MODELING A CASCADE OF CONTINUOUS MSMPR CRYSTALLIZERS WITH AGGLOMERATION

Cascade models have been used to account for real flow patterns in cry stallizers that are not well-mixed and to better control the character istics of the crystal size distribution (CSD). Such models have been s olved under two different sets of boundary conditions describing nucle ation in each stage. In this article, we have solved (numerically and analytically) population balance equations that include the mechanism of agglomeration in each stage of the cascade without considering clas sification or recycle, and have derived expressions for the moments of the CSD in closed forms. We then obtained analytic solutions to our m odel equations for two stages in the cascade under two different sets of boundary conditions. When there were more than two stages in the ca scade, we found out that it was necessary and also efficient (computin g timewise) to use numerical schemes to solve and analyze our model eq uations. Our results show that the agglomeration kernel has a signific ant influence on the coefficient of variation of the CSD, and hence it should be considered in applying the cascade models to describe the m ixing and performance of crystallizers with significant particle agglo meration.