Abstract
Abstract Crystallization problem is one of the popular problems in wide area of science. The first principles are not used to design a crystallizer in which complicated processes include nucleation, crystal growth, attrition and agglomeration of crystals. It is modeled by the population balance model, which is one of the important models of mathematical biology and engineering, is a nonlinear partial integro-differential equation and examines the exchange of particles and the production of new particles in a system of particles. For the crystallization problem, one-dimensional and multi-dimensional models are considered and semi-analytical solutions are obtained via the linear separation method.
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