Relation of Microstructure to Constitutive Equations

  • Donald A. Drew
  • Stephen L. Passman
Part of the Applied Mathematical Sciences book series (AMS, volume 135)


This chapter is devoted to deriving and using microstructural information to find constitutive equations, giving relationships between certain average quantities and the average fields. The physical situation is one in which corpuscular models can be highly useful in motivating the forms of the constitutive equations. In effect, the study of the mechanics of multicomponent fluids necessitates the study of the form of the momentum exchange term and the stress in the momentum equation. The study of these terms is aided by a physically appropriate corpuscular model, consisting of solutions for flows in this model, which are sometimes exact but usually approximate. Once these solutions are found, they can be averaged to find the force of interaction in the continuum equations.


Constitutive Equation Reynolds Stress Ensemble Average Effective Viscosity Disperse Component 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Donald A. Drew
    • 1
  • Stephen L. Passman
    • 2
  1. 1.Department of Mathematical ScienceRensselaer Polytechnic InstituteTroyUSA
  2. 2.Sandia National LaboratoriesAlbuquerqueUSA

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