Mathematical modeling of fluid energy milling based on a stochastic approach

In this study, the stochastic method is used to simulate the grinding process in a fluid energy mill: the product particle size distribution is regarded as the result of repeating elementary breakage events, i.e. Mp=M0[Tm]m, where M0 is the row vector of the size distribution of feed particles, Mp is the row vector of the size distribution of product particles, m is the number of elementary steps, and Tm is the matrix of transition probabilities representing the elementary breakage event. The matrix of transition probabilities can be related to the breakage rate function and the breakage distribution function of the elementary breakage event. A specially designed apparatus, named single-event fluid mill, was employed to experimentally estimate those two breakage functions of the elementary breakage event with a breakage rate correction factor θ. The classification effect is taken into consideration by defining a cutting size under which the particle will not break any more. Using this strategy, the product particle size distribution is calculated. The good consistency between the simulation and the experimental results indicates that this model is valid to quantitatively estimate the grinding performance of the fluid energy mill.