Bimodal Size Distributions in Grinding and Attrition

This Demonstration simulates the varying particle size distributions during the disintegration of particulates. It enables visualization of the difference when either particle shattering or surface attrition dominates the disintegration process or when the two play a comparable role. The actual scenario is determined by the relative time scale of the size reduction of the coarse fraction and that of the fines formation. The Demonstration is based on both fractions having normal size distributions and hence not all plots generated by the Demonstration correspond to real-life particulates.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


Snapshot 1: initial particle size distribution
Snapshot 2: dominant shattering of the coarse fraction, after time = 2 (arbitrary units)
Snapshot 3: dominant erosion of the coarse fraction, after time = 2 (arbitrary units)
Snapshot 4: shattering and erosion playing a comparable role, after time = 2 (arbitrary units)
This Demonstration simulates the evolution of the size distribution of particulates undergoing grinding or attrition. It starts with a coarse fraction whose normal size distribution's parameters are and . As the process progresses, the coarse fraction's mean, , and standard deviation, , vary in a manner controlled by a characteristic time, , and a span parameter, . At the same time, a fines fraction, which has a constant size distribution characterized by and , is formed. The rate of its formation, in terms of its mass fraction, is controlled by a characteristic time, .
The momentary size distribution, , is calculated with the equation , where is the momentary mass fraction of the fines, and is the probability density function (PDF) of the normal distribution having the chosen mean, , and standard deviation, , of the fines, or the time dependent and standard deviation, , of the course fraction, respectively.
The instantaneous weight fraction of the fines is calculated using .
During the process, the momentary coarse fraction's mean and standard deviation are calculated with the equations and , respectively.
The time, , and all model parameters, , , , , , , and are in arbitrary units and are entered with sliders.
The upper limit of the axis is also entered with a slider.
[1] L. M. Popplewell, O. H. Campanella, and M. Peleg, "Simulation of Bimodal Size Distributions in Aggregation and Disintegration Processes," Chemical Engineering Progress, 85, 1989 pp. 56–62.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2017 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+