Hostname: page-component-745bb68f8f-grxwn Total loading time: 0 Render date: 2025-01-27T09:06:13.007Z Has data issue: false hasContentIssue false
  • English
  • Français

Inertial migration of a small sphere in linear shear flows

Published online by Cambridge University Press:  26 April 2006

John B. McLaughlin
John B. McLaughlin
Affiliation:
Department of Chemical Engineering, Clarkson University, Potsdam, NY 13676, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The motion of a small, rigid sphere in a linear shear flow is considered. Saffman's analysis is extended to other asymptotic cases in which the particle Reynolds number based on its slip velocity is comparable with or larger than the square root of the particle Reynolds number based on the velocity gradient. In all cases, both particle Reynolds numbers are assumed to be small compared to unity. It is shown that, as the Reynolds number based on particle slip velocity becomes larger than the square root of the Reynolds number based on particle shear rate, the magnitude of the inertial migration velocity rapidly decreases to very small values. The latter behaviour suggests that contributions that are higher order in the particle radius may become important in some situations of interest.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 224 , March 1991 , pp. 261 - 274
Copyright
© 1991 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

Auton, T. R.: 1987 J. Fluid Mech. 183, 199–218.
Brenner, H.: 1966 Adv. Chem. Engng 6, 287–438.
Cherukat, P.: 1990 Wall and shear induced lift on a rigid sphere. M. S. thesis, Clarkson University.
Chbrukat, P. & Mclaughlin, J. B., 1990 Wall-induced lift on a sphere. Intl. J. Multiphase Flow 16, 899–907.Google Scholar
Cox, R. G. & Brenner, H., 1968 Chem. Engng Sci. 23, 147–173.
Cox, R. G. & Hsu, S. K., 1977 Intl J. Multiphase Flow 3, 201–222.
Cox, R. G. & Mason, S. G., 1971 Ann. Rev. Fluid Mech. 3, 291–316.
Drew, D. A.: 1978 J. Fluid Mech. 88, 393–400.
Drew, D. A.: 1988 Chem. Engng Sci. 43, 769–773.
Drew, D. A. & Lahey, R. T., 1987 Intl J. Multiphase Flow 13, 113–121.
Goldsmith, H. L. & Mason, S. G., 1967 The microrheology of dispersions. In Rheology, Theory and Applications (ed. F. R. Eirich), vol. 4, pp. 85–250. Academic.
Harper, E. Y. & Chang, I.-D. 1968 J. Fluid Mech. 33, 209–225.
Leal, L. G.: 1980 Ann. Rev. Fluid Mech. 12, 435–476.
Leighton, D. & Acrivos, A., 1985 Z. Angew. Math. Phys. 36, 174–178.
Mclaughlin, J. B.: 1989 Phys. Fluids l, 1211–1224.
Oseen, C. W.: 1910 Ark. Mat. Astr. Fys 6, No. 29.
Proudman, I. & Pearson, J. R. A. 1957 J. Fluid Mech. 2, 237–262.
Rubinow, S. I. & Keller, J. B., 1961 J. Fluid Mech. 11, 447–459.
Saffman, P. G.: 1965 J. Fluid Mech. 22, 385–400 (and Corrigendum, 31, 1968, 624).
Schonberg, J. A. & Hinch, E. J., 1989 J. Fluid Mech. 203, 517–524.
Segré, G. & Silberberg, A. 1962a J. Fluid Mech. 14, 115–135.
Segré, G. & Silberberg, A. 1962b J. Fluid Mech. 14, 136–157.
Vasseur, P. & Cox, R. G., 1976 J. Fluid Mech. 78, 385–413.
Vasseur, P. & Cox, R. G., 1977 J. Fluid Mech. 80, 561–591.