Hydrodynamics of a Confined Surfactant-Laden Compound Droplet under Steady and Pulsatile Flows

Compound droplets, consisting of a liquid core encapsulated within another liquid shell, find extensive applications in the food, pharmaceutical, and cosmetic industries to encapsulate nutrients, flavors, and active ingredients, as well as in drug delivery and the fabrication of porous particles and functional materials. These compound droplets are generally stabilized by surfactants, which increase interfacial deformability, thereby preventing coalescence. Motivated by these applications, this study numerically investigates the dynamics of a deformable compound droplet laden with an insoluble surfactant within a vertical channel. An in-house solver based on the level-set method is employed to analyze the interfacial transport under both steady and pulsatile inflows. Three initial surfactant configurations are considered: (C1) surfactant present only on the outer shell interface, (C2) surfactant distributed only on the inner core interface, and (C3) surfactant present on both interfaces. This work presents the first systematic investigation simultaneously considering multiple surfactant distribution scenarios and different inflow conditions. The study reveals the existence of relatively stronger surfactant concentration gradients on the outer shell interface, which is directly exposed to the external flow, while the inner core interface remains encapsulated and largely isolated from the effects of the imposed inflow. Consequently, configurations with surfactant on the shell (cases (C1) and (C3)) have a higher impact on droplet velocity, shell-core deformation, and core eccentricity, compared with surfactant on the core (C2), under both steady and pulsatile inflows. Moreover, our analysis of the coupled interaction between pulsation frequency and surfactant transport indicates that the Strouhal number (St) has a more pronounced effect on the overall droplet dynamics than the Péclet number (Pe).