Four Alternative Population Balance Frameworks

In the following sections four alternative approaches for deriving population balance equations are outlined. The four types of PBEs comprise a macroscopic PBE, a local instantaneous PBE, a microscopic PBE, and a PBE on the moment form. Two of these population balance forms are formulated in accordance with the conventional continuum mechanical theory. 

In a first modeling approach, a macroscopic population balance is formulated directly on the averaging scales in terms of number density functions [80, 102], A corresponding set of macroscopic source term closures are presented as well. Reviews of numerous fluid particle breakage and coalescence kernels on macroseopie scales can be found elsewhere [60,73,74, 122], This modeling framework resembles the mixture model concept. 

In the fourth modeling approach the general local instantaneous- and microscopic forms of the PBE are written in terms of the moments of the number density function. The moment form of the PBE might be providing sufficient information for many applications and reduces greatly the computational costs. 

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