Modeling of breakage and coalescence of dispersed phases such as bubbles or droplets in multiphase systems is of paramount importance to the control of the dispersed phase size distribution in process industry. Population balance model (PBM) has become a rountine tool to simulate the breakage, coalescence and size distribuiton of dispersed phase. However, the current kernel functions for breakage and coalescence in PBM are either derived from statistical models or based on some phenomenological models, empirical correlations or semi-theoretical methods, since the physics of breakage and coalescence in multi-phase systems is complex. As a result, few models could completely considers all of the physical constraints relevant to the complex flow field and material properties, and it is still a challenging issue to accurately predict the breakage and coalescence for different operating conditions. This article gives a systematic overview of the mechanisms and models about the breakage and coalescence of bubbles or droplets, and the numerical algothirm for population balance equations as well as the application of PBM simulation in gas-liquid or liquid-liquid systems. Finally, the state-of-the-art and future development of PBM are analyzed.

Contents
1 Introduction
2 Population balance model
2.1 Coalecence rate
2.2 Breakage rate and daughter size distribution
3 Solving population balance equation
3.1 Class method
3.2 Method of moments
4 Application of population balance model
4.1 Application in gas-liquid systems
4.2 Application in liquid-liquid systems
5 Conclusion and outlook