Two-dimensional population balance modeling for shape dependent crystal attrition

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25 Scopus citations


Many suspension crystallization processes can be described by growth and secondary nucleation. The prevailing mechanism for secondary nucleation in industrial processes is attrition caused by crystal-impeller collisions. The understanding and prediction of attrition rates is of fundamental importance for product and process design. Attrition of a crystal is affected by the size of the crystals and, as experimental evidence reveals, by their shape. For crystals with the same mass, the attrition rate is significantly larger if crystals have distinct and sharp corners, than if they were spherical. Because of the associated modeling and computational effort, shape dependent behavior has mostly been disregarded in crystallization process modeling. In this work, a two-dimensional population balance model is formulated. The inner variables are the size and the shape of the crystals. Consequently, the model accounts for size and shape dependent process behavior. In order to close the model equation shape modification function are introduced. The reinforcement function specifies the increase in attrition resistance by rounding the sharp corners and increasing material strength. The face attrition ratio represents the differences of material removal from sharp corners and flat faces. The sensitivity of the results with respect to these shape modification functions is investigated. The results show that the model is capable of reflecting shape dependent attrition behavior in a physically meaningful way. To fit experimental data, mainly the parameters of the shape modification function need to be tuned.

Original languageEnglish
Pages (from-to)661-672
Number of pages12
JournalChemical Engineering Science
Issue number4
StatePublished - Feb 2009
Externally publishedYes


  • Attrition
  • Population balance
  • Secondary nucleation
  • Two-dimensional


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