Self-Similar Distributions of Fine Particles Produced in Non-Linear Batch Grinding

A parametric approach is described for tracking the evolut-ion of particle size distribution with time in batch grinding in micron and sub-micron range. The approach is based on an asymptotic self-similarity solution to populat-ion balance equation of grinding. The possible presence of non-linearity in the fine grinding regime is captured by a modification to the model formulation scheme. It is assu-med that the breakage rate is a function of the grind time and therefore, indirectly of the time-dependent mean, median or a percentile size. It is shown that the self-similar character is preserved under a wide class of functions that can in principle describe the non-linear characteristics of the comminution process. The resulting parametric model describes the evolution of particle spectra. Several sets of published data are employed
to validate the model.