A new turbulence-induced theoretical breakage kernel in the context of the population balance equation

The current paper develops a new breakage kernel for use in the population balance equation. The study properly accounts for the direction of the relative velocity of the eddy and determines the size of the daughter bubble from the angle at which the eddy hits the parent bubble and its orientation at the point of impact. The breakup kernel considers both the capillary pressure of the parent bubble and the surface energy increase of the daughter bubbles in its formulation. The model predictions agree very well with the experimental data available in the literature. A parametric study of the breakage kernel further analyzes its behavior over a range of flow conditions. The parameterization also leads to a simplified breakage kernel.