Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-19T02:53:26.540Z Has data issue: false hasContentIssue false
  • English
  • Français

Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid. Part 2. Couette and Poiseuille flows

Published online by Cambridge University Press:  26 April 2006

J. Feng ,
H. H. Hu  and
D. D. Joseph
J. Feng
Affiliation:
Department of Aerospace Engineering and Mechanics and The Minnesota Supercomputer Institute, University of Minnesota, Minneapolis, MN 55455–0153, USA
H. H. Hu
Affiliation:
Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104–6315, USA
D. D. Joseph
Affiliation:
Department of Aerospace Engineering and Mechanics and The Minnesota Supercomputer Institute, University of Minnesota, Minneapolis, MN 55455–0153, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper reports the results of a two-dimensional finite element simulation of the motion of a circular particle in a Couette and a Poiseuille flow. The size of the particle and the Reynolds number are large enough to include fully nonlinear inertial effects and wall effects. Both neutrally buoyant and non-neutrally buoyant particles are studied, and the results are compared with pertinent experimental data and perturbation theories. A neutrally buoyant particle is shown to migrate to the centreline in a Couette flow, and exhibits the Segré-Silberberg effect in a Poiseuille flow. Non-neutrally buoyant particles have more complicated patterns of migration, depending upon the density difference between the fluid and the particle. The driving forces of the migration have been identified as a wall repulsion due to lubrication, an inertial lift related to shear slip, a lift due to particle rotation and, in the case of Poiseuille flow, a lift caused by the velocity profile curvature. These forces are analysed by examining the distributions of pressure and shear stress on the particle. The stagnation pressure on the particle surface are particularly important in determining the direction of migration.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 277 , 25 October 1994 , pp. 271 - 301
Copyright
© 1994 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aoki, H, Kurosaki, Y. & Anzai, H. 1979 Study on the tubular pinch effect in a pipe flow. I. Lateral migration of a single particle in laminar Poiseuille flow. Bull. JSME 22, 206.Google Scholar
Brenner, H. 1966 Hydrodynamic resistance of particles at small Reynolds numbers. Adv. Chem. Engng 6, 287.Google Scholar
Bretherton, F. P. 1962a Slow viscous motion round a cylinder in a simple shear. J. Fluid Mech. 12, 591.Google Scholar
Bretherton, F. P. 1962b The motion of rigid particles in a shear flow at low Reynolds number. J. Fluid Mech. 14, 284.Google Scholar
Cox, R. G. 1965 The steady motion of a particle of arbitrary shape at small Reynolds numbers. J. Fluid Mech. 23, 625.Google Scholar
Cox, R. G. & Brenner, H. 1968 The lateral migration of solid particles in Poiseuille flow. Part 1. Theory. Chem. Engng Sci. 23, 147.Google Scholar
Cox, R. G. & Hsu, S. K. 1977 The lateral migration of solid particles in a laminar flow near a plane. Intl. J. Multiphase Flow 3, 201.Google Scholar
Cox, R. G. & Mason, S. G. 1971 Suspended particles in fluid flow through tubes. Ann. Rev. Fluid Mech. 3, 291.Google Scholar
Cox, R. G., Zia, I. Y. & Mason, S. G. 1968 Particle motions in sheared suspensions. XXV. Streamlines around cylinders and spheres. J. Colloid Interface Sci. 27, 7.Google Scholar
Denson, C. D., Christiansen, E. B. & Salt, D. L. 1966 Particle migration in shear fields. AIChE J. 12, 589.Google Scholar
Feng, J., Hu, H. H. & Joseph, D. D. 1994 Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid. Part 1. Sedimentation. J. Fluid Mech. 261, 95.Google Scholar
Feuillebois, F. 1989 Some theoretical results for the motion of solid spherical particles in a viscous fluid. In Multiphase Science and Technology (ed. G. F. Hewitt et al.), vol. 4, p. 583. Hemisphere.
Goldsmith, H. L. & Mason, S. G. 1966 The microrheology of dispersions. In Rheology, Theory and Applications (ed. F. R. Eirich), vol. 4, p. 85. Academic.
Halow, J. S. & Wills, G. B. 1970a Radial migration of spherical particles in Couette systems. AIChE J. 16, 281.Google Scholar
Halow, J. S. & Wills, G. B. 1970b Experimental observations of sphere migration in Couette systems. Indust. Engng Chem. Fundam. 9, 603.Google Scholar
Happel, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics. Prentice-Hall.
Ho, B. P. & Leal, L. G. 1974 Inertial migration of rigid spheres in two-dimensional unidirectional flows. J. Fluid Mech. 65, 365.Google Scholar
Hu, H. H., Crochet, M. J. & Joseph, D. D. 1992 Direct simulation of fluid particle motions. Theor. Comput. Fluid Dyn. 3, 285.Google Scholar
Huang, Y., Feng, J. & Joseph, D. D. 1994 The turning couples on an elliptic particle settling in a vertical channel. J. Fluid Mech. 271, 1.Google Scholar
Jeffery, R. C. & Pearson, J. R. A. 1965 Particle motion in laminar vertical tube flow. J. Fluid Mech. 22, 721.Google Scholar
Karnis, A., Goldsmith, H. L. & Mason, S. G. 1966 The flow of suspensions through tubes. Part 5: Inertial effects. Can. J. Chem. Engng. 44, 181.Google Scholar
Leal, L. G. 1980 Particle motion in a viscous fluid. Ann. Rev. Fluid Mech. 12, 435.Google Scholar
Liu, Y. J., Nelson, J., Feng, J. & Joseph, D. D. 1993 Anomalous rolling of spheres down an inclined plane. J. Non-Newtonian Fluid Mech. 50, 305.Google Scholar
McLaughlin, J. B. 1991 Integral migration of a small sphere in linear shear flow. J. Fluid Mech. 224, 261.Google Scholar
McLaughlin, J. B. 1993 The lift on a small sphere in wall-bounded linear shear flows. J. Fluid Mech. 246, 249.Google Scholar
Oliver, D. R. 1962 Influence of particle rotation on radial migration in the Poiseuille flow of suspensions. Nature 194, 1269.Google Scholar
Repetti, R. V. & Leonard, E. F. 1964 Segré-Silberberg annulus formation: a possible explanation. Nature 203, 1346.Google Scholar
Repetti, R. V. & Leonard, E. F. 1966 Physical basis for the axial accumulation of red blood cells. Chem. Engng Prog. Symp. Ser. 62, 80.Google Scholar
Rubinow, S. I. & Keller, J. B. 1961 The transverse force on a spinning sphere moving in a viscous fluid. J. Fluid Mech. 11, 447.Google Scholar
Saffman, P. G. 1965 The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22, 385.Google Scholar
Schonberg, J. A. & Hinch, E. J. 1989 Inertial migration of a sphere in Poiseuille flow. J. Fluid Mech. 203, 517.Google Scholar
Segré, G. & Silberberg, A. 1961 Radial Poiseuille flow of suspensions. Nature 189, 209.Google Scholar
Segré, G. & Silberberg, A. 1962 Behaviour of macroscopic rigid spheres in Poiseuille flow. Part 1. J. Fluid Mech. 14, 115.Google Scholar
Tachibana, M. 1973 On the behavior of a sphere in the laminar tube flows. Rheol. Acta 12, 58.Google Scholar
Unverdi, S. O. & Tryggvason, G. 1992 A front-tracking method for viscous, incompressible, multi-fluid flows. J. Comput. Phys. 100, 25.Google Scholar
Vasseur, P. & Cox, R. G. 1976 The lateral migration of a spherical particle in two-dimensional shear flows. J. Fluid Mech. 78, 385.Google Scholar
Vasseur, P. & Cox, R. G. 1977 The lateral migration of spherical particles sedimenting in a stagnant bounded fluid. J. Fluid Mech. 80, 561.Google Scholar