Stability and Bifurcation of Continuous Cooling Crystallizers

Abstract

Stability properties and dynamic behaviour of continuous cooling crystallizers are analysed using a detailed moment equation model. A causal loop diagram between the variables reveals that the roots of instabilities lay in the interactions of the autoinhibition generated negative feedback, a positive feedback between the four leading moments of crystal size and a varying polarity feedback between the temperature and the moments. The stability of steady states is analysed by eigenanalysis of the Jacobian matrix and using the Mikhailov criterion. Stability maps and bifurcation diagrams are presented in the planes of different pairs of system parameters.