A bubble coalescence kernel combining the characteristics of the film drainage, energy, and critical velocity models

Abstract

A novel coalescence kernel with high predictive properties is constructed to be used within the population balance framework. The kernel includes the product of a collision frequency term and a novel binary coalescence probability expression. The probability expression employs critical velocity estimations from film drainage simulations that also considers particle surface and kinetic energies. Thus, the proposed expression possesses characteristics of all three commonly used approaches: film drainage, energy, and critical velocity models. The probability of a collision having a certain velocity and angle is considered through probability density functions while adapting to the Eulerian frame. A maximum collision angle that allows coalescence is defined. The kernel is free of artificially introduced tuning parameters and predicts the size distributions in bubbly pipe flow experiments exceptionally well, including complex behaviors such as emergence of secondary peaks in the distribution. The theory presented is equally valid for bubbles and droplets.