The population-balance equation for fine particles

As a first example, we consider a population of solid particles suspended in a liquid. We assume that the density and size of the particles are such that they move together with 

As described in Chapter 4, the following PBE governs the evolution of the PSD, representing the state of the solid aggregates  

In order to highlight the different regimes exhibited by Eq. (1.1) and the different treatments that are more suitable for its solution in each regime, the PBE has to be normalized and made dimensionless. Different quantities can be used to this end, such as the moments of order zero and one of the PSD  

Knowledge of these characteristic quantities suffices for fhe calculafion of the characteristic time scales for aggregation Ta = [a, )NtY and breakage Tb =. These 

Closer observation of the aggregation time scale shows that it is inversely proportional to the characteristic total aggregate number density Nt, which is related to the characteristic disperse-phase volume fraction 0p. When the system is dilute (i.e. p 1), M is 

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