A variety of processes used across, for example the cosmetics, pharmaceutical and chemical industries involve two-phase liquid–liquid interactions. The quality of liquid–liquid emulsification systems may be importantly related to the droplet size distribution. The population balance equation (PBE) can be used to describe complex processes where the accurate prediction of the dispersed phase plays a major role for the overall behaviour of the system. In recent years, the high-order least-squares method has been applied to approximate the solution to population balance (PB) problems. From the chemical engineering point of view, the least-squares method is associated with complex algebra. Moreover, in previous chemical engineering publications the method has been outlined using rather compact mathematical notations. For this reason, in this study, details of the least-squares algebra and implementation issues are revealed. The solution strategy is illustratively applied to a test problem: a liquid–liquid emulsification system with breakage and coalescence events in a stirred tank.
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