Applying Fréchet distance to evaluate the discrepancy of product size distribution between single particle and monolayer multi-particle breakage

Abstract

Single particle breakage characterisation at fine sizes for use in mill modelling has been addressed by only a few researchers and is not utilised in engineering design. This is mainly due to the challenge of accurately imparting a range of impact energies to sub-millimetre particles and then measuring the progeny size distribution for the tiny resultant mass. In order to fill this gap, a dispersed monolayer multi-particle breakage method was applied with a mini JK Drop weight tester in this work to extend the single particle breakage test from 16 mm down to 425 µm, covering a specific energy (Ecs) range of 0.1 - 2.5 kWh/t to provide a wide range of test conditions. A challenge that had to be addressed was switching from single particle to dispersed mono-layer due to the physical constraints of drop-height and drop mass in maintaining accuracy in input energy over the orders of magnitude required to apply the required specific range of energy input. As only a limited size range could be subjected to both single particle and mono-layer bed breakage, it was necessary to establish if the two testing techniques provide the same breakage results. A novel application of the Fréchet distance was successfully applied to quantitatively evaluate the discrepancy of progeny size distribution between single particle breakage and monolayer multiple particle breakage. Extrapolation of an empirical Fréchet distance model indicated that the application of dispersed mono-layer breakage below 2 mm provides an acceptable comparison with the single particle breakage applied to coarser sizes, thus facilitating the fitting of a single appearance function across this wide range of sizes and applied breakage energies.