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Compound drops or, double emulsions, find important applications in cosmetics and food industry, biomedical devices, petroleum industry, and many others. Most naturally occurring compound drops in these applications tend to contain multiple smaller cores inside an outer shell and their interactions are expected to have significant impact on the shape and kinetics of the entire drop. Yet, the existing literature focuses heavily on probing the mechanics of only single-core compound drops. As such, in this article, we numerically explore the dynamics and the morphology of multi-core compound drops suspended in pressure-driven background flows in narrow confinements, using the phase field formalism. To this end, we specifically consider dual and triple-core compound drops in a variety of configurations. Our findings reveal that multi-core compound drops may be inherently unstable as their kinetics is largely dominated by pinch-off and merger of the cores. Such events are, in turn, strongly influenced by several factors, such as the distribution of the cores within the shell, the starting position of the drop, core eccentricity, to underline a few. It is observed that the insight gained from the behavior of single-core drops helps us understand the kinetics of dual-core drops and likewise, those of dual-core ones are crucial toward understanding the intricacies of triple-core drops. Despite such hierarchy, the complexities in the motion and deformation of the cores and the shell in the presence of background flows increase very rapidly as the number of cores increase beyond three.
Pathak et al. (Fri,) studied this question.