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.