Reformulating multidimensional population balances for predicting crystal size and shape


  • This article is dedicated to The Chief, Neal R. Amundson, who pioneered the use of mathematical modeling in chemical engineering. His legacy lives on and gathers strength with each new generation of chemical engineers.

Correspondence concerning this article should be addressed to M. F. Doherty at


There is a growing interest in predicting and controlling the size and shape of crystalline particles. Multidimensional population balances have been developed to accomplish this task but they suffer from the drawback of needing rate laws for the absolute growth rate for every family of faces that may appear on the crystal surface. Such growth rates are known for only a handful of crystalline materials and prospects are bleak for extending the library of growth rate data. This raises the question of where the surface growth rates for all the families of faces will come from to drive multidimensional population balance engineering technology. One answer is “from first principles.” We reformulate multidimensional population balances in terms of relative growth rates and show how to create first principles mechanistic models to calculate these quantities for real molecular crystals as a function of supersaturation. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3468–3474, 2013