A moment methodology for coagulation and breakage problems: Part 3—generalized daughter distribution functions

Population balances for simultaneous coagulation and breakage (and their analogs, e.g., polymerization and depolymerization) are employed in describing many systems including aerosols, powders and polymers, and many unit operations including reactors, crystallizers, and size reduction/enlargement equipment. The birth term for the breakage process is usually formulated in terms of a distribution of breakage products known as the daughter distribution. There are many daughter distribution forms proposed in the literature in part because these distributions are notoriously difficult to determine experimentally. Here, a generalization of these forms is developed for multi-particle breakup which has the flexibility to represent a wide variety of distribution shapes. The simplicity of the generalized expression renders the population balance equations for simultaneous coagulation and breakage accessible to analytical attack, leading to an analytical expression for the fine end of the steady-state product size distribution. This expression has potential utility in both design and analysis of experiments aimed at measuring daughter distribution parameters.