On the effective thermal conductivity and permeability of regular arrays of spheres

  • A. S. Sangani
  • A. Acrivos
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 154)


We consider two-phase materials in which the discrete phase consists of equalsized spheres fixed in a periodic array and summarize the results for the effective thermal conductivity and the permeability of such materials. The results are given for the whole range of volume fractions of spheres for three cubic arrays: simple, body-centered and face-centered.


Effective Thermal Conductivity Unknown Coefficient Stoke Flow Effective Permeability Periodic Array 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Batchelor, G.K.; O'Brien, R.W.: Thermal or electrical conduction through a granular material. Proc. Roy. Soc. Lond. A355, 313–333 (1977).Google Scholar
  2. 2.
    Hasimoto, H.: On the periodic fundamental solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres. J. Fluid Mech. 5, 317–328 (1959).Google Scholar
  3. 3.
    Jeffrey, D.J.: Conduction through a random suspension of spheres. Proc. Roy. Soc. Lond. A335, 355–367 (1973).Google Scholar
  4. 4.
    Levine, H.: The effective conductivity of a regular composite medium. J. Inst. Maths Applics. 2, 12–28 (1966)Google Scholar
  5. 5.
    McKenzie, D.R.; McPhedran, R.C.; Derrick, G.H.: The conductivity of lattices of spheres II. The body centered and faced centered lattices. Proc. Roy. Soc. Lond. A362, 211–232 (1978).Google Scholar
  6. 6.
    McPhedran, R.C.; McKenzie, D.R.: The conductivity of lattices of spheres I. The simple cubic lattice. Proc. Roy. Soc. Lond. A359, 45–62 (1978).Google Scholar
  7. 7.
    Meredith, R.E.; Tobias, C.W.: Resistance to potential flow through a cubical array of spheres. J. Appl. Phys. 31, 1270–1273 (1960).Google Scholar
  8. 8.
    O'Brien, R.W.: A method for the calculation of the effective transport properties of suspensions of interacting particles. J. Fluid Mech. 91, 17–39 (1979).Google Scholar
  9. 9.
    Runge, I.: On the electrical conductivity of metallic aggregates. Z. Tech. Physik. 6, 61–68 (1925).Google Scholar
  10. 10.
    Sangani, A.S.; Acrivos, A.: The effective conductivity of a periodic array of spheres. To be submitted (1981).Google Scholar
  11. 11.
    Sangani, A.S.; Acrivos, A.: Slow flow through a periodic array of spheres. To be submitted (1981).Google Scholar
  12. 12.
    Zick. A.A.; Homsy, G.M.: Stokes flow through periodic arrays of spheres. (to appear) J. Fluid Mech. (1981).Google Scholar
  13. 13.
    Zuzovski, M.; Brenner, H.: Effective conductivities of composite materials composed of cubic arrangements of spherical particles embedded in an isotropic matrix. J. Appl. Math. Phys. (ZAMP) 28, 979–992 (1977).Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • A. S. Sangani
    • 1
  • A. Acrivos
    • 1
  1. 1.Department of Chemical EngineeringStanford UniversityStanford

Personalised recommendations