Toward a unified framework for the derivation of breakage functions based on the statistical theory of turbulence

The evolution of droplet or bubble size distribution in turbulent flow is of great significance in a variety of technological fields. Modeling this evolution by employing a population balance approach requires knowledge of the so-called breakage functions (rate and kernel). Over the years, a large number of phenomenological breakage functions with various degrees of sophistication have been proposed in the literature. Among them, those based on the statistical theory of turbulence are of particular interest, in that they attempt to take into account the structure of the flow field responsible for breakage. The purpose of the present work is to present a unified framework for developing this type of breakage functions and to show how existing models can be derived in a systematic and consistent way. The key parameters in this modeling approach are identified, which have to be determined by comparison with experimental data. It is also shown that the breakage functions, obtained within the framework presented here, lead to predictions of a droplet size evolution whose main features are consistent with experimental observations. It is suggested that this framework is an important step toward the development of a standard approach for modeling droplet size evolution in turbulent flow.