Journal of Engineering Mathematics

, Volume 27, Issue 2, pp 147–160

The velocity potential and the interacting force for two spheres moving perpendicularly to the line joining their centers

  • L. Li
  • W. W. Schultz
  • H. MerteJr.
Article

Abstract

The velocity potential around two spheres moving perpendicularly to the line joining their centers is given by a series of spherical harmonics. The appropriateness of the truncation is evaluated by determining the residual normal surface velocity on the spheres. In evaluating the residual normal velocity, a recursive procedure is constructed to evaluate the spherical harmonics to reduce computational effort and truncation error as compared to direct transformation or numerical integration. We estimate the lift force coefficient for touching spheres to be 0.577771, compared to the most accurate earlier estimate of 0.51435 by Miloh (1977).

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D. Leighton and A. Acrivos, The lift on a small sphere touching a plane in the presence of a simple shear flow. ZAMP 36 (1985) 174–178.Google Scholar
  2. 2.
    D.A. Drew, The lift force on a small sphere in the presence of a wall. J. of Chemical Engineering Science 43 (4) (1988) 769–773.Google Scholar
  3. 3.
    P. Cherukat and J.B. McLaughlin, Wall-induced lift on a sphere. Int. J. Multiphase Flow 16 (5) (1990) 899–907.Google Scholar
  4. 4.
    P. Vasseur and R.G. Cox, The lateral migration of spherical particles sedimenting in a stagnant bounded fluid. J. Fluid Mech. 80 (1977) 561–591.Google Scholar
  5. 5.
    W.M. Hicks, On the motion of two spheres in a fluid. Philosophical Transaction. Royal Society of London 171 (1880) 455–492.Google Scholar
  6. 6.
    A.B. Basset, On the Motion of Two Spheres in a Liquid, and Allied Problems. Proceedings, Mathematical Society 18 (1887) 369–377.Google Scholar
  7. 7.
    R.A. Herman, On the motion of two spheres in fluid and allied problems. Quartly Journal of Pure and Applied Mathematics xxii (1887) 204–262.Google Scholar
  8. 8.
    D. Endo, The Force on Two Spheres Placed in Uniform Flow. Proc. Phys.-Math. Soc. Japan 20 (1938) 667–703.Google Scholar
  9. 9.
    J.D. Love, Dielectric sphere-sphere and sphere-plane problems in electrostatics. Quartly Journal of Mech. Appl. Math. 28 (4) (1975) 449–471.Google Scholar
  10. 10.
    R.D. Small and D. Weihs, J. of Applied Mechanics. Trans. A.S.M.E. 42 (1975) 763.Google Scholar
  11. 11.
    O.V. Voinov, On the motion of two spheres in a perfect fluid. J. of Applied Mathematics and Mechanics 33 (4) (1969) 638–646.Google Scholar
  12. 12.
    T. Miloh, Hydrodynamics of deformable contiguous spherical shapes in an incompressible inviscid fluid. J. of Engineering Mathematics 11 (4) (1977) 349–372.Google Scholar
  13. 13.
    E.W. Hobson, Theory of spherical and ellipsoidal harmonics. Cambridge University Press (1931).Google Scholar
  14. 14.
    R.L. Burden, and J.D. Faires, Numerical Analysis, 3rd edn. Prindle, Weber & Schmidt, 1985.Google Scholar

Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • L. Li
    • 1
  • W. W. Schultz
    • 1
  • H. MerteJr.
    • 1
  1. 1.Department of Mechanical EngineeringUniversity of MichiganAnn ArborUSA

Personalised recommendations