGoogle Scholar
  3. Cha, W. and Beissinger, R. L., “Evaluation of Shear-induced Particle Diffusivity in Red Blood Cell Ghost Suspensions,”Korean J. Chem. Eng.,18, 479 (2001).CrossRefGoogle Scholar
  4. Chow, A.W., Sinton, S.W. and Iwamiya, J.H., “Direct Observation of Particle Microstructure in Concentrated Suspensions During the Falling-ball Experiment,”J. Rheol.,37, 1 (1993).CrossRefGoogle Scholar
  5. Chow, A.W., Sinton, S.W., Iwamiya, J. H. and Stephens, T. S., “Shearinduced Particle Migration in Couette and Parallel-plate Viscometers: NMR Imaging and Stress Measurements,”Phys. Fluids,6, 2561 (1994).CrossRefGoogle Scholar
  6. Chin, B.D. and Park, O.O., “Electrorheological Responses of Particulate Suspensions and Emulsions in a Small-strain Dynamic Shear Flow: Viscoelasticity and Yielding Phenomena,”Korean J. Chem. Eng.,18, 54 (2001).CrossRefGoogle Scholar
  7. Eastman, J.A. and Choi, S.U. S., Li, S., Yu, W. and Thompson, L. J., “Anomalously Increased Effective Thermal Conductivities of Ethylene Glycol-based Nanofluids Containing Copper Nanoparticles,”Appl. Phys. Lett.,78, 718 (2001).CrossRefGoogle Scholar
  8. Graham, A. L., Altobelli, S.A., Fukushima, E., Mondy, L.A. and Stevens, T. S., “NMR Imaging of Shear-induced Diffusion and Structure in Concentrated Suspensions Undergoing Couette Flow,”J. Rheol.,35, 191 (1991).CrossRefGoogle Scholar
  9. Hampton, R. E., Mammoli, A. A., Graham, A. L., Tetlow, N. and Altobelli, S.A., “Migration of Particles Undergoing Pressure-driven Flow in a Circular Conduit,”J. Rheol.,41, 621 (1997).CrossRefGoogle Scholar
  10. Han, M. S., Kim, C., Kim, M. and Lee, S., “Particle Migration in Tube Flow of Suspension,”J. Rheol.,43, 1157 (1999).CrossRefGoogle Scholar
  11. Happel, J. and Brenner, H., “Low Reynolds Number Hydrodynamics,” Martinus Nijhoff (1983).Google Scholar
  12. Ho, B. P. and Leal, L. G., “Inertial Migration of Rigid Spheres in Twodimensional Unidirectional Flows,”J. Fluid Mech.,65, 365 (1974).CrossRefGoogle Scholar
  13. Koh, C. J., Hookam, P. and Leal, L. G., “An Experimental Investigation of Concentrated Suspension Flow in a Rectangular Channel,”J. Fluid Mech.,266, 1 (1994).CrossRefGoogle Scholar
  14. Krieger, I.M. and Dougherty, T. J., “A Mechanism for Non-newtonian Flow in Suspensions of Rigid Spheres,”Trans. Soc. Rheol.,3, 137 (1959).CrossRefGoogle Scholar
  15. Leighton, D. and Acrivos, A., “The Shear-induced Migration of Particles in Concentrated Suspension,”J. Fluid Mech.,181, 415 (1987).CrossRefGoogle Scholar
  16. Lim, J. S., Kim, J.H., Kim, C. and Kim, S.W., “Morphological and Rheological Properties of Culture Broth ofCephalosporium acremonium M25,”Korea-Australia Rheology Journal,14, 11 (2002).Google Scholar
  17. Mondy, L. A., Brenner, H., Altobelli, S.A., Abott, J. R. and Graham, A. L., “Shear-induced Particle Migration in Suspensions of Rods,”J. Rheol.,38, 444 (1994).CrossRefGoogle Scholar
  18. Nott, P. B. and Brady, J., “Pressure-driven Flow of Suspensions: Simulation and Theory,”J. Fluid Mech.,275, 157 (1994).CrossRefGoogle Scholar
  19. Okada, K., Mitsunaga, T. and Nagase, Y., “Properties and Particles Dispersion of Biodegradable Resin/Clay Nanocomposite,”Korea-Australia Rheology Journal,15, 43 (2003).Google Scholar
  20. Phillips, R. J., Armstrong, R. C., Brown, R.A., Graham, A. L. and Abott, J. R., “A Constitutive Equation for Concentrated Suspensions that Accounts for Shear-induced Particle Migration,”Phys. Fluids A,4, 30 (1992).CrossRefGoogle Scholar
  21. Segre, G. and Silberberg, A., “Behavior of Macroscopic Rigid Spheres in Poiseuille flow: Part 1. Determination of Local Concentration by Statistical Analysis of Particle Passages through Crossed Light Beams,”J. Fluid Mech.,14, 115 (1962).CrossRefGoogle Scholar

Copyright information

© Korean Institute of Chemical Engineering 2004

Authors and Affiliations

  1. 1.Department of Chemical Engineering and Applied Rheology CenterKorea UniversitySeoulKorea

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