Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Comminution: a Modified Logistic Growth Function

Abstract

HOLMES'S equation1 rewritten in terms of specific surface area, S, can be derived from the differential equation: where E is energy input per unit volume and r is Kick's law deviation exponent1. Equation (1) reduces to Kick's equation2 when r = 0, Bond's third theory3 when r = ½ and Rittinger's equation4 when r = 1. These equations suggest that material of unlimited fineness can be produced by milling.

This is a preview of subscription content, access via your institution

Access options

Buy this article

USD 39.95

Prices may be subject to local taxes which are calculated during checkout

Similar content being viewed by others

References

  1. Holmes, J. A., Trans. Inst. Chem. Eng., 35, 125 (1957).

    Google Scholar 

  2. Kick, F., Das Gesetz der Proportionalem Widerstand und Seine Anwendung (Leipzig, 1885).

    Google Scholar 

  3. Bond, F. C., Trans. Amer. Inst. Min. Eng., 193, 484 (1952).

    Google Scholar 

  4. Rittinger, P. R. von, Lehrbuch der Aufbersitungskunde (Berlin, 1867).

    Google Scholar 

  5. Kempthorne, O., et al. (eds.), Statistics and Mathematics in Biology (Iowa State College Press, 1954).

  6. Lotka, A. J., Mathematical Biology (Dover Publications, New York, 1956).

    MATH  Google Scholar 

  7. Harris, C. C., Second Symp. on Coal Preparation, 191 (Univ. of Leeds. 1957).

    Google Scholar 

  8. Harris, C. C., J. App. Phys., 31, 215 (1960).

    Article  ADS  Google Scholar 

  9. Frangiskos, N. Z., Harris, C. C., and Jowett, A., Intern. Surface Activity Cong., Cologne, 4, 404 (1960).

    Google Scholar 

  10. Svensson, J., and Murkes, J., Intern. Mineral Dressing Cong., 37 (Stockholm, 1957).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

HARRIS, C. Comminution: a Modified Logistic Growth Function. Nature 197, 371 (1963). https://doi.org/10.1038/197371a0

Download citation

  • Issue date:

  • DOI: https://doi.org/10.1038/197371a0

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing