Relation of Microstructure to Constitutive Equations

  • Donald A. Drew
  • Gary S. Arnold
  • Richard T. LaheyJr
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 26)


A set of equations for the averaged motion of a suspension of spheres in an inviscid fluid is derived by applying an ensemble average to the exact equations of motion. Constitutive equations to close the system for dilute, incompressible flow are derived by averaging the solution for the flow around a single sphere. The ensemble average is performed by allowing the center of the sphere to take random locations around an arbitrary spatial point. The corresponding volume average yields different results.


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  1. [1]
    J. H. Stuhmiller, The influence of interfacial pressure on the character of two-phase flow model equations International Journal of Multiphase Flow.Google Scholar
  2. [2]
    Love, A. E. H., A Treatise on the Mathematical Theory of Elasticity, Cambridge University Press, London, 1927.zbMATHGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1990

Authors and Affiliations

  • Donald A. Drew
    • 1
    • 4
  • Gary S. Arnold
    • 2
  • Richard T. LaheyJr
    • 3
  1. 1.Department of Mathematical SciencesRensselaer Polytechnic InstituteTroyUSA
  2. 2.General Electric CompanySchenectadyUSA
  3. 3.Department of Nuclear Engineering and Engineering PhysicsRensselaer Polytechnic InstituteTroyUSA
  4. 4.Mathematical Sciences InstituteCornell UniversityIthacaUSA

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