Skip to main content
SpringerLink
Log in

The influence of the degree of heterogeneity on the elastic properties of random sphere packings

  • Original Paper
  • Published:
Granular Matter Aims and scope Submit manuscript

Abstract

The macroscopic mechanical properties of colloidal particle gels strongly depend on the local arrangement of the powder particles. Experiments have shown that more heterogeneous microstructures exhibit up to one order of magnitude higher elastic properties than their more homogeneous counterparts at equal volume fraction. In this paper, packings of spherical particles are used as model structures to computationally investigate the elastic properties of coagulated particle gels as a function of their degree of heterogeneity. The discrete element model comprises a linear elastic contact law, particle bonding and damping. The simulation parameters were calibrated using a homogeneous and a heterogeneous microstructure originating from earlier Brownian dynamics simulations. A systematic study of the elastic properties as a function of the degree of heterogeneity was performed using two sets of microstructures obtained from Brownian dynamics simulation and from the void expansion method. Both sets cover a broad and to a large extent overlapping range of degrees of heterogeneity. The simulations have shown that the elastic properties as a function of the degree of heterogeneity are independent of the structure generation algorithm and that the relation between the shear modulus and the degree of heterogeneity can be well described by a power law. This suggests the presence of a critical degree of heterogeneity and, therefore, a phase transition between a phase with finite and one with zero elastic properties.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Fakhimi A., Villegas T.: Rock Mech. Rock Eng. 40, 193 (2007)

    Article  ADS  Google Scholar 

  2. Rognon P.G., Roux J.N., Wolf D., Naaím M., Chevoir F.: Europhys. Lett. 74, 644 (2006)

    Article  ADS  Google Scholar 

  3. Ottino J.M., Khakhar D.V.: Annu. Rev. Fluid Mech. 32, 55 (2000)

    Article  MathSciNet  ADS  Google Scholar 

  4. Zaccone A., Lattuada M., Wu H., Morbidelli M.: J. Chem. Phys 127, 174512 (2007)

    Article  ADS  Google Scholar 

  5. Gardiner B.S., Tordesillas A.: Powder Technol. 161, 110 (2006)

    Article  Google Scholar 

  6. Silbert L.E., Ertaş D., Grest G.S., Halsey T.C., Levine D.: Phys. Rev. E 65, 031304 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  7. Martin C.L., Bordia R.K.: Phys. Rev. E 77, 031307 (2008)

    Article  ADS  Google Scholar 

  8. Cates M.E., Wittmer J.P., Bouchaud J.P., Claudin P.: CHAOS 9, 511 (1999)

    Article  ADS  MATH  Google Scholar 

  9. Atman A.P.F., Brunet P., Geng J., Reydellet G., Combe G., Claudin P., Behringer R.P., Clément E.: J. Phys. Condens. Matter 17, S2391 (2005)

    Article  ADS  Google Scholar 

  10. Schenker I., Filser F.T., Aste T., Herrmann H.J., Gauckler L.J.: Phys. Rev. E 80, 021302 (2009)

    Article  ADS  Google Scholar 

  11. Hütter M.: J. Colloid Interface Sci. 231, 337 (2000)

    Article  Google Scholar 

  12. Schenker I., Filser F.T., Aste T., Gauckler L.J.: J. Eur. Ceram. Soc. 28, 1443 (2008)

    Article  Google Scholar 

  13. Hütter M.: Phys. Rev. E. 68, 031404 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  14. Gauckler L.J., Graule T., Baader F.: Mater. Chem. Phys. 61, 78 (1999)

    Article  Google Scholar 

  15. Tervoort E., Tervoort T.A., Gauckler L.J.: J. Am. Ceram. Soc. 87, 1530 (2004)

    Article  Google Scholar 

  16. Wyss H.M., Romer S., Scheffold F., Schurtenberger P., Gauckler L.J.: J. Colloid Interface Sci. 241, 89 (2001)

    Article  Google Scholar 

  17. Wyss H.M., Hütter M., Müller M., Meier L.P., Gauckler L.J.: J. Colloid Interface Sci. 248, 340 (2002)

    Article  Google Scholar 

  18. Balzer B., Hruschka M.K.M., Gauckler L.J.: J. Colloid Interface Sci. 216, 379 (1999)

    Article  Google Scholar 

  19. Wyss H.M., Deliormanli A.M., Tervoort E., Gauckler L.J.: AIChE J. 51, 134 (2005)

    Article  Google Scholar 

  20. Wyss H.M., Tervoort E., Meier L.P., Müller M., Gauckler L.J.: J. Colloid Interface Sci. 273, 455 (2004)

    Article  Google Scholar 

  21. Balzer B., Hruschka M.K.M., Gauckler L.J.: J. Am. Ceram. 84, 1733 (1999)

    Article  Google Scholar 

  22. Hesselbarth D., Tervoort E., Urban C., Gauckler L.J.: J. Am. Ceram. Soc. 84, 1689 (2001)

    Article  Google Scholar 

  23. Hesselbarth, D.: Quellfähige Polymerbinder in Aluminiumoxid-Suspensionen (Ph.D. thesis no. 13404, ETH Zurich, Switzerland, 2000) http://e-collection.ethbib.ethz.ch

  24. Cundall P.A., Strack O.D.L.: Géotechnique. 29, 47 (1979)

    Article  Google Scholar 

  25. PFC3D User’s manual: (Itasca Consulting Group, Inc., Minneapolis, Minnesota, USA) (1995)

  26. Brown E.T.: Analytical and computational methods in engineering rock mechanics. Allen & Unwin, London (1987)

    Google Scholar 

  27. Schenker I., Filser F.T., Gauckler L.J.: Granul. Matter. 12, 437 (2010)

    Article  Google Scholar 

  28. Hütter, M.: Brownian dynamics simulation of stable and of coagulating colloids in Aqueous Suspension (Ph.D. thesis no. 13107, ETH Zurich, Switzerland, 1999) http://e-collection.ethbib.ethz.ch

  29. Russel W.B., Saville D.A., Schowalter W.R.: Colloidal dispersions. Cambridge University Press, New York (1989)

    Google Scholar 

  30. Schenker I., Filser F.T., Herrmann H.J., Gauckler L.J.: Granul. Matter. 11, 201 (2009)

    Article  Google Scholar 

  31. Torquato S., Lu B., Rubinstein J.: Phys. Rev. A. 41, 2059 (1990)

    Article  ADS  Google Scholar 

  32. Yanez J.A., Shikata T., Lange F.F., Pearson D.S.: J. Am. Ceram. Soc. 79, 2917 (1996)

    Article  Google Scholar 

  33. Benguigui L.: Phys. Rev. Lett. 53, 2028 (1984)

    Article  ADS  Google Scholar 

  34. Bergman D.J.: Phys. Rev. E. 65, 026124 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  35. Johnson K.L., Kendall K., Roberts A.D.: Proc. R. Soc. Lond. A. 324, 301 (1971)

    Article  ADS  Google Scholar 

  36. Madadi M., Tsoungui O., Lätzel M., Luding S.: Int. J. Sol. Struct. 41, 2563 (2004)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Materials, Nonmetallic Materials, ETH Zurich, 8093, Zurich, Switzerland

    Iwan Schenker, Frank T. Filser & Ludwig J. Gauckler

  2. Materials Technology, Mechanical Engineering, Eindhoven University of Technology, 5600 MB, Eindhoven, The Netherlands

    Markus Hütter

Authors
  1. Iwan Schenker
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Frank T. Filser
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Markus Hütter
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ludwig J. Gauckler
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Iwan Schenker.

Electronic Supplementary Material

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schenker, I., Filser, F.T., Hütter, M. et al. The influence of the degree of heterogeneity on the elastic properties of random sphere packings. Granular Matter 14, 333–340 (2012). https://doi.org/10.1007/s10035-012-0316-5

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10035-012-0316-5

Keywords

Search

Navigation