New explicit models for maximum spread of impacting drops on a solid surface using symbolic regression approach

Accurate prediction of droplet maximum spreading ratio is essential for various chemical engineering applications. Despite the development of numerous empirical and analytical models, challenges remain due to the complex nature of viscous dissipation and the transition from capillary to viscous regimes. This study utilizes symbolic regression (SR) method to develop new models for predicting the maximum spreading ratio. Another seven black-box machine learning methods were developed for comparison. Among them, XGBoost achieved the best interpolation performance with a mean absolute error (MAE) of 1.82% but showed poor extrapolation with an MAE rising to 11.5%. The developed SR models with penalty-based regularization demonstrated improved extrapolation capability, reducing MAE from 9.9% (interpolation) to 8.1% (extrapolation). Additionally, a new explicit model combining SR and power-law approaches outperformed existing models. This study provides a framework for developing robust data-driven explicit models to predict the maximum spreading ratio.