A discrete population balance equation for binary breakage
A discrete population balance equation for binary breakage
Liao, Y.; Oertel, R.; Kriebitzsch, S.; Schlegel, F.; Lucas, D.
The numerical solution of the population balance equation is frequently achieved by means of discretization, i.e., by the method of classes. An important concern of discrete formulations is the preservation of a chosen set of moments of the distribution, e.g. numbers and mass, while remaining exible on the grid applied. As for the physical modeling of the breakup rate, two approaches exist. One type states the breakup rate of a mother particle and requires a function that describes the distribution of daughter particles. The other type gives the breakup rate between a mother and a daughter particle directly, usually under the assumption of binary breakage. The lack of an explicitly stated daughter size distribution function has implications on the formulation of the discrete equations, because existing formulations contain integrals over the daughter size distribution function. To the knowledge of the authors, no efficient formulations for this type of models exist. In the present work, a discrete formulation of the breakup terms due to binary breakage is proposed, which allows a direct implementation of both kinds of models and an efficient solution of the population balance equation, making it favorable for the coupling to computational fluid dynamics codes.
Keywords: Binary Breakup; Computational Fluid Dynamics; Incorporated Daughter Size Distribution; Method of Classes; Population Balance Equation
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