Population Balance Modeling of Growth and Secondary Nucleation by Attrition and Ripening

This is the authors' abstract. We don't add key points for this paper.

Secondary nucleation is ubiquitous in nature and of fundamental importance for both batch and continuous crystallization processes. Attrition is the mechanism through which fragments are formed after the collision of a crystal with a stirrer. Those fine fragments, if small enough, are considered secondary nuclei. In this work, starting from the mechanistic description of attrition by Gahn and Mersmann ( Crystallization Technology Handbook; CRC Press, 2001), two population balance equation models to simulate secondary nucleation processes have been derived. The first simulates attrition as a breakage term, and growth rate is the result of size-dependent solubility. The second model considers attrition as a boundary condition at zero crystal size, where the expression for secondary nucleation rate already takes into account the effect of supersaturation, while the growth rate is size-independent. The two models are proven equivalent in the growth regime, thus where secondary nucleation and growth are the dominant phenomena. At extremely low values of supersaturation, thanks to size-dependent solubility, the first model yields to further development of the crystal population, e.g., ripening and aging. The main result is that secondary nucleation by attrition can be described as a birth/death term or, alternatively, as a source term according to the final application of the model. Since the two approaches have very different computational intensities, one can choose the right model based on the objective of the simulation study. The evolution of the crystal population for high values of supersaturation will be the same in both cases.