A population balance approach to describing bulk attrition

Attrition arising from mechanical damage during processing has been studied in annular shear cells, these having the ability to vary readily the testing stress and shear strain. A population balance approach has been deployed to analyse the evolution of the size distribution with strain which bases its arguments on the kinetic theory of grinding. This incorporates the ideas of a selection function and a breakage function. The extent of attrition is determined in terms of three parameters, one related to the selection function, one to the breakage function, and additionally one which allows for the balance of fracture and abrasion. The product size distribution of the Gaudin-Schuhmann form is consistent with experimental findings from annular shear cells. Whatever reasonable physical assumptions are made about the form of the selection and breakage functions, and of the balance between fracture and abrasion, particle size distributions of the same form arise. From comparisons with several materials, the index in the breakage function is consistent with the particle fracture pattern observed experimentally.