Advertisement

Stochastic Modelling of a Dilute Fluid-Particle Suspension

  • Russel E. Caflisch
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 9)

Abstract

The bulk properties (such as average sedimentation speed and diffusion coefficient) in a sedimenting suspension of solid particles are sensitive to the statistical distribution of the particles. In this paper a method for determining the two particle distribution is described. In this method the particles are treated as point forces and only three particle interactions are included. Under several approximations it is shown that the two particle distribution separates into a product of functions of distance between the pair and of angle between the pair and the vertical.

Keywords

Stokes Equation Single Particle Impact Parameter Particle Distribution Particle Interaction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    G.K. Batchelor, “Sedimentation in a dilute suspension of spheres.” JFM 52 (1972) 245–268.MATHCrossRefGoogle Scholar
  2. 2.
    R.E. Caflisch and J.H.C. Luke, “Variance in the sedimentation speed of a suspension.” Physics of Fluids 28 (1985) 759–760.MATHCrossRefGoogle Scholar
  3. 3.
    R.E. Caflisch and J. Rubinstein, Lectures on the Mathematical Theory of Multi-Phase Flow (1986) CIMS.Google Scholar
  4. 4.
    J. Happel and H. Brenner, Law Reynolds Number Hydrodynamics (1983) Nijhoff.Google Scholar
  5. 5.
    H. Hasimoto, “On the periodic fundamental solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres.” JFM 5 (1959) 317–328.MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    J. Rubinstein, private communicationGoogle Scholar
  7. 7.
    P.G. Saffman, “On the settling speeds of free and fixed suspensions.” Studies in Appl. Math. 52 (1973) 115–127MATHGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1987

Authors and Affiliations

  • Russel E. Caflisch
    • 1
  1. 1.Courant Institute of Mathematical SciencesNew York UniversityUSA

Personalised recommendations