We investigated experimentally, analytically, and numerically the formation process of double emulsion formations under a dripping regime in a tri-axial co-flow capillary device. The results show that mismatches of core and shell droplets under a given flow condition can be captured both experimentally and numerically. We propose a semi-analytical model using the match ratio between the pinch-off length of the shell droplet and the product of the core growth rate and its pinch-off time. The mismatch issue can be avoided if the match ratio is lower than unity. We considered a model with the wall effect to predict the size of the matched double emulsion. The model shows slight deviations with experimental data if the Reynolds number of the continuous phase is lower than 0.06 but asymptotically approaches good agreement if the Reynolds number increases from 0.06 to 0.14. The numerical simulation generally agrees with the experiments under various flow conditions.
Keywords: computational fluid dynamics; core–shell droplet; double emulsion; dripping regime; microfluidics; tri-axial capillary.