Development of a coalescence model due to turbulence for the population balance equation

The current research introduces a new mathematical framework to develop coalescence models for turbulent flows in the context of population balance equations. Previous researchers have modeled the coalescence term as two independent factors: the collision rate and the coalescence efficiency. In contrast, the new approach formulates the coalescence term as a single entity and directly accounts for the effect of turbulence on the probability of coalescence. It also considers the angle between the line of centers and the relative velocity of the bubbles. The coalescence model becomes complete when the interaction and the drainage times are incorporated in the new framework. The model is then tested successfully against experimental data from the literature. A few parametric runs to study the behavior of the coalescence kernel complete the paper.