Solution of population balance equations for prediction of particle size distribution in emulsion polymerization: comparison and evaluation of different numerical methods

Abstract

For the solution of population balance equations for the prediction of particle size distribution in emulsion polymerization, this chapter compares and evaluates different numerical methods. The use of population balance equations (PBE) to describe the development of panicle size distribution in a paniculate process is a well-known method and has been utilized in a diverse range of problems—including crystallization, liquid-liquid dispersions, and polymerization. The continuous distribution of panicles in an emulsion polymerization reactor is usually described by a number density function n(x,t), which represents the number of panicles within a differential volume size range per unit volume of latex. The rate of change of the panicle number density function is described by a nonlinear integro-differential population balance equation. The PBE can also be solved in the continuous form, using orthogonal collocation on finite element methods (OCFE). The collocation on finite elements is used with cubic Hermite basis functions and equally spaced (nonorthogonal) nodes to simplify "bookkeeping." The method was successful to the solution of pure aggregation problems and also in the case of a combined growth-aggregation problem.