Dynamics and stability of continuous MSMPR agglomerative precipitation: Numerical analysis of the dual particle coordinate model

This article presents a bi-variant dynamic model of continuous mixed-suspension, mixed-product-removal (MSMPR) precipitation with agglomeration (aggregation and disruption) using the dual particle coordinate (agglomerate size and primary crystal number) population balance approach. Several finite difference methods were first examined for numerical solution of simplified model equations. The implicit forward time central space (FTCS j+1) was selected as the best for prediction of dynamic particle size distribution (PSD) and then applied to the agglomerative case. For specific values of aggregation and disruption coefficients, K_a, and K_d, bimodal distributions are observed and the system can also exhibit unstable dynamics. It is also predicted, however, that a supersaturation dependence of aggregation efficiency together with crystal disruption can stabilize the system transient response.