Description and modelling of disintegrating and segregating particle populations

• Main Author: Popplewell, Lewis Michael
• Language: ENG
• Published: ScholarWorks@UMass Amherst 1989
• Subjects: Agricultural engineering
• Online Access: https://scholarworks.umass.edu/dissertations/AAI9001556

It is often desired to represent the size distribution of particle populations with a continuous function. Three functions commonly used for this purpose, the normal, log-normal, and Rosin-Rammler distributions, have drawbacks in this regard related to infinite range, shape, and for the last two mentioned, dependent mode and variance. Two functions which avoid these problems have been proposed elsewhere, the modified beta and modified normal distributions. It was shown in this work that these distributions are virtually interchangeable, so the modified beta distribution is favored for use due to its having greater explicitness and fewer constants. The modified beta distribution was then successfully fit via both non-linear regression and direct calculation to reasonably narrow versions of the normal, log-normal, and Rosin-Rammler distributions. Aggregation or disintegration of a particle population often results in multi-modal size distributions. The first of these processes may be viewed as taking place via two mechanisms, either unit or cluster growth, with the second occurring via either erosion or shattering. A bimodal form of the modified beta distribution was used in combination with simple assumptions to describe aggregation and disintegration processes via each of these mechanisms. The same distribution was used to successfully fit size data from disintegrating instant coffee. An erosion index for bimodal size distributions was introduced, and seen to be useful in characterizing disintegration processes. Correlation of the erosion and shattering mechanisms of breakage with the first-order kinetic model of disintegration was attempted. A modification of this model, incorporating the bimodal modified beta distribution to define the breakage function, was used successfully to simulate disintegration processes occurring via either erosion or shattering. Empirical segregation distributions for binary powder mixtures were introduced along with a related index of segregation. These distributions were seen to be useful for comparing the new segregation index with Williams' index of segregation. The new index was found to be generally more sensitive to the progress of segregation than Williams' index, having the further advantage of being unaffected by compaction. Density variation had little effect on both indices.