(300a) Breakage Functions for Single Impact of Spheres

In modeling particle breakage, it is often assumed that all particles have the same shape factor.  While this is often a good approximation for the original parent particles, the shape of the child particles frequently are quite different.  Other models that do account for changes in shape focus on how a cuboid crystal changes shape due to the corners being chipped, but excludes the shapes of the particles formed by the chipped off material [1].  Later models are more general and use shapes other than cubes, but still use the attrition approach [2].  However, not all breakage is by attrition. Single impact of spheres causes fragmentation that results in different size and shape distributions as shown experimentally [3].  These experimental results cannot be accounted for by the attrition models.

This work presents recent developments in modeling fragmentation of spheres based on the experimental results.  Since the number of particles formed depends on the force of impact, the models allow the user to adjust the number of particles formed.  The models are general in that they can be applied to any unit operation where particles are impacted such as crystallizers. 

1. Briesen, H., “Two-dimensional population balance modeling for shape dependent crystal attrition,” Chem. Eng. Sci., 64, 661-672 (2009). 
2. Reinhold, A., and H. Briesen,  “Convex geometry for the Morphological Modeling and Characterization of Crystal Shapes,”  Part. Part. Syst. Charact., 28, 37-56 (2011). 
3. Salman, A.D., G.K. Reynolds, J.S. Fu, Y.S. Cheong, C.A. Biggs, M.J. Adams, D.A. Gorham, J. Lukenics, and M.J. Hounslow, “Descriptive classification of the impact failure modes of spherical particles,” Powder Tech., 143– 144,  19–30 (2004).