Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-18T16:23:00.675Z Has data issue: false hasContentIssue false
  • English
  • Français

Inertial migration of rigid spheres in two-dimensional unidirectional flows

Published online by Cambridge University Press:  29 March 2006

B. P. Ho  and
L. G. Leal
B. P. Ho
Affiliation:
Chemical Engineering, California Institute of Technology, Pasadena
L. G. Leal
Affiliation:
Chemical Engineering, California Institute of Technology, Pasadena
Get access Rights & Permissions [Opens in a new window]

Abstract

The familiar Segré-Silberberg effect of inertia-induced lateral migration of a neutrally buoyant rigid sphere in a Newtonian fluid is studied theoretically for simple shear flow and for two-dimensional Poiseuille flow. It is shown that the spheres reach a stable lateral equilibrium position independent of the initial position of release. For simple shear flow, this position is midway between the walls, whereas for Poiseuille flow, it is 0·6 of the channel half-width from the centre-line. Particle trajectories are calculated in both cases and compared with available experimental data. Implications for the measurement of the rheological properties of a dilute suspension of spheres are discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 65 , Issue 2 , 28 August 1974 , pp. 365 - 400
Copyright
© 1974 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

Batchelor, G. K. & Green, J. T. 1972 J. Fluid Mech. 56, 375.
Brenner, H. 1966 Advances in Chemical Engineering, vol. 4. Academic.
Bretherton, F. P. 1962 J. Fluid Mech. 14, 284.
Cox, R. G. & Brenner, H. 1968 Chem. Engng Sci. 23, 147.
Goldsmith, H. L. & Mason, S. G. 1966 Rheology: Theory and Applications (ed. F. R. Eirich), vol. 4. Academic.
Halow, J. S. 1968 Ph.D. thesis, Virginia Polytechnic Institute.
Halow, J. S. & Wills, G. B. 1970a A.I.Ch.E.J. 16, 281.
Halow, J. S. & Wills, G. B. 1970b Ind. Eng. Chem. Fund. 9, 603.
Happel, J. & Brenner, H. 1973 Low Reynolds Number Hydrodynamics. Noordhoff.
Ho, B. P. 1974 Ph.D. thesis, California Institute of Technology.
Lin, C. J., Peery, J. H. & Schowalter, W. R. 1970 J. Fluid Mech. 44, 1.
Repetti, R. V. & Leonard, E. F. 1966 Chem. Engng Prog. Symp. Ser. 62, 80.
Rubinow, S. I. & Keller, J. B. 1961 J. Fluid Mech. 11, 447.
Saffman, P. G. 1965 J. Fluid Mech. 22, 385.
Segré, G. & Silberberg, A. 1962a J. Fluid Mech. 14, 115.
Segré, G. & Silberberg, A. 1962b J. Fluid Mech. 14, 136.
Segré, G. & Silberberg, A. 1963 J. Colloid Sci. 18, 312.
Starkey, T. V. 1956 Brit. J. Appl. Phys. 7, 52.
Tachibana, M. 1973 Rheol. Acta, 12, 58.
Wakiya, S. J. 1956 Res. Rep. Fac. Engng, Niigata University (Japan), 5, 1.
Wakiya, S., Darabaner, C. L. & Mason, S. G. 1967 Rheol. Acta, 6, 264.