An exact formula is obtained for the term of order c 2 in the expression for the bulk stress in a suspension of force-free spherical particles in Newtonian ambient fluid, where c is the volume fraction of the spheres and c ≪ 1. The particles may be of different sizes, and composed of either solid or fluid of arbitrary viscosity. The method of derivation circumvents the familiar obstacle, of non-absolutely convergent integrals representing the effect of all pair interactions in which one specified particle takes part, by the judicious use of a certain quantity which is affected by the presence of distant particles in a similar way and whose mean value in known exactly. The bulk stress is in general of non-Newtonian form and depends on the statistical properties of the suspension which in turn are dependent on the type of bulk flow.

Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • G. K. Batchelor
    • 1
  • J. T. Green
    • 1
  1. 1.Department of Applied Mathematics and Theoretical PhysicsUniversity of CambridgeEngland

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