Measuring the critical length scale of percolation of fine particles under vibration using discrete element method

Understanding percolation is vital for improving transport and mixing in multiple industrial applications. The vibrated packed bed system is ideal for studying percolation as it provides good control over various parameters. Dynamic voids refer to the continuously evolving gaps within the vibrated granular system. These gaps play an active role in determining the extent of percolation. To quantify the impact of these dynamic voids, a novel index, the critical length scale of percolation, is introduced. This index is defined by a new 80–20 criterion representing the maximum void size that allows free particle percolation at a steady state. The results reveal that non-spherical particles have a lower critical length scale of percolation. Increasing the fine particle composition or adding intermediate particles reduces the critical length scale of percolation. Multiple machine learning models—including Linear Regression, Polynomial Regression, Artificial Neural Network (ANN), Random Forest (RF), and Extreme Gradient Boosting (XGBoost)—are trained on data from Discrete Element Method (DEM) simulations to predict the percentage of percolated fine. A subsequent error analysis identified the Extreme Gradient Boosting (XGBoost) model as the top performer, achieving R2 value of 0.97. The model confirmed that the particle size ratio is a more dominant factor than sphericity in governing percolation. This machine learning model effectively generalizes the Discrete Element Method (DEM) findings, providing a powerful and accurate predictive tool for industrial applications.