Comminution: a modified logistic growth function

Comminution: a modified logistic growth function

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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. Access through your institution Buy or subscribe This is a preview of subscription content, access via your institution ACCESS OPTIONS Access through your institution Subscribe to this journal Receive 51 print issues and online access $199.00 per year only $3.90 per issue Learn more Buy this article * Purchase on SpringerLink * Instant access to full article PDF Buy now Prices may be subject to local taxes which are calculated during checkout ADDITIONAL ACCESS OPTIONS: * Log in * Learn about institutional subscriptions * Read our FAQs * Contact customer support SIMILAR CONTENT BEING VIEWED BY OTHERS COMPARISON BETWEEN RESPONSE SURFACE METHODOLOGY AND TAGUCHI METHOD FOR DYEING PROCESS PARAMETERS OPTIMIZATION IN FABRIC MANUFACTURING BY EMPIRICAL PLANNING Article Open access 25 March 2025 FAST CALCULATION OF SCATTERING PATTERNS USING HYPERGEOMETRIC FUNCTION ALGORITHMS Article Open access 15 January 2023 A UNIVERSAL MODEL FOR THE LORENZ CURVE WITH NOVEL APPLICATIONS FOR DATASETS CONTAINING ZEROS AND/OR EXHIBITING EXTREME INEQUALITY Article Open access 23 March 2023 REFERENCES * Holmes, J. A., _Trans. Inst. Chem. Eng._, 35, 125 (1957). Google Scholar  * Kick, F., _Das Gesetz der Proportionalem Widerstand und Seine Anwendung_ (Leipzig, 1885). Google Scholar  * Bond, F. C., _Trans. Amer. Inst. Min. Eng._, 193, 484 (1952). Google Scholar  * Rittinger, P. R. von, _Lehrbuch der Aufbersitungskunde_ (Berlin, 1867). Google Scholar  * Kempthorne, O., _et al._ (eds.), _Statistics and Mathematics in Biology_ (Iowa State College Press, 1954). * Lotka, A. J., _Mathematical Biology_ (Dover Publications, New York, 1956). MATH  Google Scholar  * Harris, C. C., _Second Symp. on Coal Preparation_, 191 (Univ. of Leeds. 1957). Google Scholar  * Harris, C. C., _J. App. Phys._, 31, 215 (1960). Article  ADS  Google Scholar  * Frangiskos, N. Z., Harris, C. C., and Jowett, A., _Intern. Surface Activity Cong., Cologne_, 4, 404 (1960). Google Scholar  * Svensson, J., and Murkes, J., _Intern. Mineral Dressing Cong._, 37 (Stockholm, 1957). Google Scholar  Download references AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * Department of Mining, University of Leeds, C. C. HARRIS Authors * C. C. HARRIS View author publications You can also search for this author inPubMed Google Scholar 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: 26 January 1963 * DOI: https://doi.org/10.1038/197371a0 SHARE THIS ARTICLE Anyone you share the following link with will be able to read this content: Get shareable link Sorry, a shareable link is not currently available for this article. Copy to clipboard Provided by the Springer Nature SharedIt content-sharing initiative

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. Access through your institution Buy or subscribe This is a preview of subscription content, access via your


institution ACCESS OPTIONS Access through your institution Subscribe to this journal Receive 51 print issues and online access $199.00 per year only $3.90 per issue Learn more Buy this


article * Purchase on SpringerLink * Instant access to full article PDF Buy now Prices may be subject to local taxes which are calculated during checkout ADDITIONAL ACCESS OPTIONS: * Log in


* Learn about institutional subscriptions * Read our FAQs * Contact customer support SIMILAR CONTENT BEING VIEWED BY OTHERS COMPARISON BETWEEN RESPONSE SURFACE METHODOLOGY AND TAGUCHI METHOD


FOR DYEING PROCESS PARAMETERS OPTIMIZATION IN FABRIC MANUFACTURING BY EMPIRICAL PLANNING Article Open access 25 March 2025 FAST CALCULATION OF SCATTERING PATTERNS USING HYPERGEOMETRIC


FUNCTION ALGORITHMS Article Open access 15 January 2023 A UNIVERSAL MODEL FOR THE LORENZ CURVE WITH NOVEL APPLICATIONS FOR DATASETS CONTAINING ZEROS AND/OR EXHIBITING EXTREME INEQUALITY


Article Open access 23 March 2023 REFERENCES * Holmes, J. A., _Trans. Inst. Chem. Eng._, 35, 125 (1957). Google Scholar  * Kick, F., _Das Gesetz der Proportionalem Widerstand und Seine


Anwendung_ (Leipzig, 1885). Google Scholar  * Bond, F. C., _Trans. Amer. Inst. Min. Eng._, 193, 484 (1952). Google Scholar  * Rittinger, P. R. von, _Lehrbuch der Aufbersitungskunde_ (Berlin,


1867). Google Scholar  * Kempthorne, O., _et al._ (eds.), _Statistics and Mathematics in Biology_ (Iowa State College Press, 1954). * Lotka, A. J., _Mathematical Biology_ (Dover


Publications, New York, 1956). MATH  Google Scholar  * Harris, C. C., _Second Symp. on Coal Preparation_, 191 (Univ. of Leeds. 1957). Google Scholar  * Harris, C. C., _J. App. Phys._, 31,


215 (1960). Article  ADS  Google Scholar  * Frangiskos, N. Z., Harris, C. C., and Jowett, A., _Intern. Surface Activity Cong., Cologne_, 4, 404 (1960). Google Scholar  * Svensson, J., and


Murkes, J., _Intern. Mineral Dressing Cong._, 37 (Stockholm, 1957). Google Scholar  Download references AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * Department of Mining, University of


Leeds, C. C. HARRIS Authors * C. C. HARRIS View author publications You can also search for this author inPubMed Google Scholar 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: 26 January


1963 * DOI: https://doi.org/10.1038/197371a0 SHARE THIS ARTICLE Anyone you share the following link with will be able to read this content: Get shareable link Sorry, a shareable link is not


currently available for this article. Copy to clipboard Provided by the Springer Nature SharedIt content-sharing initiative