Non-isothermal spreading and solidification of a molten droplet on solid substrates: An experimental and machine learning-based study

Understanding the dynamics of non-isothermal droplet spreading is critical for various industrial applications, including turbine blade cooling, biodiagnostics, and aerospace manufacturing. This study investigates the behavior of molten droplets impacting cold solid substrates, where simultaneous spreading and solidification occur due to heat exchange. Traditional analytical and numerical methods often fall short in accurately predicting key outcomes such as arrested diameter ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mi>D</mml:mi> <mml:mo>*</mml:mo> </mml:msup> </mml:mrow> </mml:math> ) and contact angle ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mi>θ</mml:mi> <mml:mo>*</mml:mo> </mml:msup> </mml:mrow> </mml:math> ), largely due to oversimplified assumptions that neglect complex dynamics like viscous dissipation and solidification effects. Here, for the first time, we employ machine learning (ML) models to develop a predictive framework for nonisothermal droplet spreading. A comprehensive dataset was generated from 100 controlled experiments, capturing the effects of varying temperature gradients and flow rates on droplet behavior. Ensemble ML models, including Extra Trees Regressor, Random Forest, Gradient Boosting, and AdaBoost, were trained and evaluated using input features such as temperature, flow rate, and material properties. The AdaBoost model demonstrated superior performance with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>0.885</mml:mn> </mml:mrow> </mml:math> and the lowest error metrics, effectively capturing the complex, nonlinear relationships in the dataset. A comparison with traditional analytical models highlights the ML approach’s enhanced predictive accuracy, providing a novel, data-driven tool for applications in surface coating, soldering, and microfabrication.