Controlled encapsulation and droplet size prediction in two-step microfluidic double emulsions

Double emulsions of water-in-oil-in-water (w₁/o/w₂) are critical for encapsulation and controlled release in microfluidic applications. In this work, double emulsion droplets were produced via a two-step flow-focusing process in a microchannel. A low-viscosity silicone oil (4.6 mPa s) was used as the oil phase, while the aqueous phase consisted of 48 wt% water and 52 wt% glycerol. Sodium dodecyl sulfate (SDS) was added at concentrations 0.2, 0.5, 1, and 2 times its critical micelle concentration (CMC = 11 mM) to systematically vary the interfacial tension. Three distinct formation regimes, namely drop-in-drop, drop-in-plug, and drop-in-thread, were identified under varying flow rate ratios and interfacial tensions. A semi-empirical model was developed to predict double droplet size in the drop-in-drop regime, which has significant practical relevance. For conditions with C/CMC ≥ 1, where interfacial tension is assumed to have reached equilibrium, good agreement with the experimental data was obtained, with mean absolute percentage errors (MAPE) of 8.16% for the core droplets and 9.54% for the double droplets. For lower surfactant concentrations, incorporating dynamic interfacial tension gave a MAPE of 8.17% for double droplet size prediction. These results provide a quantitative framework for droplet size prediction and offer operating guidance for the controlled generation of encapsulated droplets in microfluidic systems.