Crystallization with Sinusoidal Modulation of Stirrer Speed: Frequency Response Analysis and Secondary Nucleation Kinetics

Abstract

In crystallization, obtaining the proper nucleation and growth parameters is essential to the design of crystallization processes. This paper studies the response of crystal size distribution (CSD) to periodic oscillations in the stirrer speed within a mixed suspension mixed product removal (MSMPR) crystallizer. We start from a model in which all processes are coupled. Stirrer speed oscillations drive oscillations in the secondary nucleation kinetics. Oscillations in the nucleation rate drive damped waves in the population distribution of growing crystals. Changes in the population of crystals drive changes in the supersaturation. Supersaturation along with the total mass of crystals influences the nucleation rate. At low frequencies, including the pseudosteady-state limit, effects of a change in stirring rate are attenuated by the coupling to other processes. At high frequencies, stirring rate oscillations lead to pronounced waves in the CSD that might facilitate studies of secondary nucleation.

Pharmaceutical Digital Design: From Chemical Structure through Crystal Polymorph to Conceptual Crystallization Process

“…280,[296][297][298] Quantitative models have been developed for secondary nucleation, assuming that crystals can fracture on collision, accounting for crystal-crystal collisions, impeller-crystal collisions, and other mechanisms. 267,294,295,299 The solute morphology and mechanical properties 300 are important in https://doi.org/10.26434/chemrxiv-2024-lctpz ORCID: https://orcid.org/0000-0002-7633-1987 Content not peer-reviewed by ChemRxiv. License: CC BY-NC-ND 4.0 determining the ease of fracture, but this is not explicit in current models, in which fracture enters through an experimental parameter.…”

Pharmaceutical Digital Design: From Chemical Structure through Crystal Polymorph to Conceptual Crystallization Process

“…While homogeneous nucleation involves molecular-scale spontaneous assembly from solution with no crystals present, secondary nucleation occurs by mechanical breakage of existing macroscopic crystals into preformed viable crystallites. ,, Homogeneous nucleation rarely (if ever) occurs in an industrial crystallizer. In contrast, secondary nucleation is considered to be the dominant mechanism. ,− Quantitative models have been developed for secondary nucleation, assuming that crystals can fracture on collision, accounting for crystal–crystal collisions, impeller-crystal collisions, and other mechanisms. ,,, The solute morphology and mechanical properties are important in determining the ease of fracture, but this is not explicit in current models, in which fracture enters through a parameter that is experimentally determined. Secondary nucleation models are extremely useful for industrial crystallization but not for polymorph screening, where the main targets are low-energy solid forms that are predicted to be kinetically stable but are yet to be experimentally realized (Section ).…”

“…238,248−250 Quantitative models have been developed for secondary nucleation, assuming that crystals can fracture on collision, accounting for crystal−crystal collisions, impeller-crystal collisions, and other mechanisms. 223,246,247,251 The solute morphology and mechanical properties 252 are important in determining the ease of fracture, but this is not explicit in current models, in which fracture enters through a parameter that is experimentally determined. Secondary nucleation models are extremely useful for industrial crystallization 253 but not for polymorph screening, where the main targets are low-energy solid forms that are predicted to be kinetically stable but are yet to be experimentally realized (Section 3.3).…”