Population balance models and self-similar size distributions

To illustrate the fallaciousness of the linear population balance model (PBM) currently used in the mineral industry, a $10,000 challenge was made by Professor Thomas P. Meloy. In spite of numerous early promises, only one challenge response has been received to date. This response claims to generate self-similar size distributions. This paper: 1) shows that the challengerʹs response of a dynamic batch grinding solution is not a valid answer to this challenge, 2) examines and explores the implications of the proposed solution, and 3) offers the only actual dynamic batch PBM solution to the problem. The challengerʹs response to the Meloy Challenge has not accomplished the generation of a self-similar product size distribution using the dynamic batch PBM. The actual solution, not an approximation which was offered, is the dynamic PBM with different, time-varying breakage rate functions with unrealistic large values.