Strength distribution of particles under compression

From time immemorial people dealt with size reduction processes (mill, mineral liberation, etc.). As time has passed industrial units for comminution processes have become larger and more sophisticated, but still they perform with low efficiencies [1], [2] and [3]. The strength of a particle is one of its most crucial characteristics due to the mechanical stresses experienced by each particle within an industrial unit. This is because the final size of particles is mostly dependant on the strength distribution of the raw material [4]. In this present study, the ability of a number of statistical formulations to accurately describe the strength distribution of particles was examined. Additionally, selected equations were analyzed and a general expression including the effect of the material and particle size was developed. A number of approaches to define particle strength were considered, and strength in terms of crushing force was chosen. Particle strength in terms of force and in terms of energy was also compared and found to be size independent. Finally, particle strength in terms of stress was examined and compared to the particle strength in terms of force.The ability to describe the compression strength distribution will significantly improve the accuracy of the comminution processes simulation, design and optimization.

Graphical AbstractThis work presents the experimental results and empirical analysis of initial particle strength distribution for a variety of particulate solids. Additionally, particle strength in different expression terms was also considered.As a validation of the proposed model, the experimental results are compared to the predicted ones by the following comparison chart. The calculated breakage probability results are bounded within the limits of ± 20%.Figure optionsDownload as PowerPoint slideResearch highlights
► Introduction of a model which describes initial particle strength distribution.
► The selection of the initial particle strength model, among other models from the literature, was done according to the high value of coefficient of determination, mathematical simplicity and statistical meaning of its parameters.
► Model validation by the experimental data from different experimental systems was also satisfying.
► Investigation of particles strength expressions in different terms (crushing force, breakage energy, crushing stress, specific energy) was conducted.
► The relationship between breakage energy and crushing force was confirmed to be size independent.