Multiple emulsions: A new level-set based two-and-three dimensional simulation of multiphase immiscible flows for droplet formation

The present paper introduces a numerical approach based on the level-set framework to simulate multiphase flow in the context of multiple emulsion formation. The present technique, designed for the flow of n-phases, is applicable for the production of multiphase emulsions and also for the modeling of two and three-dimensional systems. This method is utilized to simulate the formation of single, double, and triple emulsions in a microfluidic cross-junction. The accuracy of the findings is confirmed by conducting an investigation of a single emulsion at home, as well as by referencing experimental and numerical literature on multiple emulsions. Until recently, the prospect of a shift in the double droplet formation regime at a constant capillary ratio between phases had not been taken into account. The present study yielded a flow regime mapping diagram that exhibits a transition in the double droplet formation regime under a constant capillary number ratio between the inner and middle phases. Using a morphological diagram, our method takes into consideration the effect of varying values of interfacial tension between the phases on the formation of double droplets. A comparison of two-dimensional and three-dimensional modeling strategies for double emulsion is also conducted, with the aim of clarifying the dissimilar results obtained from these two techniques.