Fractal evaluation of particle size distributions of chromites in different comminution environments

Abstract Particle size distributions (PSDs) are often rendered as cumulative functions, either as number of particles larger than a certain diameter, or as mass smaller than a certain diameter. The fractional exponent of the number/mass-size power law has been interpreted as the fractal dimension of the distribution. An application of PSD in comminuted chromites by means of the fractal mass distribution is presented. The five types of chromite samples were subjected to four comminution events; jaw, cone, hammer crushing and ball milling. The PSDs generated by different comminution devices has been evaluated by mass-based fractal fragmentation theory and the fractal dimensions of fragmentation (DF), a value quantifying the intensity of fragmentation, have been obtained for each chromite ore. The results of the present study show that the particle size distributions of the comminuted chromites having different mineralogical characteristics are fractal in nature. Single and multifractal methods have been successfully applied to characterize particle size distributions (PSD) of chromite samples comminuted by different comminution devices. In general, depending on the energy events, the chromite ores having different mineralogical characteristics showed a general trend of PSDs, and hence, the ranges of DF for a specific device. It can be concluded that breakage mechanisms have more effective on fractal dimensions of chromite samples although the mineralogical properties and size of the chromite ores broken are also a factor.

[1]  L. Vallejo,et al.  Fractal analysis of the roughness and size distribution of granular materials , 1997 .

[2]  Nicholas J. Miles,et al.  Fractal Characterization of Pulverised Materials , 1993 .

[3]  W. Gong,et al.  Effects of process parameters on the comminution capability of high pressure water jet mill , 2006 .

[4]  R. Segars,et al.  Effect of particle size distribution in determining a powder's fractal dimension by single gas BET: A mathematical model , 1992 .

[5]  R. Hogg,et al.  Particle Shape Modification in Comminution , 2002 .

[6]  Donald L. Turcotte,et al.  Fractals and fragmentation , 1986 .

[7]  Mark Cross,et al.  Modeling and Simulation of Mineral Processing Systems , 2003 .

[8]  M. Ghomshei,et al.  Influence of impact velocity on fragmentation and the energy efficiency of comminution , 2006 .

[9]  Thomas G. Blenkinsop,et al.  Fractal Characterization of Particle Size Distributions in Chromitites from the Great Dyke, Zimbabwe , 2000 .

[10]  Alberto Carpinteri,et al.  A multifractal comminution approach for drilling scaling laws , 2003 .

[11]  I. Jefferson,et al.  Fractal characteristics of loess formation: evidence from laboratory experiments , 2003 .

[12]  F. Bartoli,et al.  Structure and self‐similarity in silty and sandy soils: the fractal approach , 1991 .

[13]  Alberto Carpinteri,et al.  A fractal comminution approach to evaluate the drilling energy dissipation , 2002 .

[14]  J. Drzymała,et al.  Two-dimensional fractal linearization of distribution curves , 2005 .

[15]  Adem Tasdemir,et al.  Evaluation of grain size distribution of unbroken chromites , 2008 .

[16]  Lev Filippov,et al.  Fractures, fractals and breakage energy of mineral particles , 1999 .

[17]  G. Campbell,et al.  Characterization of Particle-Size Distribution in Soils with a Fragmentation Model , 1999 .

[18]  Models of fragmentation with power law log-normal distributions , 2000, cond-mat/0003092.

[19]  T. Allen.  Particle Size Measurement , 1965, Nature.

[20]  H. Millán,et al.  On the fractal scaling of soil data. Particle-size distributions , 2003 .

[21]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[22]  D. S. Yan,et al.  Mineral Processing Design and Operation: An Introduction , 2006 .

[23]  Giuseppe Lacidogna,et al.  Scaling of energy dissipation in crushing and fragmentation: a fractal and statistical analysis based on particle size distribution , 2004 .

[24]  Scott W. Tyler,et al.  Fractal scaling of soil particle-size distributions: analysis and limitations , 1992 .