Fragmentation is often of interest to scientists and engineers because it affects many systems. In particle technology, breakage can be desirable or something to be avoided. For example, particle fracture is desired when trying to reduce particle size; but it is unwanted in solid catalysts in a fluidized bed.

In modeling particulate processes, it is necessary to account for particle breakage. At the macro-scale, researchers often use breakage distribution functions to describe the particle size distribution produced by a parent particle breaking. Many of the breakage distribution functions are empirical. At the micro-scale, researchers often model the fracture of an individual particle using fundamental fracture mechanics. However, fracture mechanics is not usually connected to the breakage distribution functions. Although the Weibull and Rosin-Rammler distributions were originally developed empirically, later research (Brown and Wohletz, 1995) showed that they have a theoretical basis. However, this approach has not been applied to shape factors.

This work discusses the connection between the micro-scale fracture mechanics and the macro-scale breakage distribution functions. More specifically, a branching crack model is used to develop bivariate breakage functions that include both size and shape. The development and the resulting functions will be presented.

Brown, W. K., and K. H. Wohletz, “Derivation of the Weibull distribution based on physical principles and its connection to the Rosin-Rammler and lognormal distributions,” J. Appl. Phys., 78, 2758-2763 (1995).