Minerals Beneficiation - A Random Model for Mineral Liberation by Size Reduction

This article proposes a physical model for an idealized binary mineral system and for the process of liberation by size reduction. Based on this model, equations are derived relating the amount of each component liberated as a function of the ratio of the volumetric abundance of the two mineral components and the ratio of the mineral grain size to particle size. A definite relationship is shown to exist between the mineral concentration within a locked particle and the frequency of occurrence of such a particle. These relationships are used to obtain theoretical expressions for the concentration-recovery diagram. Physical mineral beneficiation processes are based on breaking a mineral aggregate to liberate the dissimilar mineral grains and then making use of their physical properties to separate the mixture into its components. The effectiveness of the process is therefore dependent on how well the minerals are liberated and how efficiently they are separated. Although a substantial amount of work is being done to improve our understanding of mineral separation processes, the study of mineral liberation itself has been almost completely neglected. The purpose of this theoretical study is to shed some light on the liberation phenomenon by: 1) proposing a physical model for an ideal binary mineral system, 2) treating mathematically the fracture of this system into liberated and locked particles, and 3) deriving an expression for the liberation characteristics of this system. The results of this study are useful in understanding the effect and importance of various parameters in liberation, and provide a basis for comparison with real mineral systems. 'RANDOM' MODEL It is recognized that liberation can be caused by detachment which results from fractures occurring at the mineral grain boundaries, or by size reduction which restricts the occurrence of dissimilar mineral locking to a portion of the resulting particles. The detachment effect is dependent on the relative strengths of the mineral grains and the bonds between them, and must be treated empirically for each mineral system. The size reduction effect, however, can be treated analytically if certain assumptions are made concerning the shape and geometrical arrangement of the mineral grains.