Employing global optimization techniques to establish an empirical model for ultrasound emulsification: Predicting the droplet size of various O/W-Emulsions

Current theoretical correlations, based on Hinze’s and Taylor's foundational theories, predominantly attribute droplet deformation in turbulent regimes during ultrasound emulsification (USE) to hydrodynamic pressure fluctuations and viscous stresses at the droplet interface, generated by turbulent eddies. However, these existing theoretical models lack comprehensive validation with experimental data and broader applicability. Thus, this paper introduces an empirically validated model for USE, applicable to a wide range of O/W-emulsion systems by establishing and fitting an emulsification dataset of three distinct O/W-emulsions produced through batch and flow USE. This dataset was modelled by implementing AI-tools in a fitting-algorithm, assuming power-law relationships between several dimensionless groups which characterize the droplet formation process. This study compares the performance of three Global Optimization Techniques - Bayesian Optimization, Particle Swarm Optimization, and Differential Evolution - with the latter exhibiting the most optimal performance. In the end, an empirical correlation was obtained achieving an adjusted coefficient of determination (R_adj²) of 0.81 and a Relative Root Mean Squared Error (RRMSE) of 22 %, ensuring droplet size prediction accuracy within ±61 nm at a 95 % confidence level, corresponding to an prediction accuracy of 37 % relative to the average droplet size. Furthermore, this empirical correlation was validated using literature emulsification data of a wide range of O/W-emulsions, yielding an R_adj²-coefficient of 0.89 and a RRMSE of 15 %, underscoring its broader applicability.