(422f) The Relationship Between Structure and Breakage Selectivity

Population balance modeling has been used to characterize the type of breakage in a given particle system. The basic approach to understanding particle breakage from a mechanistic point of view is to divide a given particle size distribution into bin sizes where adjacent bin sizes differ in particle size by a factor of two or possibly three. The next step is to expose the bulk material to a stimulus that will induce stress-strain or impact events on the particles in an increasing manner. The particle size distribution prior to any stress-strain event or impact events is measured as well as several particle size distributions after incremental application of stress-strain events or repeated impact events. Incremental mass balances as a function of stressâ??strain rates or time at impact conditions are written for the breakage of any size particle bin into all particles of a smaller size bin. This set of equations is solved for the rate of breakage of any size particle, as well as the selectivity parameters that governs the size of new particles created from a broken particle. This can provide good information to easily fit breakage kernels with simple relationships between particle size, breakage type, and breakage stimulus when the particles are homogenous and are all a consistent shape. However, complex relationships exists when the original particles are of anisotropic structure or a non-random prescribed structure. This often causes breakage along preferred planes due to stress intensity functions that are structure dependent. The shape of the particle clusters and structured particles often determines the size of the broken particle pieces. However, a critical stress analysis of these structured particles can reveal points or planes of preferred breakage that can be coupled with selection coefficients to predict complex bimodal breakage models were the breakage is structure dependent. The paper provides a means of coupling these effects to generate a better estimate of the breakage mode for structured particles when exposed to stress-strain events.