Population balance framework

Instead of arbitrarily considering two bubble classes, it may be useful to incorporate a coalescence break-up model based on the population balance framework in the CFD model (see for example, Carrica et al., 1999). Such a model will simulate the evolution of bubble size distribution within the column and will be a logical extension of previously discussed models to simulate flow in bubble columns with wide bubble size distribution. Incorporation of coalescence break-up models, however, increases computational requirements by an order of magnitude. For example, a two-fluid model with a single bubble size generally requires solution of ten equations (six momentum, pressure, dispersed phase continuity and two turbulence characteristics). A ten-bubble class model requires solution of 46 (33 momentum, pressure. 

The fundamental derivation of the population balance equation is considered general and not limited to describe gas-liquid dispersions. However, to employ the general population balance framework to model other particulate systems like solid particles and droplets appropriate kernels are required for the particle growth, agglomeration/aggregation/coalescence and breakage processes. Many droplet and solid particle closures are presented elsewhere (e.g., [96, 122, 25, 117, 75, 76, 46]). 

The number density function, along with the environmental phase variables, completely determines the evolution of all properties of the dispersed phase system. The population balance framework is thus an indispensable tool for dealing with dispersed phase systems. This book seeks to address the various aspects of the methodology of population balance necessary for its successful application. Thus Chapter 2 develops the mathematical framework leading to the population balance equation. It... 

The value of this example lies in showing how the population balance framework, viewed in suitably abstract terms can accommodate even the detail of spatial morphology of the particles. The author is not aware of such models in the literature. 

Chang (1990) used a population balance framework (discussed in Section 12-4) to develop correlations for d32(t). For nonviscous oils dispersed in water, he obtained... 

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