Breakage point process

The manner in which a particle fractures depends on (i) the nature of the particle and (ii) the manner in which the fracture force is applied. A number of terms have been used to describe the different mechanisms of single particle fracture. The different terms considered here are abrasion, cleavage, shatter, and chipping. It may be pointed out that in practice these events do not occur in isolation. Real breakage involves a combination of these processes, with the proportions changing, depending on the equipment, and on the manner each particle is stressed within it. 

From the multi-scale point of view, the total energy dissipation Nj can be grouped into three portions, namely, Nsurf, Nturb, and Nbreak- The last portion is generated from bubble breakage and finally dissipated in the process of bubble coalescence. While Nsurf and Nln rb are considered to be directly dissipated on micro-scale, Nbreak is counted as a kind of meso-scale energy dissipation. Therefore, the stability condition can be either expressed with the minimization of micro-scale energy dissipation Nsurf + Nturb 7 min or conveyed as the maximization of meso-scale energy dissipation Nbreak max. 

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