(389cj) Integrated Multiscale Simulation of Crystallization: Bridging Macro, Meso, and Micro Scales for Crystal Growth

Crystallization is a crucial step in industries ranging from pharmaceuticals to specialty chemicals yet developing robust and scalable processes remains challenging. Despite decades of work on crystallization modeling, major knowledge gaps remain in accurately linking the macroscopic fluid dynamics in stirred vessels to crystal aggregation, breakage, and molecular-level crystal growth [1]. Existing simulations often adopt well-mixed assumptions or simplified kinetics, neglecting the role of local mixing and hydrodynamic shear on processes such as crystal collision and aggregation [2]. This limitation can lead to inaccurate predictions of crystal size distributions and surface morphologies, impeding robust scale-up in pharmaceutical and specialty chemical manufacturing [3]. In previous studies, computational fluid dynamics (CFD) simulations were often used to characterize mixing and hydrodynamic conditions in crystallizers, capturing velocity profiles, local shear rates, and supersaturation distributions [4]. Subsequently, a population balance model (PBM) was employed to track the temporal evolution of the crystal size distribution (CSD) through embedded rate laws for nucleation, growth, and aggregation [5]. Meanwhile, DEM provided further insights into the conditions leading to aggregation or breakage by modeling crystal collisions in finer detail [6]. Finally, kMC models incorporate solute attachment and detachment, capturing fine-grained kinetic details that determine crystal shape and growth rates [7].

In this work, we propose an integrated multiscale approach that combines (1) macroscale CFD-PBM modeling, (2) mesoscale DEM simulations of particle collisions and aggregations, and (3) microscale kMC calculations of growth and nucleation rates. Specifically, we employ CFD to resolve the local flow field, turbulence dissipation, and residence-time distributions in a batch or continuous crystallizer. These CFD results feed into a PBM that tracks the evolution of CSD. Local collision frequencies, derived from DEM simulations of crystal-crystal interactions under shear, inform the aggregation rate used in the PBM. Concurrently, the kMC component predicts crystal growth and nucleation kinetics at the molecular scale, ensuring that aspects such as surface integration mechanisms or site-blocking by additives are accurately represented. The PBM then integrates these mesoscale and microscale inputs aggregation/breakage rates from DEM and size-dependent growth rates from kMC, along with the reactor-scale mixing data from CFD, enabling a self-consistent, spatially resolved simulation of the crystallization process.

Our recent work builds on a previously developed kMC mass/energy balance framework by explicitly incorporating mixing, a key omission in earlier studies [2]. This expanded model captures the interplay between local velocity fields, supersaturation gradients, particle collisions, and molecular-level growth processes. By leveraging this multiscale architecture, we can track how small fluctuations in local shear or turbulence pockets trigger aggregation, which then alters the effective crystal surface area available for growth. Conversely, surface kinetics determined from the kMC model feed back into the macroscale population balance, refining the predicted CSD and crystal morphology under various operating conditions. Such a holistic approach not only offers deeper mechanistic insight into controlling crystal size distributions but also supports scale-up strategies and process intensification. Ultimately, this integrated multiscale simulation framework paves the way for improved crystallizer design, better understanding of scale-dependent phenomena, and robust control of critical crystallization outcomes in industrial practice.

References:

[1] C. A. da Rosa and R. D. Braatz, “Multiscale Modeling and Simulation of Macromixing, Micromixing, and Crystal Size Distribution in Radial Mixers/Crystallizers,” Ind Eng Chem Res, vol. 57, no. 15, pp. 5433–5441, Apr. 2018, doi: 10.1021/acs.iecr.8b00359.

[2] J. S. Kwon, M. Nayhouse, G. Orkoulas, and P. D. Christofides, “Crystal shape and size control using a plug flow crystallization configuration,” Chem Eng Sci, vol. 119, pp. 30–39, 2014, doi: https://doi.org/10.1016/j.ces.2014.07.058.

[3] J. S. Kwon, M. Nayhouse, P. D. Christofides, and G. Orkoulas, “Modeling and control of crystal shape in continuous protein crystallization,” Chem Eng Sci, vol. 107, pp. 47–57, Apr. 2014, doi: 10.1016/J.CES.2013.12.005.

[4] L. M. de Souza, E. Temmel, G. Janiga, A. Seidel-Morgenstern, and D. Thévenin, “Simulation of a batch crystallizer using a multi-scale approach in time and space,” Chem Eng Sci, vol. 232, p. 116344, 2021, doi: https://doi.org/10.1016/j.ces.2020.116344.

[5] L. Bosetti and M. Mazzotti, “Population Balance Modeling of Growth and Secondary Nucleation by Attrition and Ripening,” Cryst Growth Des, vol. 20, no. 1, pp. 307–319, Jan. 2020, doi: 10.1021/acs.cgd.9b01240.

[6] T. Wang, F. Zhang, J. Furtney, and B. Damjanac, “A review of methods, applications and limitations for incorporating fluid flow in the discrete element method,” Journal of Rock Mechanics and Geotechnical Engineering, vol. 14, no. 3, pp. 1005–1024, 2022, doi: https://doi.org/10.1016/j.jrmge.2021.10.015.

[7] S. Nagpal, N. Sitapure, Z. Gagnon, and J. S. Kwon, “Advancing crystal growth prediction: An adaptive kMC model spanning multiple regimes,” Chem Eng Sci, vol. 299, p. 120472, 2024, doi: https://doi.org/10.1016/j.ces.2024.120472.