A review of population balance modelling for isothermal bubbly flows

In this article, we present a review of the state-of-the-art population balance modelling techniques that have been adopted to describe the phenomenological nature of isothermal bubbly flows. The main focus of the review can be broadly classified into three categories: (i) Numerical approaches or solution algorithms of the PBE; (ii) Applications of the PBE in practical gas-liquid multiphase problems and (iii) Possible aspects of the future development in population balance modelling. For the first category, details of solution algorithms based on both method of moment (MOM) and discrete class method (CM) that have been proposed in the literature are provided. Advantages and drawbacks of both approaches are also discussed from the theoretical and practical viewpoints. For the second category, applications of existing population balance models in practical multiphase problems that have been proposed in the literature are summarized. Selected existing mathematical closures for modelling the 'birth' and 'death' rate of bubbles in gas-liquid bubbly flows are introduced. Particular attention is devoted to assess the capability of some selected models in predicting bubbly flow conditions through detail validation studies against experimental data. These studies demonstrate that good agreement can be achieved by the present model by comparing the predicted results against measured data with regards to the radial distribution of void fraction and sauter mean bubble diameter. Finally, weaknesses and limitations of the existing models are revealed are suggestions for further development are discussed. Emerging topics for future population balance studies are provided as to complete the aspect of population balance modelling.