Similarity Behavior of Population Balance Equations

Our concern in this chapter is of certain similarity properties of the solution of population balance equations. These properties are of considerable value not only to the characterization of experimental data, but also to the identification of key model parameters associated with system behavior, and frequently in the elucidation of behavior at the particle level from population data. The property of similarity manifests in the form of what is often described as a self-similar or self-preserving solution associated with the behavior of many partial differential and integro-partial differential equations. 

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Chapter 4 deals with methods for the solution of population balance equations. It also probes into Monte Carlo simulation techniques. In Chapter 5, the self-similarity behavior of solutions to the population balance equations is considered with various examples. The subject of inverse problems for the identification of population balance models from experimental data on dynamic particle distributions is treated in Chapter 6. The exploitation of self-similar solutions in inverting experimental data is of particular interest. 

The application of similar advanced distribution functions in the context of population balance analysis of polymerization processes is familiar in reaction engineering [40, 97]. However, the microscopic balance equations used for this purpose are normally averaged over the whole reactor volume so that simplified macroscopic (global) reactor analysis of the chemical process behavior is generally performed [35]. 

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