Introduction: Particulate processes are central to many scientific and industrial systems, from materials synthesis to astrophysical processes. A comprehensive understanding of particle dynamics—nucleation, growth, aggregation, and diffusion—is essential for process design, optimization, and control. This review integrates disparate modelling techniques and control strategies from fields like flame synthesis of nanoparticles, batch and continuous crystallization, and stellar evolution driven by particle motion.
Methodology: Embedded at the center of particulate modelling is the Population Balance Model (PBM) that follows particle size distributions via internal coordinates such as geometry, composition, and age. The model is designed to handle a range of complexities from basic spherical particles to full agglomerate structures. Numerical solutions, such as a method of moments, sectional methods, finite element analysis, and Monte Carlo simulations, are explained with applications to laminar as well as turbulent flows. On the control side, predictive control algorithms—specifically hybrid MPC systems—are presented for stabilizing and optimizing particulate processes. Complementary optical monitoring methods like turbidity and light scattering are reviewed, in addition to stochastic models based on Markov chain theory for the characterization of mesoscopic behaviors.
Results: Model predictive control in batch crystallization demonstrates tangible advantages, e.g., a 13.4% decrease in fines volume using linear vs. nonlinear cooling. Hybrid MPC systems improve the robustness and stability of continuous operations. In flame synthesis, different numerical solutions precisely reproduce particle growth and interaction behavior. In astrophysical applications, novel formulations of diffusion and radiative acceleration information improve stellar evolution models and better match observed phenomena like the lithium gap and chemical stratification in AmFm stars.
Conclusion: This summary emphasizes the interfacing of modeling, simulation, and control methodology required for the predictive analysis of particulate systems. Although rapid progress has been made, overlooked methods like Markov-based stochastic models offer a window of new innovation.
