Single-particle fracture as a basis for microscale modeling of comminution processes

The Population Balance Model has proven to be a very successful model for describing all types of particulate processes. It has been particularly fruitful for modeling and optimizing industrial ball mills. However, the inherent empiricism of its current form has been and still is the center of vigorous criticisms. This model would gain significantly if a solid meaning could be given to the classical breakage and selection functions. Cho and Hofler were the first researchers to initiate the work that aims at finding the true physical meaning of these functions. They have shown that simple drop tests on particle beds produce good estimates of the breakage function in actual ball mills. This study takes Hofler's work one step further. It shows that the breakage and selection functions can both be derived and calculated from fundamental and meaningful single-particle fracture data, that is using a microscale approach. Furthermore, these data are easily measured in the laboratory on what is known as the ultrafast load cell (UFLC). It has been shown that single-particle impact-breakage is completely characterized by the measurement of the mass specific fracture energy distribution and the one-parameter single-particle impact-breakage function referred to as the {dollar}tsb{lcub}10{rcub}{dollar}-procedure. The first deals with the probability of a single-particle to fracture under impact, and the second models its fragment size distribution. It was shown that particle bed breakage can be predicted from the breakage of the individual particles within. Moreover, based on Herbst and Hofler's pioneering ideas, the ball mill breakage function is calculated based on the single-particle breakage model only, giving a new meaning to the breakage function. Unfortunately, it turns out that insufficient understanding of particle interactions remains an obstacle for predicting the selection function using the same microscale approach as for the breakage function. However, it is shown throughout this work that the missing pieces of the puzzle are all measurable in the laboratory.