Interfacial Area Transport Equation for Bubble Coalescence and Breakup: Developments and Comparisons

Bubble coalescence and breakup play important roles in physical-chemical processes and bubbles are treated in two groups in the interfacial area transport equation (IATE). This paper presents a review of IATE for bubble coalescence and breakup to model five bubble interaction mechanisms: bubble coalescence due to random collision, bubble coalescence due to wake entrainment, bubble breakup due to turbulent impact, bubble breakup due to shearing-off, and bubble breakup due to surface instability. In bubble coalescence, bubble size, velocity and collision frequency are dominant. In bubble breakup, the influence of viscous shear, shearing-off, and surface instability are neglected, and their corresponding theory and modelling are rare in the literature. Furthermore, combining turbulent kinetic energy and inertial force together is the best choice for the bubble breakup criterion. The reviewed one-group constitutive models include the one developed by Wu et al., Ishii and Kim, Hibiki and Ishii, Yao and Morel, and Nguyen et al. To extend the IATE prediction capability beyond bubbly flow, two-group IATE is needed and its performance is strongly dependent on the channel size and geometry. Therefore, constitutive models for two-group IATE in a three-type channel (i.e., narrow confined channel, round pipe and relatively larger pipe) are summarized. Although great progress in extending the IATE beyond churn-turbulent flow to churn-annual flow was made, there are still some issues in their modelling and experiments due to the highly distorted interface measurement. Regarded as the challenges to be addressed in the further study, some limitations of IATE general applicability and the directions for future development are highlighted.