**4**

**The generalized population-balance equation**

The goal of this chapter is to provide a relatively rigorous derivation of the generalized population-balance equation (GPBE) starting from the microscale description of a disperse multiphase system. We begin by defining the number-density function (NDF) for a system of discrete particles using a probability-density-function (PDF) approach. Once the NDF has been defined, we proceed to the derivation of the GPBE by introducing the concept of conditional expected values. The latter contain the mesoscale representation of the microscale physics and thus contain the mesoscale models needed to close the GPBE. Next, we provide a detailed explanation of how the transport equations are found from the GPBE ...

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