Predictive modeling of bubble formation from a submerged orifice: Machine learning approaches and a new semi-empirical model

Accurate prediction of the bubble detachment diameter is crucial for the design and optimization of gas–liquid reactors, boiling systems, and other applications where bubble behavior significantly impacts performance. Traditional models, such as empirical, potential flow theory, and force balance models, often fall short in capturing the complexities inherent in bubble detachment. However, recent advancements in machine learning (ML) present promising alternatives that may overcome these limitations. This study evaluates the effectiveness of advanced ML models, such as Kolmogorov–Arnold Network (KAN) and extreme gradient boosting (XGBoost), in predicting bubble detachment diameter from submerged orifices. A comprehensive database of 1950 data points from 24 sources is utilized to train and test several ML methods, including random forest regression (RFR), light gradient boosting machine (LightGBM), and categorical boosting (CatBoost). Additionally, a new explicit model is developed to account for the effects of orifice diameter and gas flow rate on bubble dynamics. The results demonstrate that the XGBoost model outperforms other methods, achieving the lowest MAE of 3.15 % and RMSE of 0.32 mm, while also offering insights into the key factors influencing bubble detachment. The study also introduces SHapley Additive exPlanations (SHAP) for model interpretation, providing a deeper understanding of the physical parameters affecting bubble detachment.