Rotor-Stator Emulsification in the Turbulent Inertial Regime: Experiments toward a Robust Correlation for the Droplet Size

The Sauter mean diameter, d32, is a representative parameter in emulsions that indicates the average size of the oil droplets once the emulsion becomes stable. Several mathematical and physical approaches have been employed in the literature to seek expressions for d32 under different conditions. The present work sheds light on this rich literature and emphasizes that the characterization of emulsions is still a fertile field for investigation. In this paper, a new Π-theorem-based model to predict the normalized Sauter mean diameter for the specific case of rotor-stator emulsification is sought by applying a multiple regression analysis on experimental data of oil-in-water (O-W) emulsions produced using three different oils: paraffin, soybean oil, and isopropyl myristate, at different oil-to-water (O/W) ratios and rotor speeds. The proposed model quantifies the roles of the viscous, inertial, and interfacial tension forces, besides the O/W ratio, in the emulsification process within the turbulent inertial subrange. The developed empirical correlation is then contrasted with relevant literature models for reliability assessment; predictions of the present explicit model are proven to be more accurate for the fluid properties and the experimental conditions under study.