Machine learning analysis of droplet spreading and splashing for various liquids and different surface wettability

Panjan, Nejc (author), Berce, Jure (author), Jereb, Samo (author), Zupančič, Matevž (author), Golobič, Iztok (author), Može, Matic (author)

Accurate prediction of droplet impact behavior is essential for applications including spray cooling, coating technologies, additive manufacturing, and inkjet printing. Conventional analytical and empirical models often have limited predictive capability because of the nonlinear interactions among liquid properties, impact conditions, and surface wettability. This study develops machine learning models to predict the maximum spreading coefficient and the critical spreading–splashing threshold velocity using an experimental dataset of more than 700 droplet impacts spanning multiple liquids and hydrophilic, hydrophobic, and superhydrophobic surfaces. Gaussian process regression (GPR) achieved the highest predictive accuracy, predicting the maximum spreading coefficient with coefficients of determination exceeding 0.99 and outperforming widely used empirical correlations. Evaluation using an externally sourced dataset demonstrated satisfactory model transferability, while a second GPR model accurately predicted the critical spreading–splashing threshold velocity within the investigated parameter space. Shapley Additive Explanations (SHAP) and Individual Conditional Expectation (ICE) analyses showed that impact velocity is the dominant predictor of maximum spreading, whereas surface tension primarily governs splash onset, consistent with established droplet-impact physics. These results demonstrate that interpretable machine learning models provide accurate, physically meaningful predictions across diverse liquid–surface systems, in regimes where the input parameters are not scarcely populated, and offer an alternative to conventional empirical correlations.

• Language: English
• Keywords: droplet impact, machine learning, maximum spreading coefficient, splashing threshold
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FS - Faculty of Mechanical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2026
• Number of pages: 25 str.
• Numbering: Vol. 8, iss. 9, art. 262
• PID: 20.500.12556/RUL-188115
• UDC: 532:004.85
• ISSN on article: 2413-4155
• DOI: 10.3390/sci8090262
• COBISS.SI-ID: 291538691
• Publication date in RUL: 18.09.2026

Record is a part of a journal

• Title: Sci
• Publisher: MDPI
• ISSN: 2413-4155
• COBISS.SI-ID: 21674006

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: trk kapljice, strojno učenje, maksimalni koeficient širjenja kapljice, meja razpada kapljice

Projects

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: P2-0223
• Name: Prenos toplote in snovi

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: J2-50085
• Name: Raziskave medfaznih pojavov kapljic in mehurčkov na funkcionaliziranih površinah ob uporabi napredne diagnostike za razvoj okoljskih tehnologij prihodnosti in izboljšanega prenosa toplote (DroBFuSE)