Solution of Population Balance Equations for Emulsion Polymerization: Zero−One and Zero−One−Two Systems

Abstract

A numerical method was developed to solve the sets of population balance equations (PBEs) that govern the evolution of the particle size distribution (PSD) in emulsion polymerization processes and, more specifically, in zero−one and zero−one−two systems. The technique is based on the finite-volume method and uses high-resolution schemes and a generalized fixed pivot technique to discretize the growth and aggregation terms, respectively. Implicit−explicit methods are used to integrate the semidiscrete equations in time. The performance of the method was evaluated by comparing the computed distributions and/or their moments to analytical solutions determined for selected cases. In all four cases analyzed, good qualitative and quantitative agreement was found between numerical and analytical results. The present algorithm made possible to simulate, for the first time, the evolution of PSD for an actual emulsion polymerization system using the zero−one−two model.