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Keywords:

  • morphological population balance;
  • crystal morphology;
  • crystal growth;
  • potash alum (KAl(SO4)2·12H2O);
  • shape control

Abstract

A morphological (or polyhedral) population balance (PB) model is presented for modeling the dynamic size evolution of crystals grown from solution in all crystal growth directions. The morphological PB approach uses the crystal shape information for a single crystal obtained from morphology prediction, or experiment as the initial face locations, as well as face growth rates to predict the shape evolution of the crystal population. For each time instant during the crystallization process, the prediction uses its shape at the previous time moment, and the growth rate for the specific crystal habit plane. The methodology is demonstrated through a study of potash alum (KAl (SO4)2·12H2O), for which literature data is available for comparison and validation. The discretization method, method of classes, was used to convert the equations to ordinary differential form with the computational domain being discretized into small meshes. The ordinary differential equations (>1.5 million) were then solved simultaneously using the Runge-Kutta-Fehlbergh 4th/5th-order solver with automatic time-step control. The results obtained clearly demonstrate that the morphological PB model developed can predict crystal growth and surface area of individual habit faces in detail, together with crystal shape and size evolution. © 2007 American Institute of Chemical Engineers AIChE J, 2008