Teaching old laws new tricks: Specific energy requirements for breakage based on modern kernels and a population balance model

A general expression for specific energy requirements in particle breakage is derived from a population balance model. The model employs power-law rate kernels, self-similar fragment distributions and an energy dependence based on the Vogel-Peukert master curve. This model connects the empirical constants and exponents of size in older empirical energy laws to the parameters of the population balance model, the nature of the particles, and certain moments of the self-similar particle size distribution predicted by the model. The resulting model is used to extract values of the order of the power-law rate kernel from literature data. The extracted order values are consistent with known expressions for individual particle breakage. The model developed here may be coupled with experimental determination of the material parameter needed in the Vogel-Peukert master curve to enable extraction of energy utilization efficiency values from experimentally determined values of the size-independent portion of the selection function.