Towards generalizable wet foamability predictions: A dimensional analysis approach incorporating dynamic surface tension and symbolic regression

This study presents an original chemical engineering approach to modelling wet foam formation through mechanical mixing and gas-sparging processes. Situated at the intersection of physico-chemistry, dimensional analysis, chemical engineering, and predictive modelling, this work utilizes an representative experimental dataset covering a broad spectrum of operating conditions. For each foaming process examined, a single dimensionless correlation – capable of accurately predicting foam heights across the studied surfactant types – is derived, provided that dynamic surface tension is explicitly accounted for. The findings emphasize the pivotal role of surfactant dynamics in macroscopic foaming behaviour, demonstrating that the time-dependent evolution of surface tension must be incorporated into foaming process models. This study serves as a compelling example of how chemical engineering principles can bridge molecular-scale mechanisms (e.g., surfactant migration at bubble interfaces) with macroscopic physical variables (e.g., foam height) observed at the process scale. Beyond its immediate relevance to the foaming community, this work highlights the feasibility of integrating non-constant properties into dimensional analysis frameworks – a practice rarely applied in the chemical engineering field – while adhering to rigorous similarity theory principles. Most importantly, the study underscores a broader message for chemical engineers: modern semi-empirical correlations can provide robust performance by synergistically combining dimensional analysis (retaining physical interpretability and scalability, unlike purely data-driven approaches) with AI-driven techniques.