Predictive Modeling of Globule Size Distribution in Double Emulsions Stabilized by Blended Surfactants and Nanoparticles using Hinze-Kolmogorov Theory

Emulsion liquid membrane (ELM) is effective for heavy metal extraction, with efficiency closely linked to stability, which is largely governed by the size of the water-in-oil-in-water (W/O/W) emulsion globules. The applicability of Hinze-Kolmogorov theory for predicting Sauter mean diameters (D32) of W/O/W emulsion embedded with blended surfactant-nanoparticle was scrutinized. A MATLAB code was developed based on this theory and the experimental data on zinc extraction was used for validation. Afterwards, several parameters such as impeller diameter, agitation speed, interfacial tension, and holdup fraction were investigated. The developed model is viable for predicting globule size, with minimal average absolute relative deviation of less than 5%. The new empirical correlation with C1=0.0436 and C2=-3.2561 was obtained. Based on the simulation, it can be deduced that the impeller diameter and agitation speed are inversely proportional to the globule size, and smaller interfacial tensions typically produce smaller globules.