The generalized population-balance equation GPBE

By using a very similar approach to the one outlined above for the PBE, it is possible to derive a GPBE for an NDF that includes particle velocity as an internal variable. We will denote this general NDF as n(t,x,, ) (i.e. without subscripts on n). The simplest GPBE (i.e. velocity without other internal coordinates) is known as the Boltzmann kinetic equation and was first derived in the context of gas theory (Chapman Cowling, 1961). The final form of the GPBE is 

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This book provides a consistent treatment of these issues that is based on a general theoretical framework. This, in turn, stems from the generalized population-balance equation (GPBE), which includes as special cases all the other governing equations previously mentioned (e.g. PBE and BE). After discussing how this equation originates, the different computational models for its numerical solution are presented. The book is structured as follows. 

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