A review of the statistical turbulence theory required extending the population balance closure models to the entire spectrum of turbulence

The models for fluid particle breakage and coalescence due to turbulence are generally limited to the inertial subrange of isotropic turbulence and infinite Reynolds numbers. A rigorous procedure for extending the fluid particle breakage and coalescence closures to the entire spectrum of isotropic turbulence and for a wider range of Reynolds numbers can be established based on statistical turbulence theory. The modeling procedure consists of a three‐dimensional (3‐D) literature model energy spectrum for the dissipation, inertial, and energy containing subranges of isotropic turbulence, and an exact literature integral relation for determining the second‐order longitudinal structure function from the 3‐D energy spectrum. A review of the requisite statistical turbulence theory and the use of the model energy spectrum is provided, because the necessary details are not easily accessible in the chemical engineering literature and misconceptions are found in the publications of the previous modeling attempts. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1795–1820, 2016