Wolfram Demonstrations Project

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.

Contributed by: Mark D. Normand and Micha Peleg

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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.

Reference

[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.

Bimodal Normal Distribution Mixtures (Wolfram Demonstrations Project)

Mark D. Normand and Micha Peleg

"Bimodal Size Distributions in Grinding and Attrition"
http://demonstrations.wolfram.com/BimodalSizeDistributionsInGrindingAndAttrition/
Wolfram Demonstrations Project
Published: August 5, 2011