Some solutions for the kinetics of combined fracture and abrasion breakage

Abstract

A phenomenological description of autogenous breakage of ores is accomplished by considering the simultaneous occurrence of fracture- and abrasion-like processes. A general differential equation is derived and solved for the batch abrasion phenomenon with and without fracture breakage of lumps within a screen size interval. For short grinding times, that is, for less than 50% of breakage, pure abrasion produces an almost first-order disappearance of the top size class material. A strong increase in the kinetic of disappearance occurs when the larger lumps reduce to the lower sieve size of the interval. Approximate solutions for the complete batch and continuous steady-state equations are developed by using a first-order fracture and the limiting first-order abrasion kinetics. In accordance with experimental findings, non-normalized B values with regard to particle size and bimodal distributions of progeny fragments are predicted by the model.