Population balance method distribution theory

At the simplest level, the rate of flow-induced aggregation of compact spherical particles is described by Smoluchowski s theory [Eq. (32)]. Such expressions may then be incorporated into population balance equations to determine the evolution of the agglomerate size distribution with time. However with increase in agglomerate size, complex (fractal) structures may be generated that preclude analysis by simple methods as above. 

The population balance approach is employed for the description of droplet dynamics in various flow fields. A significant advantage of the method is that a vehicle is provided to include the details of the breakage and coalescence processes in terms of the physical parameters and conditions of operation. A predictive multidimensional particle distribution theory is at hand which, in the case of well-defined droplet processes, can be employed for a priori prediction of the form and the magnitude of the particle size distribution. The physical parameters which affect the form... 

We will see that the techniques that have been developed to handle these questions utilize notions of distributions of properties of the reacting fluids in the vessel, in the sense of probability theory. These properties can be the residence times of elements of flowing fluid(s), catalyst activity of particles, crystal size in a crystallizer, and others. The first type is usually termed a residence time distribution (RTD) and the others are handled by particle population balances that are more general and can be used for properties other than just residence time. The more widely developed and utilized RTD methods will first be discussed, followed by the general population balances. 

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