A Mathematical Framework for Monte Carlo Simulation of Particulate‐Filled Systems

ABSTRACT The Monte Carlo (MC) simulation is an effective technique for capturing the dynamic evolution of Particulate‐Filled Systems (PFS), as it allows detailed tracking of individual droplet histories. This flexible method is widely applied across many fields and, owing to its simple implementation and robust performance, often has no suitable alternative. However, the long computational time, especially when a large number of droplets is simulated, remains a significant drawback. The primary aim of this study is to address this limitation by introducing a novel strategy for incorporating large droplet populations into MC simulations, thereby reducing the time required to model extensive systems. A new mathematical procedure is combined with a time‐increment MC model to develop a hybrid framework, referred to as the Combinatorial Approach (CAx), which enables the use of sufficiently large initial sample populations to predict the dynamic evolution of particle size distributions in suspension polymerization. The key feature of CAx is the combination of multiple distinct simulation runs into a single vector, providing higher precision than conventional MC simulations. This framework significantly reduces computational time while maintaining high accuracy in the predicted results.