Transport Processes in Concentrated Suspensions: The Role of Particle Fluctuations

  • James T. Jenkins
  • David F. McTigue
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 26)


Transport of momentum in slow flows of concentrated suspensions may be strongly dependent upon the fluctuations of particles about their mean motion. The intensity of the velocity fluctuations is an internal field that is the analog of temperature in classical kinetic theories. This viscous temperature is governed by a balance law that includes flux, production, and dissipation terms. We provide heuristic arguments to motivate the forms of the viscosity, conductivity, dissipation, and pressure in a theory that includes the viscous temperature. The approach parallels previous developments for dry, granular materials. Phenomena observed in flows of concentrated suspensions, including apparent normal stresses and shear-induced diffusion, are contained within the structure of this theory.

Key words

concentrated suspension diffusion effective viscosity normal stress rheology 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    R. A. Bagnold, Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear, Proc. Royal Soc. London, A223 (1954), pp. 49–63.CrossRefGoogle Scholar
  2. [2]
    S. B. Savage and M. Sayed, Stresses developed by dry cohesionless granular materials sheared in an annular shear cell, J. Fluid Mech., 142 (1984), pp. 391–430.CrossRefGoogle Scholar
  3. [3]
    D. M. Hanes and D. L. Inman, Observations of rapidly flowing granular-fluid materials, J. Fluid Mech., 150 (1985), pp. 357–380.CrossRefGoogle Scholar
  4. [4]
    P. K. Haff, Grain flow as a fluid mechanical phenomenon, J. Fluid Mech., 134 (1983), pp. 401–433.CrossRefzbMATHGoogle Scholar
  5. [5]
    J. T. Jenkins and S. B. Savage, A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles, J. Fluid Mech., 130 (1983), pp. 187–202.CrossRefzbMATHGoogle Scholar
  6. [6]
    C.-J. Lin, J. H. Peery, and W. R. Schowalter, Simple shear flow round a rigid sphere: inertial effects and suspension rheology, J. Fluid Mech., 44 (1970), pp. 1–17.CrossRefzbMATHGoogle Scholar
  7. [7]
    J. F. Brady and G. Bossis, The rheology of concentrated suspensions of spheres in simple shear flow by numerical simulation, J. Fluid Mech., 155 (1985), pp. 105–129.CrossRefGoogle Scholar
  8. [8]
    F. A. Gadala-Maria, The rheology of concentrated suspensions, Ph.D. thesis, Stanford University, 1979.Google Scholar
  9. [9]
    W. R. Schowalter, Mechanics of Non-Newtonian Fluids Pergamon, Oxford, 1978.Google Scholar
  10. [10]
    J. T. Jenkins and S. C. Cowin, Theories for flowing granular materials, Mechanics Applied to the Transport of Bulk Materials, S. C. Cowin, ed., Am. Soc. Mech. Eng., AMD-31 (1979), pp. 79–89.Google Scholar
  11. [11]
    D. J. Jeffrey and Y. Onishi, Calculation of the resistance and mobility functions for two unequal rigid spheres in low-Reynolds-number flow, J. Fluid Mech., 139 (1984), pp. 261–290.CrossRefzbMATHGoogle Scholar
  12. [12]
    D. J. Jeffery and A. Acrivos, The rheological properties of suspensions of rigid particles, AIChE J., 22 (1976), pp. 417–432.CrossRefGoogle Scholar
  13. [13]
    D. Leighton and A. Acrivos, Measurement of shear-induced self-diffusion in concentrated suspensions of spheres, J. Fluid Mech., 177 (1987), pp. 109–131.CrossRefGoogle Scholar
  14. [14]
    J. T. Jenkins and D. F. McTigue, Viscous fluctuations and the rheology of concentrated supensions, in preparation.Google Scholar
  15. [15]
    D. Leighton and A. Acrivos, The shear-induced migration of particles in concentrated suspensions, J. Fluid Mech., 181 (1987), pp. 415–439.CrossRefGoogle Scholar
  16. [16]
    R. H. Davis and A. Acrivos, Sedimentation of noncolloidal particles at low Reynolds numbers, Ann. Rev. Fluid Mech., 17 (1985), pp. 91–118.CrossRefGoogle Scholar
  17. [17]
    D. Leighton and A. Acrivos, Viscous resuspension, Chem. Eng. Sci., 41 (1986), pp. 1377–1384.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1990

Authors and Affiliations

  • James T. Jenkins
    • 1
  • David F. McTigue
    • 2
  1. 1.Department of Theoretical and Applied MechanicsCornell UniversityIthacaUSA
  2. 2.Fluid Mechanics and Heat Transfer Division ISandia National LaboratoriesAlbuquerqueUSA

Personalised recommendations