Fractal approach of particle size distribution description of ball milling products: effects of ore type, feed and particle size

References

• Sadrai S, Meech JA, Ghomshei M, et al. Influence of impact velocity on fragmentation and the energy efficiency of comminution. Int J Impact Eng. 2006;33:723–734.
   Web of Science ®Google Scholar
• Allen T. Particle size measurement. powder sampling and particle size measurement. Powder Technology Series. 1997; vol.1, p. 50–84, Chapman and Hall.
   Google Scholar
• Ahmed HAM, Drzymala J. Two-dimensional fractal linearization of distribution curves. Physicochem Probl Miner Process. 2005;39:129–139.
   Google Scholar
• Lu P, Jefferson IF, Rosenbaum MS, et al. Fractal characteristics of loess formation: evidence from laboratory experiments. Eng Geol. 2003;69(3–4):287–293.
   Web of Science ®Google Scholar
• Casini F, Viggiani GMB, Springman SM. Breakage of an artificial crushablematerial under loading. GranularMatter. 2013;15(5):661–673.
   Web of Science ®Google Scholar
• Wang Y, Dan W, Xu Y, et al. Fractal and morphological characteristics of single marble particle grinding in uniaxial compression tests. Hindawi Publ Corporation; Adv Mat Sci Eng. 2015;2015:10.
   Web of Science ®Google Scholar
• Mandelbrot BB. The fractal geometry of nature. New York: Freeman; 1982.
   Google Scholar
• Falconer K. Fractal geometry mathematical foundations and applications. New Jersey: J. Willi and sons; 2003.
   Google Scholar
• Arhangel’skii AV, van Mill J. Some aspects of dimension theory for topological groups. Indagationes Mathematicae. 2018;29:202–225.
   Web of Science ®Google Scholar
• Bartoli F, Philippy R, Doirisse M, et al. Structure and selfsimilarity in silty and sandy soils: the fractal approach. J. Soil Sci. 1991;42:167–185.
   Web of Science ®Google Scholar
• Carpinteri A, Pugno N. A multifractal comminution approach for drilling scaling laws. Powder Technol. 2003;131:93–98.
   Web of Science ®Google Scholar
• Filippov LO, Joussemet R, Irannajad M, et al. An approach of the whiteness quantification of comminuted and floated talc concentrate. Powder Technol. 1999;105:106–112.
   Web of Science ®Google Scholar
• Irannajad M. (1998). Chapter vii: study of particles morphology by fractal approach. in PhD thesis, entitled: Valorization of talcose mining rejects by physico-chemical (flotation) processing: influence of treatments on the whiteness of concentrates”. Department of Environment and Mineralurgy (Laboratoire Environnment et Mineralurgie (L.E.M.)), National Superior School of Applied Mineralogy (Ecole Nationale Superieure de Geologie Applique (ENSG)), University of Lorraine (ex. Lorraine National Polytechnics Institute (Institut National Polytechnique de Lorraine (INPL))), Nancy, France.
   Google Scholar
• Cai G, Xiong Y, Lin L. Experimental study on the fractal characteristics of rocks grinding. MATEC Web of Conferences. 2015;25:02008.
   Google Scholar
• Delagrammatikas G, Delagrammatikas M, Tsimas S. Particle size distributions a new approach. Powder Technol. 2007;176:57–65.
   Web of Science ®Google Scholar
• Mohammadi M, Shabanpour M, Mohammadi MH, et al. Characterizing spatial variability of soil textural fractions and fractal parameters derived from particle size distributions. Pedosphere. 2019;29–22:224–234.
   Web of Science ®Google Scholar
• Moradi I, Irannajad M. (2020). Particles morphology description by fractal geometry in mineral processing operations. 3rd National Conference on Materials Engineering, Metallurgy & Mining. Ahvaz. Iran. 19 February.
   Google Scholar
• Powell MS. (2006). The unified comminution model – a conceptually new model. In: Proceedings of the XXIII IMPC. 3–8 September, Istanbul, Turkey. 1783–1788. ISBN: 975-7946-27-3.
   Google Scholar
• Powell MS, Govender I, McBride AT. Applying DEM outputs to the unified comminution model. Miner Eng. 2008;21(11):744–750.
   Web of Science ®Google Scholar
• Powell MS, Weerasekara NS, Cole S, et al. DEM modelling of liner evolution and its influence on grinding rate in ball mills. Miner Eng. 2011;24:341–351.
   Web of Science ®Google Scholar
• Kotake N, Daibo K, Yamamoto T, et al. Experimental investigation on a grinding rate constant of solid materials by a ball mill - effect of ball diameter and feed size. Powder Technol. 2004;143–144:196–203.
   Web of Science ®Google Scholar
• Yekeler M, Ozkan A, Austin LG. Kinetics of fine wet grinding in a laboratory ball mill. Powder Technol. 2001;114(1–3):224–228.
   Web of Science ®Google Scholar
• Gupta VK. (1986). 1st World Particle Technology Conf. “Part H-Comminution, 6th Eur”. Syrup. Nurember∼ Germany.
   Google Scholar
• Gupta VK. (1987). SME-AIME Ann. Meet. Denver. CO,: USA, Prepr. No. 87-152.
   Google Scholar
• Bu X, Chen Y, Ma G, et al. Differences in dry and wet grinding with a high solid concentration of coking coal using a laboratory conical ball mill: breakage rate morphological characterization and induction time. Adv Powder Technol. 2019;30(11):2703–2711.
   Web of Science ®Google Scholar
• Gupta VK. Effect of size distribution of the particulate material on the specific breakage rate of particles in dry ball milling. Powder Technol. 2017;305:714–722.
   Web of Science ®Google Scholar
• Hlabangana H, Danha G, Muzenda E. Effect of ball and feed particle size distribution on the milling efficiency of a ball mill: An attainable region approach. S Afr J Chem Eng. 2018;25:79–84.
   Google Scholar
• Chimwania N, Mohalea TM, Bwalya MM. Tailoring ball mill feed size distribution for the production of a size-graded product. Miner Eng. 2019;141:105891.
   Web of Science ®Google Scholar
• Acar C, Hosten C. Grinding kinetics of steady-state feeds in locked-cycle dry ball milling. Powder Technol. 2013;249:274–281.
   Web of Science ®Google Scholar
• Turcotte DL. Fractals and fragmentation. J Geophys Res. 1986;91:1921–1926.
   Web of Science ®Google Scholar
• Brown GJ, Miles NJ, Hall ST. Fractal characterization of pulverized materials. Part Part Syst Char. 1993;10(1):1–6.
   Web of Science ®Google Scholar
• Zhang J, Li M, Liu Z, et al. Fractal characteristics of comminuted particles of coal gangue under compaction. Powder Technol. 2017;305:12–18.
   Web of Science ®Google Scholar
• Moradi I, Irannajad M. (2020). Influence of mill feeding size on particle size distribution by fractal geometry approach. 3rd National Conference on Materials Engineering, Metallurgy & Mining. Ahvaz. Iran. 19 February.
   Google Scholar
• Moradi I, Mohammadzadeh MH, Irannajad M. (2019). Calculation of fractal dimension of crushing product by variation of ore type and feed size. The 2nd Iranian Conference of Green Mining &Mine Industry. Zanjan, Iran. 18 December.
   Google Scholar
• Moradi I, Irannajad M. Fractal dimension of crushing products: effects of feed size distribution and feed rate. Part Sci Technol. 2021a;39(7):877–886. doi:10.1080/02726351.2020.1856248.
   Web of Science ®Google Scholar
• Moradi I, Irannajad M. Effect of feeding rate on comminution products by fractal geometry. Amirkabir J Civil Eng. 2021b;53–55:19–19.
   Google Scholar
• Alaei Kakhki A, Kohsari AH, Barati Harati M. (2013). Mineralogical studies and economic geology of copper deposit Ghale Zari Birjand. 20st Symposium of Crystallography and Mineralogy of Iran.
   Google Scholar
• Mehdilo A, Irannajad M. Applied mineralogical studies on Iranian hard rock titanium deposit. J Miner Mat Charact Eng. 2010;9(3):247–262.
   Google Scholar
• Mehdilo A, Irannajad M. Effects of mineralogical and textural characteristics of ilmenite concentrate on synthetic rutile production. Arab J Geosci. 2013;6:3865–3876.
   Web of Science ®Google Scholar
• Irannajad M. (2002). Mineral Processing Studies of Iranian Titanomagnetites: Case Study on Qara-aghaj Titanium Ore. Report of investigation, Amirkabir University of Technology, Tehran, Iran.
   Google Scholar
• Flook AG. The use of dilation logic on the quantimet to achieve fractal dimension characterization of textured surfaces. Powder Technol. 1978;21:295–298.
   Web of Science ®Google Scholar
• Hyslip J, Vallejo LE. Fractal analysis of the roughness and size distribution of granular materials. Eng Geol. 1997;48:231–244.
   Web of Science ®Google Scholar
• Tyler SW, Wheatcract SW. Fractal scaling of soil particle-size distribution: analyses and limitations. Soil Sci Soc Am J. 1992;56:362–369.
   Web of Science ®Google Scholar