Morphology of multicore compound drops in oscillatory shear flows

Dynamics and morphology of two-dimensional multicore (dual and triple core) compound drops, subjected to oscillating shear flows have been addressed in this work. We use the binary-phase-field method to deduce numerical solutions for the flow field and the droplet deformation characteristics. Our results reveal that depending on the geometric configuration, the inner cores as well as the outer drop may exhibit irregular temporal variations in the deformation, because of a relatively larger number of modes contributing to their shapes. We establish that displacement of the center of masses of the drops generally facilitates this irregular deformation pattern, while for stationary drops, smooth and periodic temporal variations in the shape are observed. As a result, the inner cores in multicore drops are far more prone to exhibit irregular shape variations, while the outer drops tend to follow similar trends when the inner cores are not symmetrically distributed with respect to the imposed flow. The time period of oscillation does not fundamentally alter the morphological characteristics, although it does increase the extent of deformation and impacts the phase lag between the deformation and the imposed flow. Our results may have important implications in characterizing the rheology of double emulsions, when subject to unsteady flows.